index
stringlengths
21
21
question
stringlengths
87
406
A
stringlengths
3
170
B
stringlengths
2
280
C
stringclasses
1 value
D
stringclasses
1 value
bounding_box
listlengths
1
3
direction
listlengths
0
3
answer
stringclasses
4 values
answer_cot
stringlengths
385
3.54k
answer_name
stringlengths
6
164
category
stringclasses
12 values
image_url
stringlengths
20
20
002519f868563098_609b
Consider the real-world 3D locations and orientations of the objects. Which side of a pink car is facing the camera?
front
left
back
right
[ { "bbox_3d": [ 1.6, 0.5, 15 ], "label": "a pink car" } ]
[ { "front_dir": [ 0, 0, -1 ], "label": "a pink car", "left_dir": [ -1, 0, 0 ] } ]
A
To solve this problem, we first estimate the 3D location of a pink car. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a pink car, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a pink car that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a pink car is (1.6, 0.5, 15.0). The vector from a pink car to camera is hence (-1.6, -0.5, -15.0). The left direction of a pink car is (-1.0, 0.0, 0.0). The cosine similarity between the vector pointing to camera and the left direction is 0.07, corresponding to an angle of 85.77 degrees. Thus the angle between the vector pointing to camera and the right direction is 94.23 degrees. The front direction of a pink car is (-0.0, 0.0, -1.0). The cosine similarity between the vector pointing to camera and the front direction is 1.00, corresponding to an angle of 4.74 degrees. Thus the angle between the vector pointing to camera and the back direction is 175.26 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 4.74 degrees. Thus the front side of a pink car is facing the camera. Therefore, the final answer is A. front.
A. front.
orientation_viewpoint
002519f868563098.jpg
002584d32e42036c_e3d5
Consider the real-world 3D locations of the objects. Which object has a higher location?
a woman sitting
a woman in a black shirt sitting
null
null
[ { "bbox_3d": [ 0.1, 0.5, 1.9 ], "label": "a woman sitting" }, { "bbox_3d": [ 0.3, 0.8, 2.7 ], "label": "a woman in a black shirt sitting" } ]
[]
B
To solve this problem, we first estimate the 3D heights of the two objects. The object with a larger height value is at a higher location. The object with a smaller height value is at a lower location. The 3D height of a woman sitting is 0.9. The 3D height of a woman in a black shirt sitting is 1.3. The 3D height of a woman in a black shirt sitting is larger, meaning that the location of a woman in a black shirt sitting is higher. Therefore, the answer is B. a woman in a black shirt sitting.
B. a woman in a black shirt sitting.
height_higher
002584d32e42036c.jpg
0025bf0880a0e8e2_41b9
Consider the real-world 3D locations and orientations of the objects. If I stand at a blue chair with wooden arms's position facing where it is facing, is a man in a red shirt standing in front of a white wall in front of me or behind me?
in front of
behind
null
null
[ { "bbox_3d": [ -0.2, 1.7, 4.1 ], "label": "a man in a red shirt standing in front of a white wall" }, { "bbox_3d": [ 1.3, 0.4, 2.9 ], "label": "a blue chair with wooden arms" } ]
[ { "front_dir": [ -0.9, 0.1, 0.4 ], "label": "a blue chair with wooden arms", "left_dir": [ 0.3, -0.1, 0.9 ] } ]
A
To solve this problem, we first determine the 3D locations of a man in a red shirt standing in front of a white wall and a blue chair with wooden arms. Then we estimate the vector pointing from a blue chair with wooden arms to a man in a red shirt standing in front of a white wall, as well as the front direction of a blue chair with wooden arms. Next we compute the cosine similarities between the vector and the front direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a man in a red shirt standing in front of a white wall is in front of a blue chair with wooden arms. Otherwise, a man in a red shirt standing in front of a white wall is behind a blue chair with wooden arms. The 3D location of a man in a red shirt standing in front of a white wall is (-0.2, 1.7, 4.1). The 3D location of a blue chair with wooden arms is (1.3, 0.4, 2.9). The vector from a blue chair with wooden arms to a man in a red shirt standing in front of a white wall is hence (-1.5, 1.3, 1.2). The front direction of a blue chair with wooden arms is (-0.9, 0.1, 0.4). The cosine similarity between the vector and the front direction is 0.85, corresponding to an angle of 32.16 degrees. The angle is smaller than 90 degrees, meaning that a man in a red shirt standing in front of a white wall is in front of a blue chair with wooden arms. Therefore, the final answer is A. in front of.
A. in front of.
orientation_in_front_of
0025bf0880a0e8e2.jpg
0025bf0880a0e8e2_0f32
Consider the real-world 3D locations and orientations of the objects. Which object is a blue chair with wooden arms facing towards, a boy wearing a red shirt or the a blue armchair with a patterned seat?
a boy wearing a red shirt
a blue armchair with a patterned seat
null
null
[ { "bbox_3d": [ 1.3, 0.4, 2.9 ], "label": "a blue chair with wooden arms" }, { "bbox_3d": [ 0, 0.4, 3.4 ], "label": "a boy wearing a red shirt" }, { "bbox_3d": [ 0.4, 0.5, 2.3 ], "label": "a blue armchair with a patterned seat" } ]
[ { "front_dir": [ -0.9, 0.1, 0.4 ], "label": "a blue chair with wooden arms", "left_dir": [ 0.3, -0.1, 0.9 ] }, { "front_dir": [ -0.1, 0.3, -0.9 ], "label": "a blue armchair with a patterned seat", "left_dir": [ -1, 0.1, 0.1 ] } ]
A
To solve this problem, we first detect the 3D location of a blue chair with wooden arms, a boy wearing a red shirt, and a blue armchair with a patterned seat. Then we compute the cosine similarities between the front direction of a blue chair with wooden arms and the vectors from a blue chair with wooden arms to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a blue chair with wooden arms is facing towards. The 3D location of a blue chair with wooden arms is (1.3, 0.4, 2.9). The 3D location of a boy wearing a red shirt is (0.0, 0.4, 3.4). The 3D location of a blue armchair with a patterned seat is (0.4, 0.5, 2.3). The front direction of a blue chair with wooden arms is (-0.9, 0.1, 0.4). First we consider if a blue chair with wooden arms is facing towards the a boy wearing a red shirt. The vector from a blue chair with wooden arms to a boy wearing a red shirt is (-1.3, 0.0, 0.5). The cosine similarity between the front direction and the vector is 1.00, corresponding to an angle of 3.89 degrees. First we consider if a blue chair with wooden arms is facing towards the a blue armchair with a patterned seat. The vector from a blue chair with wooden arms to a blue armchair with a patterned seat is (-0.9, 0.1, -0.6). The cosine similarity between the front direction and the vector is 0.57, corresponding to an angle of 55.44 degrees. We find that the angle between the front direction and a boy wearing a red shirt is smaller. Therefore, the final answer is A. a boy wearing a red shirt.
A. a boy wearing a red shirt.
multi_object_facing
0025bf0880a0e8e2.jpg
0025cf75bf36d7c0_07cc
Consider the real-world 3D locations and orientations of the objects. Which side of a long train with many cars is facing a large white building?
front
left
back
right
[ { "bbox_3d": [ -20, 0.7, 55 ], "label": "a long train with many cars" }, { "bbox_3d": [ -5.9, 3.6, 74.8 ], "label": "a large white building" } ]
[ { "front_dir": [ 0.9, 0, -0.3 ], "label": "a long train with many cars", "left_dir": [ -0.3, -0.1, -0.9 ] } ]
D
To solve this problem, we first detect the 3D locations of a long train with many cars and a large white building. Then we compute the vector pointing from a long train with many cars to a large white building. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a long train with many cars, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a long train with many cars that is facing a large white building corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The 3D location of a long train with many cars is (-20.0, 0.7, 55.0). The 3D location of a large white building is (-5.9, 3.6, 74.8). The vector from a long train with many cars to a large white building is hence (14.1, 2.8, 19.8). The left direction of a long train with many cars is (-0.3, -0.1, -0.9). The cosine similarity between the vector pointing to a large white building and the left direction is -0.96, corresponding to an angle of 163.95 degrees. Thus the angle between the vector pointing to a large white building and the right direction is 16.05 degrees. The front direction of a long train with many cars is (0.9, 0.0, -0.3). The cosine similarity between the vector pointing to a large white building and the front direction is 0.27, corresponding to an angle of 74.25 degrees. Thus the angle between the vector pointing to a large white building and the back direction is 105.75 degrees. Among the four directions, the smallest angle is the right direction, with an angle of 16.05 degrees. Thus the right side of a long train with many cars is facing the a large white building. Therefore, the final answer is D. right.
D. right.
multi_object_viewpoint_towards_object
0025cf75bf36d7c0.jpg
002622b2e05df66a_323f
Consider the real-world 3D locations and orientations of the objects. Which side of a large boat in the water is facing the camera?
front
left
back
right
[ { "bbox_3d": [ 56.6, -8, 130.8 ], "label": "a large boat in the water" } ]
[ { "front_dir": [ -0.3, 0.1, -0.9 ], "label": "a large boat in the water", "left_dir": [ -0.9, 0.1, 0.3 ] } ]
A
To solve this problem, we first estimate the 3D location of a large boat in the water. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a large boat in the water, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a large boat in the water that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a large boat in the water is (56.6, -8.0, 130.8). The vector from a large boat in the water to camera is hence (-56.6, 8.0, -130.8). The left direction of a large boat in the water is (-0.9, 0.1, 0.3). The cosine similarity between the vector pointing to camera and the left direction is 0.08, corresponding to an angle of 85.63 degrees. Thus the angle between the vector pointing to camera and the right direction is 94.37 degrees. The front direction of a large boat in the water is (-0.3, 0.1, -0.9). The cosine similarity between the vector pointing to camera and the front direction is 0.99, corresponding to an angle of 7.00 degrees. Thus the angle between the vector pointing to camera and the back direction is 173.00 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 7.00 degrees. Thus the front side of a large boat in the water is facing the camera. Therefore, the final answer is A. front.
A. front.
orientation_viewpoint
002622b2e05df66a.jpg
002635f5f3dfd5b9_34f5
Consider the real-world 3D locations and orientations of the objects. If I stand at a red car's position facing where it is facing, is a woman in a red jacket in front of me or behind me?
in front of
behind
null
null
[ { "bbox_3d": [ -2.6, 1.3, 9.8 ], "label": "a woman in a red jacket" }, { "bbox_3d": [ -7.6, 0.6, 20.9 ], "label": "a red car" } ]
[ { "front_dir": [ -0.4, 0, 0.9 ], "label": "a red car", "left_dir": [ 0.9, -0.1, 0.4 ] } ]
B
To solve this problem, we first determine the 3D locations of a woman in a red jacket and a red car. Then we estimate the vector pointing from a red car to a woman in a red jacket, as well as the front direction of a red car. Next we compute the cosine similarities between the vector and the front direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a woman in a red jacket is in front of a red car. Otherwise, a woman in a red jacket is behind a red car. The 3D location of a woman in a red jacket is (-2.6, 1.3, 9.8). The 3D location of a red car is (-7.6, 0.6, 20.9). The vector from a red car to a woman in a red jacket is hence (5.0, 0.6, -11.1). The front direction of a red car is (-0.4, 0.0, 0.9). The cosine similarity between the vector and the front direction is -1.00, corresponding to an angle of 175.51 degrees. The angle is smaller than 90 degrees, meaning that a woman in a red jacket is behind a red car. Therefore, the final answer is B. behind.
B. behind.
orientation_in_front_of
002635f5f3dfd5b9.jpg
0026bed8759ef2b6_16e0
Consider the real-world 3D locations and orientations of the objects. If I stand at a car's position facing where it is facing, is a blue car on the left or right of me?
on the left
on the right
null
null
[ { "bbox_3d": [ 3, 1.7, 17 ], "label": "a blue car" }, { "bbox_3d": [ 0.8, 1.7, 15 ], "label": "a car" } ]
[ { "front_dir": [ 0.1, 0.1, 1 ], "label": "a blue car", "left_dir": [ 1, -0.1, -0.1 ] }, { "front_dir": [ 0, -0.1, -1 ], "label": "a car", "left_dir": [ -1, 0, 0 ] } ]
B
To solve this problem, we first determine the 3D locations of a blue car and a car. Then we estimate the vector pointing from a car to a blue car, as well as the left direction of a car. Next we compute the cosine similarities between the vector and the left direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a blue car is on the left of a car. Otherwise, a blue car is behind a car. The 3D location of a blue car is (3.0, 1.7, 17.0). The 3D location of a car is (0.8, 1.7, 15.0). The vector from a car to a blue car is hence (2.2, 0.0, 2.0). The left direction of a car is (-1.0, 0.0, -0.0). The cosine similarity between the vector and the left direction is -0.75, corresponding to an angle of 138.93 degrees. The angle is smaller than 90 degrees, meaning that a blue car is on the right of a car. Therefore, the final answer is B. on the right.
B. on the right.
orientation_on_the_left
0026bed8759ef2b6.jpg
0026bed8759ef2b6_15d5
Consider the real-world 3D orientations of the objects. Are a blue car and a blue car parked in a parking lot facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ 3, 1.7, 17 ], "label": "a blue car" }, { "bbox_3d": [ 5.1, 1.6, 17.6 ], "label": "a blue car parked in a parking lot" } ]
[ { "front_dir": [ 0.1, 0.1, 1 ], "label": "a blue car", "left_dir": [ 1, -0.1, -0.1 ] }, { "front_dir": [ -0.2, -0.1, -1 ], "label": "a blue car parked in a parking lot", "left_dir": [ -1, 0.1, 0.2 ] } ]
B
To solve this problem, we first detect the front directions of a blue car and a blue car parked in a parking lot. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a blue car is (0.1, 0.1, 1.0). The front direction of a blue car parked in a parking lot is (-0.2, -0.1, -1.0). The cosine similarity between the two front directions is -0.99, corresponding to an angle of 173.69. The angle is large, meaning that the two objects are facing very different directions. Therefore, the final answer is B. very different directions.
B. very different directions.
multi_object_same_direction
0026bed8759ef2b6.jpg
002729cb73943ee8_6215
Consider the real-world 3D locations and orientations of the objects. Which side of a red stool with a wooden top is facing the camera?
front
left
back
right
[ { "bbox_3d": [ -0.2, 0.6, 5.7 ], "label": "a red stool with a wooden top" } ]
[ { "front_dir": [ 0.4, 0, -0.9 ], "label": "a red stool with a wooden top", "left_dir": [ -0.9, 0.1, -0.4 ] } ]
A
To solve this problem, we first estimate the 3D location of a red stool with a wooden top. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a red stool with a wooden top, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a red stool with a wooden top that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a red stool with a wooden top is (-0.2, 0.6, 5.7). The vector from a red stool with a wooden top to camera is hence (0.2, -0.6, -5.7). The left direction of a red stool with a wooden top is (-0.9, 0.1, -0.4). The cosine similarity between the vector pointing to camera and the left direction is 0.35, corresponding to an angle of 69.75 degrees. Thus the angle between the vector pointing to camera and the right direction is 110.25 degrees. The front direction of a red stool with a wooden top is (0.4, 0.0, -0.9). The cosine similarity between the vector pointing to camera and the front direction is 0.93, corresponding to an angle of 21.99 degrees. Thus the angle between the vector pointing to camera and the back direction is 158.01 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 21.99 degrees. Thus the front side of a red stool with a wooden top is facing the camera. Therefore, the final answer is A. front.
A. front.
orientation_viewpoint
002729cb73943ee8.jpg
0027550c6a796f5b_9f0c
Consider the real-world 3D orientations of the objects. What is the relationship between the orientations of a car with a black and white photo and a small grey car, parallel of perpendicular to each other?
parallel
perpendicular
null
null
[ { "bbox_3d": [ 0.2, 0.1, 1 ], "label": "a car with a black and white photo" }, { "bbox_3d": [ 0, 0.8, 1 ], "label": "a small grey car" } ]
[ { "front_dir": [ -0.9, 0.2, -0.5 ], "label": "a car with a black and white photo", "left_dir": [ -0.5, -0.1, 0.9 ] }, { "front_dir": [ 0.7, -0.4, -0.7 ], "label": "a small grey car", "left_dir": [ -0.7, -0.3, -0.6 ] } ]
B
To solve this problem, we first detect the front directions of a car with a black and white photo and a small grey car. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is closer to 0 or 180, than to 90 degrees, then the two objects are parallel to each other. Otherwise, the two objects are perpendicular to each other. The front direction of a car with a black and white photo is (-0.9, 0.2, -0.5). The front direction of a small grey car is (0.7, -0.4, -0.7). The cosine similarity between the two front directions is -0.32, corresponding to an angle of 108.87. The angle is closer to 90, than to 0 or 180 degrees, meaning that the two objects are perpendicular to each other. Therefore, the final answer is B. perpendicular.
B. perpendicular.
multi_object_parallel
0027550c6a796f5b.jpg
0027bf6a5d8c382d_23cb
Consider the real-world 3D locations of the objects. Which object has a higher location?
a car with a broken window
a blue and yellow license plate from California
null
null
[ { "bbox_3d": [ 4.9, 0.1, 8.7 ], "label": "a car with a broken window" }, { "bbox_3d": [ -0.6, 0.9, 2.4 ], "label": "a blue and yellow license plate from California" } ]
[]
A
To solve this problem, we first estimate the 3D heights of the two objects. The object with a larger height value is at a higher location. The object with a smaller height value is at a lower location. The 3D height of a car with a broken window is 1.4. The 3D height of a blue and yellow license plate from California is 1.1. The 3D height of a car with a broken window is larger, meaning that the location of a car with a broken window is higher. Therefore, the answer is A. a blue and yellow license plate from California.
A. a blue and yellow license plate from California.
height_higher
0027bf6a5d8c382d.jpg
0027e4cf3e7c6497_e6aa
Consider the real-world 3D orientations of the objects. Are a car with a yellow stripe and a yellow car facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ -4.4, 4.3, 25.3 ], "label": "a car with a yellow stripe" }, { "bbox_3d": [ 0, 3.1, 14.3 ], "label": "a yellow car" } ]
[ { "front_dir": [ 0.2, -0.2, -1 ], "label": "a car with a yellow stripe", "left_dir": [ -1, 0.1, -0.2 ] }, { "front_dir": [ 0.1, 0, -1 ], "label": "a yellow car", "left_dir": [ -1, 0.1, -0.1 ] } ]
A
To solve this problem, we first detect the front directions of a car with a yellow stripe and a yellow car. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a car with a yellow stripe is (0.2, -0.2, -1.0). The front direction of a yellow car is (0.1, -0.0, -1.0). The cosine similarity between the two front directions is 0.98, corresponding to an angle of 12.81. The angle is small, meaning that the two objects are facing same or similar directions. Therefore, the final answer is A. same or similar directions.
A. same or similar directions.
multi_object_same_direction
0027e4cf3e7c6497.jpg
00287aae94dd10b4_8aa4
Consider the real-world 3D locations of the objects. Is a man wearing a black jacket and jeans directly above a blue car?
yes
no
null
null
[ { "bbox_3d": [ -1.6, 0.9, 2.5 ], "label": "a man wearing a black jacket and jeans" }, { "bbox_3d": [ -1.4, 1.6, 6 ], "label": "a blue car" } ]
[]
B
To solve this problem, we first determine the 3D locations of a man wearing a black jacket and jeans and a blue car. Then we compute the vector pointing from a blue car to a man wearing a black jacket and jeans, as well as the up direction of a blue car. We estimate the cosine similarity between the vector and the up direction, which leads to the angle between the two directions. If the angle is small, then a man wearing a black jacket and jeans is directly above a blue car. Otherwise, then a man wearing a black jacket and jeans is not directly above a blue car. The 3D location of a man wearing a black jacket and jeans is (-1.6, 0.9, 2.5). The 3D location of a blue car is (-1.4, 1.6, 6.0). The vector from a blue car to a man wearing a black jacket and jeans is hence (-0.2, -0.6, -3.6). The up direction of a blue car is (0.2, 0.9, -0.5). The cosine similarity between the vector and the up direction is 0.33, corresponding to an angle of 70 degrees. The angle between the vector and the up direction is large, meaning that a man wearing a black jacket and jeans is not directly above a blue car. Therefore, the answer is B. no.
B. no.
location_above
00287aae94dd10b4.jpg
00294a5dbf707b1f_91d3
Consider the real-world 3D locations and orientations of the objects. Which object is a green chair with a man in a black shirt sitting in it facing towards, a white chair or the a beard on a man?
a white chair
a beard on a man
null
null
[ { "bbox_3d": [ 0.4, 0, 1.4 ], "label": "a green chair with a man in a black shirt sitting in it" }, { "bbox_3d": [ -1.1, 0.2, 3.8 ], "label": "a white chair" }, { "bbox_3d": [ 0, 0.3, 0.6 ], "label": "a beard on a man" } ]
[ { "front_dir": [ -0.2, 0, -1 ], "label": "a green chair with a man in a black shirt sitting in it", "left_dir": [ -1, -0.1, 0.2 ] }, { "front_dir": [ 0.3, 0, -0.9 ], "label": "a white chair", "left_dir": [ -0.9, 0.1, -0.3 ] } ]
B
To solve this problem, we first detect the 3D location of a green chair with a man in a black shirt sitting in it, a white chair, and a beard on a man. Then we compute the cosine similarities between the front direction of a green chair with a man in a black shirt sitting in it and the vectors from a green chair with a man in a black shirt sitting in it to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a green chair with a man in a black shirt sitting in it is facing towards. The 3D location of a green chair with a man in a black shirt sitting in it is (0.4, 0.0, 1.4). The 3D location of a white chair is (-1.1, 0.2, 3.8). The 3D location of a beard on a man is (0.0, 0.3, 0.6). The front direction of a green chair with a man in a black shirt sitting in it is (-0.2, 0.0, -1.0). First we consider if a green chair with a man in a black shirt sitting in it is facing towards the a white chair. The vector from a green chair with a man in a black shirt sitting in it to a white chair is (-1.5, 0.2, 2.4). The cosine similarity between the front direction and the vector is -0.73, corresponding to an angle of 137.31 degrees. First we consider if a green chair with a man in a black shirt sitting in it is facing towards the a beard on a man. The vector from a green chair with a man in a black shirt sitting in it to a beard on a man is (-0.4, 0.2, -0.8). The cosine similarity between the front direction and the vector is 0.92, corresponding to an angle of 22.35 degrees. We find that the angle between the front direction and a beard on a man is smaller. Therefore, the final answer is B. a beard on a man.
B. a beard on a man.
multi_object_facing
00294a5dbf707b1f.jpg
002963e92a1d2742_ffac
Consider the real-world 3D locations of the objects. Which object has a higher location?
a metal tool
a wooden shelf with jewelry on it
null
null
[ { "bbox_3d": [ 0.3, 0.1, 1.5 ], "label": "a metal tool" }, { "bbox_3d": [ 0.5, 0.7, 1.4 ], "label": "a wooden shelf with jewelry on it" } ]
[]
B
To solve this problem, we first estimate the 3D heights of the two objects. The object with a larger height value is at a higher location. The object with a smaller height value is at a lower location. The 3D height of a metal tool is 0.3. The 3D height of a wooden shelf with jewelry on it is 1.6. The 3D height of a wooden shelf with jewelry on it is larger, meaning that the location of a wooden shelf with jewelry on it is higher. Therefore, the answer is B. a wooden shelf with jewelry on it.
B. a wooden shelf with jewelry on it.
height_higher
002963e92a1d2742.jpg
0029996779d5f0c4_07a1
Consider the real-world 3D locations and orientations of the objects. Which side of a black car is facing the camera?
front
left
back
right
[ { "bbox_3d": [ 2.3, 8.4, 74.3 ], "label": "a black car" } ]
[ { "front_dir": [ 0.1, 0, -1 ], "label": "a black car", "left_dir": [ -1, 0.1, -0.1 ] } ]
A
To solve this problem, we first estimate the 3D location of a black car. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a black car, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a black car that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a black car is (2.3, 8.4, 74.3). The vector from a black car to camera is hence (-2.3, -8.4, -74.3). The left direction of a black car is (-1.0, 0.1, -0.1). The cosine similarity between the vector pointing to camera and the left direction is 0.08, corresponding to an angle of 85.60 degrees. Thus the angle between the vector pointing to camera and the right direction is 94.40 degrees. The front direction of a black car is (0.1, -0.0, -1.0). The cosine similarity between the vector pointing to camera and the front direction is 0.99, corresponding to an angle of 7.19 degrees. Thus the angle between the vector pointing to camera and the back direction is 172.81 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 7.19 degrees. Thus the front side of a black car is facing the camera. Therefore, the final answer is A. front.
A. front.
orientation_viewpoint
0029996779d5f0c4.jpg
002b7b3e25072636_d66e
Consider the real-world 3D locations and orientations of the objects. Which object is a black computer facing towards, a laptop computer or the a man in a white shirt sitting?
a laptop computer
a man in a white shirt sitting
null
null
[ { "bbox_3d": [ -1.4, 0.3, 3.9 ], "label": "a black computer" }, { "bbox_3d": [ 0.4, 0.2, 2.8 ], "label": "a laptop computer" }, { "bbox_3d": [ -1.4, 0.3, 3 ], "label": "a man in a white shirt sitting" } ]
[ { "front_dir": [ -0.2, 0.1, -1 ], "label": "a black computer", "left_dir": [ -1, 0.1, 0.2 ] }, { "front_dir": [ -0.1, 0.1, -1 ], "label": "a laptop computer", "left_dir": [ -1, 0.1, 0.1 ] } ]
B
To solve this problem, we first detect the 3D location of a black computer, a laptop computer, and a man in a white shirt sitting. Then we compute the cosine similarities between the front direction of a black computer and the vectors from a black computer to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a black computer is facing towards. The 3D location of a black computer is (-1.4, 0.3, 3.9). The 3D location of a laptop computer is (0.4, 0.2, 2.8). The 3D location of a man in a white shirt sitting is (-1.4, 0.3, 3.0). The front direction of a black computer is (-0.2, 0.1, -1.0). First we consider if a black computer is facing towards the a laptop computer. The vector from a black computer to a laptop computer is (1.8, -0.1, -1.2). The cosine similarity between the front direction and the vector is 0.34, corresponding to an angle of 70.03 degrees. First we consider if a black computer is facing towards the a man in a white shirt sitting. The vector from a black computer to a man in a white shirt sitting is (0.0, -0.0, -0.9). The cosine similarity between the front direction and the vector is 0.97, corresponding to an angle of 13.82 degrees. We find that the angle between the front direction and a man in a white shirt sitting is smaller. Therefore, the final answer is B. a man in a white shirt sitting.
B. a man in a white shirt sitting.
multi_object_facing
002b7b3e25072636.jpg
002c7e555e94e033_8ba5
Consider the real-world 3D locations of the objects. Which is closer to a person wearing a white shirt, a man in a grey hoodie or a black beaded necklace?
a man in a grey hoodie
a black beaded necklace
null
null
[ { "bbox_3d": [ 0.2, 1, 0.5 ], "label": "a person wearing a white shirt" }, { "bbox_3d": [ -0.2, 0.8, 1 ], "label": "a man in a grey hoodie" }, { "bbox_3d": [ 0.3, 0.9, 1.6 ], "label": "a black beaded necklace" } ]
[]
A
To solve this problem, we first detect the 3D location of a person wearing a white shirt, a man in a grey hoodie, and a black beaded necklace. Then we compute the L2 distances between a person wearing a white shirt and a man in a grey hoodie, and between a person wearing a white shirt and a black beaded necklace. The object that is closer to a person wearing a white shirt is the one with a smaller distance. The 3D location of a person wearing a white shirt is (0.2, 1.0, 0.5). The 3D location of a man in a grey hoodie is (-0.2, 0.8, 1.0). The 3D location of a black beaded necklace is (0.3, 0.9, 1.6). The L2 distance between a person wearing a white shirt and a man in a grey hoodie is 0.7519941936917256. The L2 distance between a person wearing a white shirt and a black beaded necklace is 1.1808806989195886. Between the two distances, the distance between a person wearing a white shirt and a man in a grey hoodie is smaller. Therefore, the final answer is A. a man in a grey hoodie.
A. a man in a grey hoodie.
multi_object_closer_to
002c7e555e94e033.jpg
002c8c0d1e3fff48_0a99
Consider the real-world 3D locations and orientations of the objects. If I stand at a black forklift with a yellow seat's position facing where it is facing, is a forklift is driving through a warehouse on the left or right of me?
on the left
on the right
null
null
[ { "bbox_3d": [ 1.5, 2.2, 3.9 ], "label": "a forklift is driving through a warehouse" }, { "bbox_3d": [ -0.9, 1.3, 5.2 ], "label": "a black forklift with a yellow seat" } ]
[ { "front_dir": [ 0.8, 0, 0.7 ], "label": "a black forklift with a yellow seat", "left_dir": [ 0.7, 0, -0.8 ] } ]
A
To solve this problem, we first determine the 3D locations of a forklift is driving through a warehouse and a black forklift with a yellow seat. Then we estimate the vector pointing from a black forklift with a yellow seat to a forklift is driving through a warehouse, as well as the left direction of a black forklift with a yellow seat. Next we compute the cosine similarities between the vector and the left direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a forklift is driving through a warehouse is on the left of a black forklift with a yellow seat. Otherwise, a forklift is driving through a warehouse is behind a black forklift with a yellow seat. The 3D location of a forklift is driving through a warehouse is (1.5, 2.2, 3.9). The 3D location of a black forklift with a yellow seat is (-0.9, 1.3, 5.2). The vector from a black forklift with a yellow seat to a forklift is driving through a warehouse is hence (2.5, 0.9, -1.3). The left direction of a black forklift with a yellow seat is (0.7, 0.0, -0.8). The cosine similarity between the vector and the left direction is 0.89, corresponding to an angle of 26.62 degrees. The angle is smaller than 90 degrees, meaning that a forklift is driving through a warehouse is on the left of a black forklift with a yellow seat. Therefore, the final answer is A. on the left.
A. on the left.
orientation_on_the_left
002c8c0d1e3fff48.jpg
002c97106e3f627a_4b11
Consider the real-world 3D locations and orientations of the objects. If I stand at a wooden wheel with spokes's position facing where it is facing, is a wooden hut with a sign on it on the left or right of me?
on the left
on the right
null
null
[ { "bbox_3d": [ 6, 5.9, 20.6 ], "label": "a wooden hut with a sign on it" }, { "bbox_3d": [ 0.7, 2.4, 20.7 ], "label": "a wooden wheel with spokes" } ]
[ { "front_dir": [ 0, -0.1, -1 ], "label": "a wooden wheel with spokes", "left_dir": [ -1, 0, 0 ] } ]
B
To solve this problem, we first determine the 3D locations of a wooden hut with a sign on it and a wooden wheel with spokes. Then we estimate the vector pointing from a wooden wheel with spokes to a wooden hut with a sign on it, as well as the left direction of a wooden wheel with spokes. Next we compute the cosine similarities between the vector and the left direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a wooden hut with a sign on it is on the left of a wooden wheel with spokes. Otherwise, a wooden hut with a sign on it is behind a wooden wheel with spokes. The 3D location of a wooden hut with a sign on it is (6.0, 5.9, 20.6). The 3D location of a wooden wheel with spokes is (0.7, 2.4, 20.7). The vector from a wooden wheel with spokes to a wooden hut with a sign on it is hence (5.3, 3.5, -0.1). The left direction of a wooden wheel with spokes is (-1.0, 0.0, -0.0). The cosine similarity between the vector and the left direction is -0.81, corresponding to an angle of 144.45 degrees. The angle is smaller than 90 degrees, meaning that a wooden hut with a sign on it is on the right of a wooden wheel with spokes. Therefore, the final answer is B. on the right.
B. on the right.
orientation_on_the_left
002c97106e3f627a.jpg
002cf081eb3d469c_063f
Consider the real-world 3D orientations of the objects. What is the relationship between the orientations of a black couch in a room and a black metal chair, parallel of perpendicular to each other?
parallel
perpendicular
null
null
[ { "bbox_3d": [ -1, 1.2, 7.5 ], "label": "a black couch in a room" }, { "bbox_3d": [ -6.2, 0.8, 17.8 ], "label": "a black metal chair" } ]
[ { "front_dir": [ 0.3, -0.2, -0.9 ], "label": "a black couch in a room", "left_dir": [ -0.9, 0.1, -0.4 ] }, { "front_dir": [ 1, -0.1, 0.1 ], "label": "a black metal chair", "left_dir": [ 0.1, 0, -1 ] } ]
B
To solve this problem, we first detect the front directions of a black couch in a room and a black metal chair. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is closer to 0 or 180, than to 90 degrees, then the two objects are parallel to each other. Otherwise, the two objects are perpendicular to each other. The front direction of a black couch in a room is (0.3, -0.2, -0.9). The front direction of a black metal chair is (1.0, -0.1, 0.1). The cosine similarity between the two front directions is 0.27, corresponding to an angle of 74.15. The angle is closer to 90, than to 0 or 180 degrees, meaning that the two objects are perpendicular to each other. Therefore, the final answer is B. perpendicular.
B. perpendicular.
multi_object_parallel
002cf081eb3d469c.jpg
002cf081eb3d469c_a819
Consider the real-world 3D orientations of the objects. Are a red chair and a black couch in a room facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ -0.9, 0.9, 6.6 ], "label": "a red chair" }, { "bbox_3d": [ -1, 1.2, 7.5 ], "label": "a black couch in a room" } ]
[ { "front_dir": [ 0.2, -0.1, -1 ], "label": "a red chair", "left_dir": [ -1, 0.1, -0.2 ] }, { "front_dir": [ 0.3, -0.2, -0.9 ], "label": "a black couch in a room", "left_dir": [ -0.9, 0.1, -0.4 ] } ]
A
To solve this problem, we first detect the front directions of a red chair and a black couch in a room. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a red chair is (0.2, -0.1, -1.0). The front direction of a black couch in a room is (0.3, -0.2, -0.9). The cosine similarity between the two front directions is 0.99, corresponding to an angle of 9.51. The angle is small, meaning that the two objects are facing same or similar directions. Therefore, the final answer is A. same or similar directions.
A. same or similar directions.
multi_object_same_direction
002cf081eb3d469c.jpg
002d0921e7b22774_cb83
Consider the real-world 3D orientations of the objects. What is the relationship between the orientations of a large orange and black ship and a tall orange tower, parallel of perpendicular to each other?
parallel
perpendicular
null
null
[ { "bbox_3d": [ -14.7, 62.1, 131.2 ], "label": "a large orange and black ship" }, { "bbox_3d": [ 6.9, 25.5, 41.6 ], "label": "a tall orange tower" } ]
[ { "front_dir": [ 0.6, -0.3, -0.8 ], "label": "a large orange and black ship", "left_dir": [ -0.8, -0.2, -0.6 ] }, { "front_dir": [ 0.4, -0.4, -0.8 ], "label": "a tall orange tower", "left_dir": [ -0.9, -0.2, -0.4 ] } ]
A
To solve this problem, we first detect the front directions of a large orange and black ship and a tall orange tower. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is closer to 0 or 180, than to 90 degrees, then the two objects are parallel to each other. Otherwise, the two objects are perpendicular to each other. The front direction of a large orange and black ship is (0.6, -0.3, -0.8). The front direction of a tall orange tower is (0.4, -0.4, -0.8). The cosine similarity between the two front directions is 0.97, corresponding to an angle of 14.97. The angle is closer to 0 or 180, than to 90 degrees, meaning that the two objects are parallel to each other. Therefore, the final answer is A. parallel.
A. parallel.
multi_object_parallel
002d0921e7b22774.jpg
002d6122cc09e764_66dc
Consider the real-world 3D locations of the objects. Is a wooden podium with a silver logo directly above a white sign with blue letters?
yes
no
null
null
[ { "bbox_3d": [ -0.1, 1.7, 6.3 ], "label": "a wooden podium with a silver logo" }, { "bbox_3d": [ 0.2, 0.7, 5.7 ], "label": "a white sign with blue letters" } ]
[]
A
To solve this problem, we first determine the 3D locations of a wooden podium with a silver logo and a white sign with blue letters. Then we compute the vector pointing from a white sign with blue letters to a wooden podium with a silver logo, as well as the up direction of a white sign with blue letters. We estimate the cosine similarity between the vector and the up direction, which leads to the angle between the two directions. If the angle is small, then a wooden podium with a silver logo is directly above a white sign with blue letters. Otherwise, then a wooden podium with a silver logo is not directly above a white sign with blue letters. The 3D location of a wooden podium with a silver logo is (-0.1, 1.7, 6.3). The 3D location of a white sign with blue letters is (0.2, 0.7, 5.7). The vector from a white sign with blue letters to a wooden podium with a silver logo is hence (-0.2, 1.0, 0.6). The up direction of a white sign with blue letters is (0.0, 1.0, 0.0). The cosine similarity between the vector and the up direction is 0.83, corresponding to an angle of 34 degrees. The angle between the vector and the up direction is small, meaning that a wooden podium with a silver logo is directly above a white sign with blue letters. Therefore, the answer is A. yes.
A. yes.
location_above
002d6122cc09e764.jpg
002d85ede4e5d1f3_689c
Consider the real-world 3D locations and orientations of the objects. Which side of a red and blue stool is facing the camera?
front
left
back
right
[ { "bbox_3d": [ -0.4, 0.7, 7.2 ], "label": "a red and blue stool" } ]
[ { "front_dir": [ 0.1, 0, -1 ], "label": "a red and blue stool", "left_dir": [ -1, 0.1, -0.1 ] } ]
A
To solve this problem, we first estimate the 3D location of a red and blue stool. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a red and blue stool, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a red and blue stool that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a red and blue stool is (-0.4, 0.7, 7.2). The vector from a red and blue stool to camera is hence (0.4, -0.7, -7.2). The left direction of a red and blue stool is (-1.0, 0.1, -0.1). The cosine similarity between the vector pointing to camera and the left direction is 0.06, corresponding to an angle of 86.56 degrees. Thus the angle between the vector pointing to camera and the right direction is 93.44 degrees. The front direction of a red and blue stool is (0.1, 0.0, -1.0). The cosine similarity between the vector pointing to camera and the front direction is 0.99, corresponding to an angle of 9.16 degrees. Thus the angle between the vector pointing to camera and the back direction is 170.84 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 9.16 degrees. Thus the front side of a red and blue stool is facing the camera. Therefore, the final answer is A. front.
A. front.
orientation_viewpoint
002d85ede4e5d1f3.jpg
002dab7b4f062545_ca9d
Consider the real-world 3D locations and orientations of the objects. Which object is a green truck facing towards, a green car or the a large green tow truck?
a green car
a large green tow truck
null
null
[ { "bbox_3d": [ -0.7, 0.9, 8.7 ], "label": "a green truck" }, { "bbox_3d": [ 4.1, 1.2, 10.1 ], "label": "a green car" }, { "bbox_3d": [ -0.5, 2, 6.4 ], "label": "a large green tow truck" } ]
[ { "front_dir": [ 0.3, 0, -1 ], "label": "a green truck", "left_dir": [ -1, 0.1, -0.3 ] }, { "front_dir": [ -1, -0.1, -0.2 ], "label": "a green car", "left_dir": [ -0.2, 0, 1 ] }, { "front_dir": [ 0.4, -0.1, -0.9 ], "label": "a large green tow truck", "left_dir": [ -0.9, 0, -0.4 ] } ]
B
To solve this problem, we first detect the 3D location of a green truck, a green car, and a large green tow truck. Then we compute the cosine similarities between the front direction of a green truck and the vectors from a green truck to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a green truck is facing towards. The 3D location of a green truck is (-0.7, 0.9, 8.7). The 3D location of a green car is (4.1, 1.2, 10.1). The 3D location of a large green tow truck is (-0.5, 2.0, 6.4). The front direction of a green truck is (0.3, 0.0, -1.0). First we consider if a green truck is facing towards the a green car. The vector from a green truck to a green car is (4.8, 0.4, 1.4). The cosine similarity between the front direction and the vector is 0.01, corresponding to an angle of 89.39 degrees. First we consider if a green truck is facing towards the a large green tow truck. The vector from a green truck to a large green tow truck is (0.3, 1.1, -2.2). The cosine similarity between the front direction and the vector is 0.88, corresponding to an angle of 28.00 degrees. We find that the angle between the front direction and a large green tow truck is smaller. Therefore, the final answer is B. a large green tow truck.
B. a large green tow truck.
multi_object_facing
002dab7b4f062545.jpg
002f2d008de2f535_f5f8
Consider the real-world 3D locations and orientations of the objects. Which side of a bench with a bicycle leaning on it is facing the camera?
front
left
back
right
[ { "bbox_3d": [ -1.1, 1.2, 2.8 ], "label": "a bench with a bicycle leaning on it" } ]
[ { "front_dir": [ -0.9, 0.2, -0.4 ], "label": "a bench with a bicycle leaning on it", "left_dir": [ -0.4, 0.2, 0.9 ] } ]
D
To solve this problem, we first estimate the 3D location of a bench with a bicycle leaning on it. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a bench with a bicycle leaning on it, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a bench with a bicycle leaning on it that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a bench with a bicycle leaning on it is (-1.1, 1.2, 2.8). The vector from a bench with a bicycle leaning on it to camera is hence (1.1, -1.2, -2.8). The left direction of a bench with a bicycle leaning on it is (-0.4, 0.2, 0.9). The cosine similarity between the vector pointing to camera and the left direction is -0.97, corresponding to an angle of 166.66 degrees. Thus the angle between the vector pointing to camera and the right direction is 13.34 degrees. The front direction of a bench with a bicycle leaning on it is (-0.9, 0.2, -0.4). The cosine similarity between the vector pointing to camera and the front direction is -0.00, corresponding to an angle of 90.18 degrees. Thus the angle between the vector pointing to camera and the back direction is 89.82 degrees. Among the four directions, the smallest angle is the right direction, with an angle of 13.34 degrees. Thus the right side of a bench with a bicycle leaning on it is facing the camera. Therefore, the final answer is D. right.
D. right.
orientation_viewpoint
002f2d008de2f535.jpg
002f2d008de2f535_a4e5
Consider the real-world 3D locations and orientations of the objects. If I stand at a blue mountain bike's position facing where it is facing, is a man wearing a black jacket on the left or right of me?
on the left
on the right
null
null
[ { "bbox_3d": [ 5.7, -0.8, 33.6 ], "label": "a man wearing a black jacket" }, { "bbox_3d": [ -0.7, 1.2, 3.2 ], "label": "a blue mountain bike" } ]
[ { "front_dir": [ 1, 0, 0.1 ], "label": "a blue mountain bike", "left_dir": [ 0.1, -0.2, -1 ] } ]
B
To solve this problem, we first determine the 3D locations of a man wearing a black jacket and a blue mountain bike. Then we estimate the vector pointing from a blue mountain bike to a man wearing a black jacket, as well as the left direction of a blue mountain bike. Next we compute the cosine similarities between the vector and the left direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a man wearing a black jacket is on the left of a blue mountain bike. Otherwise, a man wearing a black jacket is behind a blue mountain bike. The 3D location of a man wearing a black jacket is (5.7, -0.8, 33.6). The 3D location of a blue mountain bike is (-0.7, 1.2, 3.2). The vector from a blue mountain bike to a man wearing a black jacket is hence (6.3, -2.0, 30.5). The left direction of a blue mountain bike is (0.1, -0.2, -1.0). The cosine similarity between the vector and the left direction is -0.92, corresponding to an angle of 157.02 degrees. The angle is smaller than 90 degrees, meaning that a man wearing a black jacket is on the right of a blue mountain bike. Therefore, the final answer is B. on the right.
B. on the right.
orientation_on_the_left
002f2d008de2f535.jpg
002f860e692757f7_1efa
Consider the real-world 3D orientations of the objects. Are a car that is black and a yellow car parked in a driveway facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ 4.9, -2, 26.1 ], "label": "a car that is black" }, { "bbox_3d": [ 8.8, -1.4, 20.1 ], "label": "a yellow car parked in a driveway" } ]
[ { "front_dir": [ -0.1, 0.1, -1 ], "label": "a car that is black", "left_dir": [ -1, 0, 0.1 ] }, { "front_dir": [ -0.3, 0.1, -0.9 ], "label": "a yellow car parked in a driveway", "left_dir": [ -1, -0.1, 0.3 ] } ]
A
To solve this problem, we first detect the front directions of a car that is black and a yellow car parked in a driveway. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a car that is black is (-0.1, 0.1, -1.0). The front direction of a yellow car parked in a driveway is (-0.3, 0.1, -0.9). The cosine similarity between the two front directions is 0.98, corresponding to an angle of 12.17. The angle is small, meaning that the two objects are facing same or similar directions. Therefore, the final answer is A. same or similar directions.
A. same or similar directions.
multi_object_same_direction
002f860e692757f7.jpg
002f860e692757f7_979d
Consider the real-world 3D locations and orientations of the objects. Which object is a black car parked near a building facing towards, a black car or the a car parked in front of a house?
a black car
a car parked in front of a house
null
null
[ { "bbox_3d": [ 8.5, -2.4, 29.6 ], "label": "a black car parked near a building" }, { "bbox_3d": [ 0.6, 1, 3.4 ], "label": "a black car" }, { "bbox_3d": [ 0.6, -3.3, 35.6 ], "label": "a car parked in front of a house" } ]
[ { "front_dir": [ -0.2, 0.1, -1 ], "label": "a black car parked near a building", "left_dir": [ -1, 0, 0.2 ] }, { "front_dir": [ -0.1, 0.2, -1 ], "label": "a black car", "left_dir": [ -1, -0.2, 0 ] }, { "front_dir": [ 0.1, 0.1, -1 ], "label": "a car parked in front of a house", "left_dir": [ -1, 0, -0.1 ] } ]
A
To solve this problem, we first detect the 3D location of a black car parked near a building, a black car, and a car parked in front of a house. Then we compute the cosine similarities between the front direction of a black car parked near a building and the vectors from a black car parked near a building to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a black car parked near a building is facing towards. The 3D location of a black car parked near a building is (8.5, -2.4, 29.6). The 3D location of a black car is (0.6, 1.0, 3.4). The 3D location of a car parked in front of a house is (0.6, -3.3, 35.6). The front direction of a black car parked near a building is (-0.2, 0.1, -1.0). First we consider if a black car parked near a building is facing towards the a black car. The vector from a black car parked near a building to a black car is (-7.9, 3.4, -26.2). The cosine similarity between the front direction and the vector is 0.99, corresponding to an angle of 6.25 degrees. First we consider if a black car parked near a building is facing towards the a car parked in front of a house. The vector from a black car parked near a building to a car parked in front of a house is (-7.9, -0.9, 6.0). The cosine similarity between the front direction and the vector is -0.44, corresponding to an angle of 116.24 degrees. We find that the angle between the front direction and a black car is smaller. Therefore, the final answer is A. a black car.
A. a black car.
multi_object_facing
002f860e692757f7.jpg
002fefb5247db49e_4c30
Consider the real-world 3D locations and orientations of the objects. If I stand at a white and blue car's position facing where it is facing, is a white and black bicycle helmet with a red stripe on the left or right of me?
on the left
on the right
null
null
[ { "bbox_3d": [ 3.8, 3.1, 13.1 ], "label": "a white and black bicycle helmet with a red stripe" }, { "bbox_3d": [ -1.1, 1.4, 2 ], "label": "a white and blue car" } ]
[ { "front_dir": [ 0.7, 0.1, -0.7 ], "label": "a white and blue car", "left_dir": [ -0.8, 0.1, -0.6 ] } ]
B
To solve this problem, we first determine the 3D locations of a white and black bicycle helmet with a red stripe and a white and blue car. Then we estimate the vector pointing from a white and blue car to a white and black bicycle helmet with a red stripe, as well as the left direction of a white and blue car. Next we compute the cosine similarities between the vector and the left direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a white and black bicycle helmet with a red stripe is on the left of a white and blue car. Otherwise, a white and black bicycle helmet with a red stripe is behind a white and blue car. The 3D location of a white and black bicycle helmet with a red stripe is (3.8, 3.1, 13.1). The 3D location of a white and blue car is (-1.1, 1.4, 2.0). The vector from a white and blue car to a white and black bicycle helmet with a red stripe is hence (4.9, 1.7, 11.1). The left direction of a white and blue car is (-0.8, 0.1, -0.6). The cosine similarity between the vector and the left direction is -0.86, corresponding to an angle of 149.06 degrees. The angle is smaller than 90 degrees, meaning that a white and black bicycle helmet with a red stripe is on the right of a white and blue car. Therefore, the final answer is B. on the right.
B. on the right.
orientation_on_the_left
002fefb5247db49e.jpg
00302a3d12649103_ebbe
Consider the real-world 3D locations and orientations of the objects. Which object is a black chair with a woman sitting in it facing towards, a man in a brown hat sitting or the a long log of wood?
a man in a brown hat sitting
a long log of wood
null
null
[ { "bbox_3d": [ -0.8, 0.4, 2.9 ], "label": "a black chair with a woman sitting in it" }, { "bbox_3d": [ 0, 0.7, 3.3 ], "label": "a man in a brown hat sitting" }, { "bbox_3d": [ -0.3, 0.3, 1.8 ], "label": "a long log of wood" } ]
[ { "front_dir": [ 0.7, 0, -0.7 ], "label": "a black chair with a woman sitting in it", "left_dir": [ -0.7, 0.1, -0.7 ] } ]
B
To solve this problem, we first detect the 3D location of a black chair with a woman sitting in it, a man in a brown hat sitting, and a long log of wood. Then we compute the cosine similarities between the front direction of a black chair with a woman sitting in it and the vectors from a black chair with a woman sitting in it to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a black chair with a woman sitting in it is facing towards. The 3D location of a black chair with a woman sitting in it is (-0.8, 0.4, 2.9). The 3D location of a man in a brown hat sitting is (-0.0, 0.7, 3.3). The 3D location of a long log of wood is (-0.3, 0.3, 1.8). The front direction of a black chair with a woman sitting in it is (0.7, 0.0, -0.7). First we consider if a black chair with a woman sitting in it is facing towards the a man in a brown hat sitting. The vector from a black chair with a woman sitting in it to a man in a brown hat sitting is (0.7, 0.3, 0.4). The cosine similarity between the front direction and the vector is 0.33, corresponding to an angle of 70.46 degrees. First we consider if a black chair with a woman sitting in it is facing towards the a long log of wood. The vector from a black chair with a woman sitting in it to a long log of wood is (0.5, -0.1, -1.1). The cosine similarity between the front direction and the vector is 0.93, corresponding to an angle of 21.38 degrees. We find that the angle between the front direction and a long log of wood is smaller. Therefore, the final answer is B. a long log of wood.
B. a long log of wood.
multi_object_facing
00302a3d12649103.jpg
00303af6c7034507_7f89
Consider the real-world 3D locations and orientations of the objects. Which object is a boat with a green cover facing towards, a small white boat or the a canal with a boat in it?
a small white boat
a canal with a boat in it
null
null
[ { "bbox_3d": [ -0.2, 3.2, 12.9 ], "label": "a boat with a green cover" }, { "bbox_3d": [ 0.8, 3.1, 6.3 ], "label": "a small white boat" }, { "bbox_3d": [ -1.9, -0.3, 18.1 ], "label": "a canal with a boat in it" } ]
[ { "front_dir": [ 0.1, -0.2, -1 ], "label": "a boat with a green cover", "left_dir": [ -1, 0.1, -0.1 ] }, { "front_dir": [ -1, 0, -0.1 ], "label": "a small white boat", "left_dir": [ -0.1, 0.2, 1 ] } ]
A
To solve this problem, we first detect the 3D location of a boat with a green cover, a small white boat, and a canal with a boat in it. Then we compute the cosine similarities between the front direction of a boat with a green cover and the vectors from a boat with a green cover to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a boat with a green cover is facing towards. The 3D location of a boat with a green cover is (-0.2, 3.2, 12.9). The 3D location of a small white boat is (0.8, 3.1, 6.3). The 3D location of a canal with a boat in it is (-1.9, -0.3, 18.1). The front direction of a boat with a green cover is (0.1, -0.2, -1.0). First we consider if a boat with a green cover is facing towards the a small white boat. The vector from a boat with a green cover to a small white boat is (0.9, -0.1, -6.6). The cosine similarity between the front direction and the vector is 0.99, corresponding to an angle of 9.50 degrees. First we consider if a boat with a green cover is facing towards the a canal with a boat in it. The vector from a boat with a green cover to a canal with a boat in it is (-1.8, -3.5, 5.2). The cosine similarity between the front direction and the vector is -0.71, corresponding to an angle of 135.17 degrees. We find that the angle between the front direction and a small white boat is smaller. Therefore, the final answer is A. a small white boat.
A. a small white boat.
multi_object_facing
00303af6c7034507.jpg
0030c312e6f8a831_443e
Consider the real-world 3D locations of the objects. Are the a tortilla with meat, sauce and yellow flowers on it and the a white plate next to each other or far away from each other?
next to each other
far away from each other
null
null
[ { "bbox_3d": [ 0, 0.8, 0.4 ], "label": "a tortilla with meat, sauce and yellow flowers on it" }, { "bbox_3d": [ 0.1, 1, 0.1 ], "label": "a white plate" } ]
[]
A
To solve this problem, we first estimate the 3D locations of a tortilla with meat, sauce and yellow flowers on it and a white plate. Then we can compute the L2 distance between the two objects. Next we estimate the rough sizes of the two objects. If the distance between the two objects is smaller or roughly the same as the object sizes, then the two objects are next to each other. Otherwise, the two objects are far away from each other. The 3D location of a tortilla with meat, sauce and yellow flowers on it is (-0.0, 0.8, 0.4). The 3D location of a white plate is (0.1, 1.0, 0.1). The L2 distance between the two objects is 0.42. The size of the a tortilla with meat, sauce and yellow flowers on it is roughly 0.42. The size of the a white plate is roughly 0.36. The distance between the two objects is smaller or roughly the same as the object sizes, meaning that they are next to each other. Therefore, the answer is A. next to each other.
A. next to each other.
location_next_to
0030c312e6f8a831.jpg
0030ef4c3497250b_148e
Consider the real-world 3D orientations of the objects. Are a multi-colored dresser with a pink drawer and a pink drawer with a blue drawer above it facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ 0.1, 1, 1.6 ], "label": "a multi-colored dresser with a pink drawer" }, { "bbox_3d": [ 0.2, 0.5, 1.5 ], "label": "a pink drawer with a blue drawer above it" } ]
[ { "front_dir": [ 0, 0.2, -1 ], "label": "a multi-colored dresser with a pink drawer", "left_dir": [ -1, 0, 0 ] }, { "front_dir": [ 0, 0.5, -0.9 ], "label": "a pink drawer with a blue drawer above it", "left_dir": [ -1, 0, 0 ] } ]
A
To solve this problem, we first detect the front directions of a multi-colored dresser with a pink drawer and a pink drawer with a blue drawer above it. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a multi-colored dresser with a pink drawer is (-0.0, 0.2, -1.0). The front direction of a pink drawer with a blue drawer above it is (-0.0, 0.5, -0.9). The cosine similarity between the two front directions is 0.97, corresponding to an angle of 14.51. The angle is small, meaning that the two objects are facing same or similar directions. Therefore, the final answer is A. same or similar directions.
A. same or similar directions.
multi_object_same_direction
0030ef4c3497250b.jpg
00310b7a00f44121_bfa0
Consider the real-world 3D locations and orientations of the objects. Which side of a blue car is facing a large tree with many branches?
front
left
back
right
[ { "bbox_3d": [ 2, 0.6, 30.8 ], "label": "a blue car" }, { "bbox_3d": [ 2.9, 5.9, 13.8 ], "label": "a large tree with many branches" } ]
[ { "front_dir": [ 0, -0.1, -1 ], "label": "a blue car", "left_dir": [ -1, 0, 0 ] } ]
A
To solve this problem, we first detect the 3D locations of a blue car and a large tree with many branches. Then we compute the vector pointing from a blue car to a large tree with many branches. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a blue car, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a blue car that is facing a large tree with many branches corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The 3D location of a blue car is (2.0, 0.6, 30.8). The 3D location of a large tree with many branches is (2.9, 5.9, 13.8). The vector from a blue car to a large tree with many branches is hence (0.9, 5.3, -17.1). The left direction of a blue car is (-1.0, 0.0, -0.0). The cosine similarity between the vector pointing to a large tree with many branches and the left direction is -0.02, corresponding to an angle of 91.37 degrees. Thus the angle between the vector pointing to a large tree with many branches and the right direction is 88.63 degrees. The front direction of a blue car is (0.0, -0.1, -1.0). The cosine similarity between the vector pointing to a large tree with many branches and the front direction is 0.93, corresponding to an angle of 20.98 degrees. Thus the angle between the vector pointing to a large tree with many branches and the back direction is 159.02 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 20.98 degrees. Thus the front side of a blue car is facing the a large tree with many branches. Therefore, the final answer is A. front.
A. front.
multi_object_viewpoint_towards_object
00310b7a00f44121.jpg
00311d28415aa937_1153
Consider the real-world 3D locations of the objects. Is a statue of a man in white directly above a white pot with flowers?
yes
no
null
null
[ { "bbox_3d": [ 0.8, 1.6, 2.5 ], "label": "a statue of a man in white" }, { "bbox_3d": [ 0.4, 0.4, 2.3 ], "label": "a white pot with flowers" } ]
[]
A
To solve this problem, we first determine the 3D locations of a statue of a man in white and a white pot with flowers. Then we compute the vector pointing from a white pot with flowers to a statue of a man in white, as well as the up direction of a white pot with flowers. We estimate the cosine similarity between the vector and the up direction, which leads to the angle between the two directions. If the angle is small, then a statue of a man in white is directly above a white pot with flowers. Otherwise, then a statue of a man in white is not directly above a white pot with flowers. The 3D location of a statue of a man in white is (0.8, 1.6, 2.5). The 3D location of a white pot with flowers is (0.4, 0.4, 2.3). The vector from a white pot with flowers to a statue of a man in white is hence (0.4, 1.2, 0.2). The up direction of a white pot with flowers is (0.0, 1.0, 0.0). The cosine similarity between the vector and the up direction is 0.95, corresponding to an angle of 18 degrees. The angle between the vector and the up direction is small, meaning that a statue of a man in white is directly above a white pot with flowers. Therefore, the answer is A. yes.
A. yes.
location_above
00311d28415aa937.jpg
0031bc79c521cb94_5293
Consider the real-world 3D locations and orientations of the objects. Which object is a computer table with a green bag on it facing towards, a flat screen TV or the a red stool?
a flat screen TV
a red stool
null
null
[ { "bbox_3d": [ -0.3, 0.7, 3.3 ], "label": "a computer table with a green bag on it" }, { "bbox_3d": [ 0.1, 1.9, 3.6 ], "label": "a flat screen TV" }, { "bbox_3d": [ 0.2, 0.5, 2 ], "label": "a red stool" } ]
[ { "front_dir": [ 0.3, -0.1, -1 ], "label": "a computer table with a green bag on it", "left_dir": [ -1, 0.1, -0.3 ] }, { "front_dir": [ 0.1, -0.1, -1 ], "label": "a flat screen TV", "left_dir": [ -1, 0.1, -0.1 ] }, { "front_dir": [ -0.1, -0.2, -1 ], "label": "a red stool", "left_dir": [ -1, 0, 0.1 ] } ]
B
To solve this problem, we first detect the 3D location of a computer table with a green bag on it, a flat screen TV, and a red stool. Then we compute the cosine similarities between the front direction of a computer table with a green bag on it and the vectors from a computer table with a green bag on it to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a computer table with a green bag on it is facing towards. The 3D location of a computer table with a green bag on it is (-0.3, 0.7, 3.3). The 3D location of a flat screen TV is (0.1, 1.9, 3.6). The 3D location of a red stool is (0.2, 0.5, 2.0). The front direction of a computer table with a green bag on it is (0.3, -0.1, -1.0). First we consider if a computer table with a green bag on it is facing towards the a flat screen TV. The vector from a computer table with a green bag on it to a flat screen TV is (0.4, 1.2, 0.3). The cosine similarity between the front direction and the vector is -0.17, corresponding to an angle of 99.63 degrees. First we consider if a computer table with a green bag on it is facing towards the a red stool. The vector from a computer table with a green bag on it to a red stool is (0.5, -0.2, -1.3). The cosine similarity between the front direction and the vector is 0.99, corresponding to an angle of 6.42 degrees. We find that the angle between the front direction and a red stool is smaller. Therefore, the final answer is B. a red stool.
B. a red stool.
multi_object_facing
0031bc79c521cb94.jpg
0031bff54b02c9c1_7220
Consider the real-world 3D locations and orientations of the objects. If I stand at a bookshelf with books and a sign's position facing where it is facing, is a mannequin wearing a scarf on the left or right of me?
on the left
on the right
null
null
[ { "bbox_3d": [ -1, 1.2, 2.6 ], "label": "a mannequin wearing a scarf" }, { "bbox_3d": [ 0.6, 1.4, 2.6 ], "label": "a bookshelf with books and a sign" } ]
[ { "front_dir": [ -0.3, -0.1, -1 ], "label": "a bookshelf with books and a sign", "left_dir": [ -1, 0, 0.3 ] } ]
A
To solve this problem, we first determine the 3D locations of a mannequin wearing a scarf and a bookshelf with books and a sign. Then we estimate the vector pointing from a bookshelf with books and a sign to a mannequin wearing a scarf, as well as the left direction of a bookshelf with books and a sign. Next we compute the cosine similarities between the vector and the left direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a mannequin wearing a scarf is on the left of a bookshelf with books and a sign. Otherwise, a mannequin wearing a scarf is behind a bookshelf with books and a sign. The 3D location of a mannequin wearing a scarf is (-1.0, 1.2, 2.6). The 3D location of a bookshelf with books and a sign is (0.6, 1.4, 2.6). The vector from a bookshelf with books and a sign to a mannequin wearing a scarf is hence (-1.5, -0.3, -0.0). The left direction of a bookshelf with books and a sign is (-1.0, 0.0, 0.3). The cosine similarity between the vector and the left direction is 0.94, corresponding to an angle of 20.57 degrees. The angle is smaller than 90 degrees, meaning that a mannequin wearing a scarf is on the left of a bookshelf with books and a sign. Therefore, the final answer is A. on the left.
A. on the left.
orientation_on_the_left
0031bff54b02c9c1.jpg
0031cf7ae9ab971d_965d
Consider the real-world 3D orientations of the objects. Are a white stool and a blue stool with a metal frame facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ 1.5, 0.5, 9.1 ], "label": "a white stool" }, { "bbox_3d": [ 1, 0.6, 8.5 ], "label": "a blue stool with a metal frame" } ]
[ { "front_dir": [ -0.1, 0, -1 ], "label": "a white stool", "left_dir": [ -1, 0.1, 0.1 ] }, { "front_dir": [ 0.3, 0, -1 ], "label": "a blue stool with a metal frame", "left_dir": [ -1, 0.1, -0.3 ] } ]
A
To solve this problem, we first detect the front directions of a white stool and a blue stool with a metal frame. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a white stool is (-0.1, 0.0, -1.0). The front direction of a blue stool with a metal frame is (0.3, -0.0, -1.0). The cosine similarity between the two front directions is 0.93, corresponding to an angle of 21.06. The angle is small, meaning that the two objects are facing same or similar directions. Therefore, the final answer is A. same or similar directions.
A. same or similar directions.
multi_object_same_direction
0031cf7ae9ab971d.jpg
003246b20f338a5d_bda5
Consider the real-world 3D locations and orientations of the objects. If I stand at a small wooden boat's position facing where it is facing, is a woman wearing a white shirt in front of me or behind me?
in front of
behind
null
null
[ { "bbox_3d": [ -0.3, 1.1, 11.9 ], "label": "a woman wearing a white shirt" }, { "bbox_3d": [ -0.1, 0.5, 11 ], "label": "a small wooden boat" } ]
[ { "front_dir": [ 0.1, 0.1, -1 ], "label": "a small wooden boat", "left_dir": [ -1, 0.1, -0.1 ] } ]
B
To solve this problem, we first determine the 3D locations of a woman wearing a white shirt and a small wooden boat. Then we estimate the vector pointing from a small wooden boat to a woman wearing a white shirt, as well as the front direction of a small wooden boat. Next we compute the cosine similarities between the vector and the front direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a woman wearing a white shirt is in front of a small wooden boat. Otherwise, a woman wearing a white shirt is behind a small wooden boat. The 3D location of a woman wearing a white shirt is (-0.3, 1.1, 11.9). The 3D location of a small wooden boat is (-0.1, 0.5, 11.0). The vector from a small wooden boat to a woman wearing a white shirt is hence (-0.2, 0.6, 0.9). The front direction of a small wooden boat is (0.1, 0.1, -1.0). The cosine similarity between the vector and the front direction is -0.74, corresponding to an angle of 138.00 degrees. The angle is smaller than 90 degrees, meaning that a woman wearing a white shirt is behind a small wooden boat. Therefore, the final answer is B. behind.
B. behind.
orientation_in_front_of
003246b20f338a5d.jpg
003246b20f338a5d_a2f9
Consider the real-world 3D orientations of the objects. What is the relationship between the orientations of a small wooden boat and a wooden boat, parallel of perpendicular to each other?
parallel
perpendicular
null
null
[ { "bbox_3d": [ -0.1, 0.5, 11 ], "label": "a small wooden boat" }, { "bbox_3d": [ -4.8, -4, 88.1 ], "label": "a wooden boat" } ]
[ { "front_dir": [ 0.1, 0.1, -1 ], "label": "a small wooden boat", "left_dir": [ -1, 0.1, -0.1 ] }, { "front_dir": [ 0.1, 0, -1 ], "label": "a wooden boat", "left_dir": [ -1, 0.1, -0.1 ] } ]
A
To solve this problem, we first detect the front directions of a small wooden boat and a wooden boat. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is closer to 0 or 180, than to 90 degrees, then the two objects are parallel to each other. Otherwise, the two objects are perpendicular to each other. The front direction of a small wooden boat is (0.1, 0.1, -1.0). The front direction of a wooden boat is (0.1, -0.0, -1.0). The cosine similarity between the two front directions is 0.99, corresponding to an angle of 9.19. The angle is closer to 0 or 180, than to 90 degrees, meaning that the two objects are parallel to each other. Therefore, the final answer is A. parallel.
A. parallel.
multi_object_parallel
003246b20f338a5d.jpg
0032c713ba623a2a_1dec
Consider the real-world 3D location of the objects. Which object is further away from the camera?
a laptop computer
a computer monitor with a green light on the bottom
null
null
[ { "bbox_3d": [ -0.2, 1.1, 1.8 ], "label": "a laptop computer" }, { "bbox_3d": [ -0.1, 0.9, 1.5 ], "label": "a computer monitor with a green light on the bottom" } ]
[]
A
To solve this problem, we first estimate the 3D locations of a laptop computer and a computer monitor with a green light on the bottom. Then we estimate the L2 distances from the camera to the two objects. The object with a smaller L2 distance is the one that is closer to the camera. The 3D location of a laptop computer is (-0.2, 1.1, 1.8). The 3D location of a computer monitor with a green light on the bottom is (-0.1, 0.9, 1.5). The L2 distance from the camera to a laptop computer is 2.15. The L2 distance from the camera to a computer monitor with a green light on the bottom is 1.69. The distance to a laptop computer is larger. Therefore, the answer is A. a laptop computer.
A. a laptop computer.
location_closer_to_camera
0032c713ba623a2a.jpg
0032c713ba623a2a_434e
Consider the real-world 3D locations and orientations of the objects. Which side of a computer monitor with a green light on the bottom is facing a man in a red shirt looking at a computer screen?
front
left
back
right
[ { "bbox_3d": [ -0.1, 0.9, 1.5 ], "label": "a computer monitor with a green light on the bottom" }, { "bbox_3d": [ 0.1, 0.6, 0.8 ], "label": "a man in a red shirt looking at a computer screen" } ]
[ { "front_dir": [ 0.6, -0.1, -0.8 ], "label": "a computer monitor with a green light on the bottom", "left_dir": [ -0.8, -0.1, -0.6 ] } ]
A
To solve this problem, we first detect the 3D locations of a computer monitor with a green light on the bottom and a man in a red shirt looking at a computer screen. Then we compute the vector pointing from a computer monitor with a green light on the bottom to a man in a red shirt looking at a computer screen. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a computer monitor with a green light on the bottom, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a computer monitor with a green light on the bottom that is facing a man in a red shirt looking at a computer screen corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The 3D location of a computer monitor with a green light on the bottom is (-0.1, 0.9, 1.5). The 3D location of a man in a red shirt looking at a computer screen is (0.1, 0.6, 0.8). The vector from a computer monitor with a green light on the bottom to a man in a red shirt looking at a computer screen is hence (0.2, -0.3, -0.6). The left direction of a computer monitor with a green light on the bottom is (-0.8, -0.1, -0.6). The cosine similarity between the vector pointing to a man in a red shirt looking at a computer screen and the left direction is 0.29, corresponding to an angle of 73.32 degrees. Thus the angle between the vector pointing to a man in a red shirt looking at a computer screen and the right direction is 106.68 degrees. The front direction of a computer monitor with a green light on the bottom is (0.6, -0.1, -0.8). The cosine similarity between the vector pointing to a man in a red shirt looking at a computer screen and the front direction is 0.92, corresponding to an angle of 23.42 degrees. Thus the angle between the vector pointing to a man in a red shirt looking at a computer screen and the back direction is 156.58 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 23.42 degrees. Thus the front side of a computer monitor with a green light on the bottom is facing the a man in a red shirt looking at a computer screen. Therefore, the final answer is A. front.
A. front.
multi_object_viewpoint_towards_object
0032c713ba623a2a.jpg
0032fb627b59792a_cb82
Consider the real-world 3D locations of the objects. Which object has a lower location?
a white church with a red roof
a tree with green leaves
null
null
[ { "bbox_3d": [ 10.1, -3, 86.2 ], "label": "a white church with a red roof" }, { "bbox_3d": [ 0.7, 2.5, 14.4 ], "label": "a tree with green leaves" } ]
[]
A
To solve this problem, we first estimate the 3D heights of the two objects. The object with a larger height value is at a higher location. The object with a smaller height value is at a lower location. The 3D height of a white church with a red roof is 8.4. The 3D height of a tree with green leaves is 11.0. The 3D height of a tree with green leaves is larger, meaning that the location of a tree with green leaves is higher. In other words, the location of a white church with a red roof is lower. Therefore, the answer is A. a white church with a red roof.
A. a white church with a red roof
height_higher
0032fb627b59792a.jpg
003426eeafa92c9b_f6fe
Consider the real-world 3D location of the objects. Which object is further away from the camera?
a blue and white pen
a woman in a black suit stands in front of a white board
null
null
[ { "bbox_3d": [ 0.4, 0.2, 4.9 ], "label": "a blue and white pen" }, { "bbox_3d": [ 0.4, 1.3, 7.6 ], "label": "a woman in a black suit stands in front of a white board" } ]
[]
B
To solve this problem, we first estimate the 3D locations of a blue and white pen and a woman in a black suit stands in front of a white board. Then we estimate the L2 distances from the camera to the two objects. The object with a smaller L2 distance is the one that is closer to the camera. The 3D location of a blue and white pen is (0.4, 0.2, 4.9). The 3D location of a woman in a black suit stands in front of a white board is (0.4, 1.3, 7.6). The L2 distance from the camera to a blue and white pen is 4.91. The L2 distance from the camera to a woman in a black suit stands in front of a white board is 7.75. The distance to a woman in a black suit stands in front of a white board is larger. Therefore, the answer is B. a woman in a black suit stands in front of a white board.
B. a woman in a black suit stands in front of a white board.
location_closer_to_camera
003426eeafa92c9b.jpg
0034825de48b36e7_35fa
Consider the real-world 3D locations and orientations of the objects. Which side of a white chair with a white shirt is facing a person with black hair?
front
left
back
right
[ { "bbox_3d": [ -0.5, 0.2, 1.1 ], "label": "a white chair with a white shirt" }, { "bbox_3d": [ -1.5, 1, 4.5 ], "label": "a person with black hair" } ]
[ { "front_dir": [ 0.9, 0.1, 0.3 ], "label": "a white chair with a white shirt", "left_dir": [ 0.3, 0, -0.9 ] } ]
D
To solve this problem, we first detect the 3D locations of a white chair with a white shirt and a person with black hair. Then we compute the vector pointing from a white chair with a white shirt to a person with black hair. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a white chair with a white shirt, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a white chair with a white shirt that is facing a person with black hair corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The 3D location of a white chair with a white shirt is (-0.5, 0.2, 1.1). The 3D location of a person with black hair is (-1.5, 1.0, 4.5). The vector from a white chair with a white shirt to a person with black hair is hence (-1.1, 0.8, 3.5). The left direction of a white chair with a white shirt is (0.3, -0.0, -0.9). The cosine similarity between the vector pointing to a person with black hair and the left direction is -0.98, corresponding to an angle of 168.66 degrees. Thus the angle between the vector pointing to a person with black hair and the right direction is 11.34 degrees. The front direction of a white chair with a white shirt is (0.9, 0.1, 0.3). The cosine similarity between the vector pointing to a person with black hair and the front direction is 0.07, corresponding to an angle of 85.86 degrees. Thus the angle between the vector pointing to a person with black hair and the back direction is 94.14 degrees. Among the four directions, the smallest angle is the right direction, with an angle of 11.34 degrees. Thus the right side of a white chair with a white shirt is facing the a person with black hair. Therefore, the final answer is D. right.
D. right.
multi_object_viewpoint_towards_object
0034825de48b36e7.jpg
003491d5229c610f_4653
Consider the real-world 3D locations and orientations of the objects. Which side of a concrete bench is facing the camera?
front
left
back
right
[ { "bbox_3d": [ 6.8, 0.9, 22.9 ], "label": "a concrete bench" } ]
[ { "front_dir": [ -0.2, -0.1, -1 ], "label": "a concrete bench", "left_dir": [ -1, 0.1, 0.2 ] } ]
A
To solve this problem, we first estimate the 3D location of a concrete bench. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a concrete bench, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a concrete bench that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a concrete bench is (6.8, 0.9, 22.9). The vector from a concrete bench to camera is hence (-6.8, -0.9, -22.9). The left direction of a concrete bench is (-1.0, 0.1, 0.2). The cosine similarity between the vector pointing to camera and the left direction is 0.08, corresponding to an angle of 85.32 degrees. Thus the angle between the vector pointing to camera and the right direction is 94.68 degrees. The front direction of a concrete bench is (-0.2, -0.1, -1.0). The cosine similarity between the vector pointing to camera and the front direction is 0.99, corresponding to an angle of 7.40 degrees. Thus the angle between the vector pointing to camera and the back direction is 172.60 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 7.40 degrees. Thus the front side of a concrete bench is facing the camera. Therefore, the final answer is A. front.
A. front.
orientation_viewpoint
003491d5229c610f.jpg
003515a369fceb32_d4b3
Consider the real-world 3D locations of the objects. Is a ladder with metal steps directly underneath a metal ladder?
yes
no
null
null
[ { "bbox_3d": [ -2.7, 3.2, 17.6 ], "label": "a metal ladder" }, { "bbox_3d": [ 2.4, 1.6, 17.2 ], "label": "a ladder with metal steps" } ]
[]
B
To solve this problem, we first determine the 3D locations of a metal ladder and a ladder with metal steps. Then we compute the vector pointing from a ladder with metal steps to a metal ladder, as well as the up direction of a ladder with metal steps. We estimate the cosine similarity between the vector and the up direction, which leads to the angle between the two directions. If the angle is small, then a metal ladder is directly above a ladder with metal steps. Otherwise, then a metal ladder is not directly above a ladder with metal steps. To solve the question, we first determine if a metal ladder is directly above a ladder with metal steps. The 3D location of a metal ladder is (-2.7, 3.2, 17.6). The 3D location of a ladder with metal steps is (2.4, 1.6, 17.2). The vector from a ladder with metal steps to a metal ladder is hence (-5.1, 1.6, 0.4). The up direction of a ladder with metal steps is (0.0, 1.0, 0.0). The cosine similarity between the vector and the up direction is 0.30, corresponding to an angle of 72 degrees. The angle between the vector and the up direction is large, meaning that a metal ladder is not directly above a ladder with metal steps. In other words, a ladder with metal steps is not directly underneath a metal ladder. Therefore, the answer is B. no.
B. no.
location_above
003515a369fceb32.jpg
00355826b3520b66_7a1c
Consider the real-world 3D locations of the objects. Are the a pond with grass and the a large tree with green leaves next to each other or far away from each other?
next to each other
far away from each other
null
null
[ { "bbox_3d": [ -0.3, 0.5, 23.8 ], "label": "a pond with grass" }, { "bbox_3d": [ -27.4, 7, 75.6 ], "label": "a large tree with green leaves" } ]
[]
A
To solve this problem, we first estimate the 3D locations of a pond with grass and a large tree with green leaves. Then we can compute the L2 distance between the two objects. Next we estimate the rough sizes of the two objects. If the distance between the two objects is smaller or roughly the same as the object sizes, then the two objects are next to each other. Otherwise, the two objects are far away from each other. The 3D location of a pond with grass is (-0.3, 0.5, 23.8). The 3D location of a large tree with green leaves is (-27.4, 7.0, 75.6). The L2 distance between the two objects is 58.89. The size of the a pond with grass is roughly 54.38. The size of the a large tree with green leaves is roughly 23.72. The distance between the two objects is smaller or roughly the same as the object sizes, meaning that they are next to each other. Therefore, the answer is A. next to each other.
A. next to each other.
location_next_to
00355826b3520b66.jpg
0035a84599375330_1a36
Consider the real-world 3D locations and orientations of the objects. If I stand at a bulletin board with a red and white tie's position facing where it is facing, is a woman in a suit in front of me or behind me?
in front of
behind
null
null
[ { "bbox_3d": [ -0.7, 1.4, 5.1 ], "label": "a woman in a suit" }, { "bbox_3d": [ 3.4, 2.3, 6.4 ], "label": "a bulletin board with a red and white tie" } ]
[ { "front_dir": [ -0.8, -0.1, -0.6 ], "label": "a bulletin board with a red and white tie", "left_dir": [ -0.6, 0, 0.8 ] } ]
A
To solve this problem, we first determine the 3D locations of a woman in a suit and a bulletin board with a red and white tie. Then we estimate the vector pointing from a bulletin board with a red and white tie to a woman in a suit, as well as the front direction of a bulletin board with a red and white tie. Next we compute the cosine similarities between the vector and the front direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a woman in a suit is in front of a bulletin board with a red and white tie. Otherwise, a woman in a suit is behind a bulletin board with a red and white tie. The 3D location of a woman in a suit is (-0.7, 1.4, 5.1). The 3D location of a bulletin board with a red and white tie is (3.4, 2.3, 6.4). The vector from a bulletin board with a red and white tie to a woman in a suit is hence (-4.1, -1.0, -1.3). The front direction of a bulletin board with a red and white tie is (-0.8, -0.1, -0.6). The cosine similarity between the vector and the front direction is 0.92, corresponding to an angle of 22.65 degrees. The angle is smaller than 90 degrees, meaning that a woman in a suit is in front of a bulletin board with a red and white tie. Therefore, the final answer is A. in front of.
A. in front of.
orientation_in_front_of
0035a84599375330.jpg
0035fff2878635fc_eec8
Consider the real-world 3D locations and orientations of the objects. Which side of a black chair is facing the camera?
front
left
back
right
[ { "bbox_3d": [ 0.1, 0.2, 1.8 ], "label": "a black chair" } ]
[ { "front_dir": [ -0.2, 0.2, -1 ], "label": "a black chair", "left_dir": [ -1, 0.1, 0.2 ] } ]
A
To solve this problem, we first estimate the 3D location of a black chair. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a black chair, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a black chair that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a black chair is (0.1, 0.2, 1.8). The vector from a black chair to camera is hence (-0.1, -0.2, -1.8). The left direction of a black chair is (-1.0, 0.1, 0.2). The cosine similarity between the vector pointing to camera and the left direction is -0.13, corresponding to an angle of 97.36 degrees. Thus the angle between the vector pointing to camera and the right direction is 82.64 degrees. The front direction of a black chair is (-0.2, 0.2, -1.0). The cosine similarity between the vector pointing to camera and the front direction is 0.93, corresponding to an angle of 21.95 degrees. Thus the angle between the vector pointing to camera and the back direction is 158.05 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 21.95 degrees. Thus the front side of a black chair is facing the camera. Therefore, the final answer is A. front.
A. front.
orientation_viewpoint
0035fff2878635fc.jpg
003673c00f44cf45_c76f
Consider the real-world 3D locations and orientations of the objects. If I stand at a man wearing a white hat's position facing where it is facing, is a red and white cable car on the left or right of me?
on the left
on the right
null
null
[ { "bbox_3d": [ -0.2, 1.7, 6.5 ], "label": "a red and white cable car" }, { "bbox_3d": [ 2, 1.3, 7.6 ], "label": "a man wearing a white hat" } ]
[ { "front_dir": [ -0.3, -0.2, -0.9 ], "label": "a red and white cable car", "left_dir": [ -0.9, 0, 0.4 ] }, { "front_dir": [ -0.2, -0.1, -1 ], "label": "a man wearing a white hat", "left_dir": [ -1, 0.1, 0.2 ] } ]
A
To solve this problem, we first determine the 3D locations of a red and white cable car and a man wearing a white hat. Then we estimate the vector pointing from a man wearing a white hat to a red and white cable car, as well as the left direction of a man wearing a white hat. Next we compute the cosine similarities between the vector and the left direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a red and white cable car is on the left of a man wearing a white hat. Otherwise, a red and white cable car is behind a man wearing a white hat. The 3D location of a red and white cable car is (-0.2, 1.7, 6.5). The 3D location of a man wearing a white hat is (2.0, 1.3, 7.6). The vector from a man wearing a white hat to a red and white cable car is hence (-2.2, 0.4, -1.2). The left direction of a man wearing a white hat is (-1.0, 0.1, 0.2). The cosine similarity between the vector and the left direction is 0.79, corresponding to an angle of 37.41 degrees. The angle is smaller than 90 degrees, meaning that a red and white cable car is on the left of a man wearing a white hat. Therefore, the final answer is A. on the left.
A. on the left.
orientation_on_the_left
003673c00f44cf45.jpg
0036d2b9eddd940a_4b7c
Consider the real-world 3D location of the objects. Which object is closer to the camera?
a red container
a train with red cars
null
null
[ { "bbox_3d": [ -4.8, 5.2, 47.4 ], "label": "a red container" }, { "bbox_3d": [ 4.4, 4.2, 76 ], "label": "a train with red cars" } ]
[]
A
To solve this problem, we first estimate the 3D locations of a red container and a train with red cars. Then we estimate the L2 distances from the camera to the two objects. The object with a smaller L2 distance is the one that is closer to the camera. The 3D location of a red container is (-4.8, 5.2, 47.4). The 3D location of a train with red cars is (4.4, 4.2, 76.0). The L2 distance from the camera to a red container is 47.92. The L2 distance from the camera to a train with red cars is 76.22. The distance to a red container is smaller. Therefore, the answer is A. a red container.
A. a red container.
location_closer_to_camera
0036d2b9eddd940a.jpg
003787b0f1e51755_1966
Consider the real-world 3D locations and orientations of the objects. If I stand at a car with a silver bumper's position facing where it is facing, is a black dog with white paws in front of me or behind me?
in front of
behind
null
null
[ { "bbox_3d": [ 0.5, 0.2, 1.9 ], "label": "a black dog with white paws" }, { "bbox_3d": [ 1.4, 0.7, 3.3 ], "label": "a car with a silver bumper" } ]
[ { "front_dir": [ 0.2, -0.1, 1 ], "label": "a car with a silver bumper", "left_dir": [ 1, -0.1, -0.2 ] } ]
B
To solve this problem, we first determine the 3D locations of a black dog with white paws and a car with a silver bumper. Then we estimate the vector pointing from a car with a silver bumper to a black dog with white paws, as well as the front direction of a car with a silver bumper. Next we compute the cosine similarities between the vector and the front direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a black dog with white paws is in front of a car with a silver bumper. Otherwise, a black dog with white paws is behind a car with a silver bumper. The 3D location of a black dog with white paws is (0.5, 0.2, 1.9). The 3D location of a car with a silver bumper is (1.4, 0.7, 3.3). The vector from a car with a silver bumper to a black dog with white paws is hence (-1.0, -0.5, -1.4). The front direction of a car with a silver bumper is (0.2, -0.1, 1.0). The cosine similarity between the vector and the front direction is -0.86, corresponding to an angle of 149.34 degrees. The angle is smaller than 90 degrees, meaning that a black dog with white paws is behind a car with a silver bumper. Therefore, the final answer is B. behind.
B. behind.
orientation_in_front_of
003787b0f1e51755.jpg
00379c739346d021_d1fb
Consider the real-world 3D locations of the objects. Which is closer to a white bread sandwich, a boy holding a plate of food or a sandwich with a bun?
a boy holding a plate of food
a sandwich with a bun
null
null
[ { "bbox_3d": [ 0, 1, 1.3 ], "label": "a white bread sandwich" }, { "bbox_3d": [ -0.6, 0.8, 2.3 ], "label": "a boy holding a plate of food" }, { "bbox_3d": [ 0.6, 1.2, 0.9 ], "label": "a sandwich with a bun" } ]
[]
B
To solve this problem, we first detect the 3D location of a white bread sandwich, a boy holding a plate of food, and a sandwich with a bun. Then we compute the L2 distances between a white bread sandwich and a boy holding a plate of food, and between a white bread sandwich and a sandwich with a bun. The object that is closer to a white bread sandwich is the one with a smaller distance. The 3D location of a white bread sandwich is (0.0, 1.0, 1.3). The 3D location of a boy holding a plate of food is (-0.6, 0.8, 2.3). The 3D location of a sandwich with a bun is (0.6, 1.2, 0.9). The L2 distance between a white bread sandwich and a boy holding a plate of food is 1.2232088192544448. The L2 distance between a white bread sandwich and a sandwich with a bun is 0.6870014399318145. Between the two distances, the distance between a white bread sandwich and a sandwich with a bun is smaller. Therefore, the final answer is B. a sandwich with a bun.
B. a sandwich with a bun.
multi_object_closer_to
00379c739346d021.jpg
0037c8073ef3f6bc_444e
Consider the real-world 3D locations and orientations of the objects. Which side of a black car is facing the camera?
front
left
back
right
[ { "bbox_3d": [ -5.5, 1, 9.2 ], "label": "a black car" } ]
[ { "front_dir": [ 0.8, 0, -0.6 ], "label": "a black car", "left_dir": [ -0.6, -0.1, -0.8 ] } ]
A
To solve this problem, we first estimate the 3D location of a black car. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a black car, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a black car that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a black car is (-5.5, 1.0, 9.2). The vector from a black car to camera is hence (5.5, -1.0, -9.2). The left direction of a black car is (-0.6, -0.1, -0.8). The cosine similarity between the vector pointing to camera and the left direction is 0.39, corresponding to an angle of 67.16 degrees. Thus the angle between the vector pointing to camera and the right direction is 112.84 degrees. The front direction of a black car is (0.8, -0.0, -0.6). The cosine similarity between the vector pointing to camera and the front direction is 0.92, corresponding to an angle of 22.94 degrees. Thus the angle between the vector pointing to camera and the back direction is 157.06 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 22.94 degrees. Thus the front side of a black car is facing the camera. Therefore, the final answer is A. front.
A. front.
orientation_viewpoint
0037c8073ef3f6bc.jpg
0037df9f4ad04cf5_24ce
Consider the real-world 3D locations and orientations of the objects. Which object is a silver car facing towards, a table with three toy cars on it or the a white car with blue wheels?
a table with three toy cars on it
a white car with blue wheels
null
null
[ { "bbox_3d": [ 1.2, 0.2, 3.8 ], "label": "a silver car" }, { "bbox_3d": [ 0.2, 0.4, 2.7 ], "label": "a table with three toy cars on it" }, { "bbox_3d": [ -1.3, 0.1, 3.8 ], "label": "a white car with blue wheels" } ]
[ { "front_dir": [ -0.2, 0.2, -1 ], "label": "a silver car", "left_dir": [ -1, -0.1, 0.2 ] }, { "front_dir": [ 0.4, 0.3, -0.9 ], "label": "a white car with blue wheels", "left_dir": [ -0.9, 0.1, -0.4 ] } ]
A
To solve this problem, we first detect the 3D location of a silver car, a table with three toy cars on it, and a white car with blue wheels. Then we compute the cosine similarities between the front direction of a silver car and the vectors from a silver car to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a silver car is facing towards. The 3D location of a silver car is (1.2, 0.2, 3.8). The 3D location of a table with three toy cars on it is (0.2, 0.4, 2.7). The 3D location of a white car with blue wheels is (-1.3, 0.1, 3.8). The front direction of a silver car is (-0.2, 0.2, -1.0). First we consider if a silver car is facing towards the a table with three toy cars on it. The vector from a silver car to a table with three toy cars on it is (-1.0, 0.2, -1.1). The cosine similarity between the front direction and the vector is 0.85, corresponding to an angle of 31.71 degrees. First we consider if a silver car is facing towards the a white car with blue wheels. The vector from a silver car to a white car with blue wheels is (-2.5, -0.0, 0.0). The cosine similarity between the front direction and the vector is 0.18, corresponding to an angle of 79.63 degrees. We find that the angle between the front direction and a table with three toy cars on it is smaller. Therefore, the final answer is A. a table with three toy cars on it.
A. a table with three toy cars on it.
multi_object_facing
0037df9f4ad04cf5.jpg
003837f2a2f08c20_9c72
Consider the real-world 3D locations and orientations of the objects. Which side of a black car is facing the camera?
front
left
back
right
[ { "bbox_3d": [ 7.5, 1.6, 65.3 ], "label": "a black car" } ]
[ { "front_dir": [ 0, -0.1, -1 ], "label": "a black car", "left_dir": [ -1, 0.1, 0 ] } ]
A
To solve this problem, we first estimate the 3D location of a black car. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a black car, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a black car that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a black car is (7.5, 1.6, 65.3). The vector from a black car to camera is hence (-7.5, -1.6, -65.3). The left direction of a black car is (-1.0, 0.1, 0.0). The cosine similarity between the vector pointing to camera and the left direction is 0.07, corresponding to an angle of 85.71 degrees. Thus the angle between the vector pointing to camera and the right direction is 94.29 degrees. The front direction of a black car is (-0.0, -0.1, -1.0). The cosine similarity between the vector pointing to camera and the front direction is 1.00, corresponding to an angle of 5.68 degrees. Thus the angle between the vector pointing to camera and the back direction is 174.32 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 5.68 degrees. Thus the front side of a black car is facing the camera. Therefore, the final answer is A. front.
A. front.
orientation_viewpoint
003837f2a2f08c20.jpg
00388903eae56d69_249b
Consider the real-world 3D orientations of the objects. Are a black plastic chair and a black chair with a wooden frame facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ -0.4, 1.2, 1.5 ], "label": "a black plastic chair" }, { "bbox_3d": [ -0.6, 1.2, 1.9 ], "label": "a black chair with a wooden frame" } ]
[ { "front_dir": [ 1, 0, 0.2 ], "label": "a black plastic chair", "left_dir": [ 0.2, 0.2, -1 ] }, { "front_dir": [ 0.4, 0.2, -0.9 ], "label": "a black chair with a wooden frame", "left_dir": [ -0.9, 0.1, -0.3 ] } ]
B
To solve this problem, we first detect the front directions of a black plastic chair and a black chair with a wooden frame. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a black plastic chair is (1.0, -0.0, 0.2). The front direction of a black chair with a wooden frame is (0.4, 0.2, -0.9). The cosine similarity between the two front directions is 0.20, corresponding to an angle of 78.31. The angle is large, meaning that the two objects are facing very different directions. Therefore, the final answer is B. very different directions.
B. very different directions.
multi_object_same_direction
00388903eae56d69.jpg
00388cebd6c59358_41e2
Consider the real-world 3D locations and orientations of the objects. If I stand at a silver car's position facing where it is facing, is a large brick building in front of me or behind me?
in front of
behind
null
null
[ { "bbox_3d": [ -6.7, 12.9, 45.5 ], "label": "a large brick building" }, { "bbox_3d": [ -2.1, 1, 16.2 ], "label": "a silver car" } ]
[ { "front_dir": [ 0.2, -0.1, -1 ], "label": "a silver car", "left_dir": [ -1, 0, -0.2 ] } ]
B
To solve this problem, we first determine the 3D locations of a large brick building and a silver car. Then we estimate the vector pointing from a silver car to a large brick building, as well as the front direction of a silver car. Next we compute the cosine similarities between the vector and the front direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a large brick building is in front of a silver car. Otherwise, a large brick building is behind a silver car. The 3D location of a large brick building is (-6.7, 12.9, 45.5). The 3D location of a silver car is (-2.1, 1.0, 16.2). The vector from a silver car to a large brick building is hence (-4.6, 11.9, 29.3). The front direction of a silver car is (0.2, -0.1, -1.0). The cosine similarity between the vector and the front direction is -0.95, corresponding to an angle of 162.14 degrees. The angle is smaller than 90 degrees, meaning that a large brick building is behind a silver car. Therefore, the final answer is B. behind.
B. behind.
orientation_in_front_of
00388cebd6c59358.jpg
00392001ecafe7c5_d766
Consider the real-world 3D locations of the objects. Which object has a higher location?
a girl with a pink bow in her hair
a pink dress
null
null
[ { "bbox_3d": [ -0.2, 0.8, 1 ], "label": "a girl with a pink bow in her hair" }, { "bbox_3d": [ -0.3, 0.7, 0.7 ], "label": "a pink dress" } ]
[]
A
To solve this problem, we first estimate the 3D heights of the two objects. The object with a larger height value is at a higher location. The object with a smaller height value is at a lower location. The 3D height of a girl with a pink bow in her hair is 2.0. The 3D height of a pink dress is 1.0. The 3D height of a girl with a pink bow in her hair is larger, meaning that the location of a girl with a pink bow in her hair is higher. Therefore, the answer is A. a pink dress.
A. a pink dress.
height_higher
00392001ecafe7c5.jpg
003956104a6b7d0d_c1aa
Consider the real-world 3D orientations of the objects. Are a black stop light and a yellow light on a traffic signal facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ -6.2, 3.9, 33.1 ], "label": "a black stop light" }, { "bbox_3d": [ 9.8, 3.6, 35.6 ], "label": "a yellow light on a traffic signal" } ]
[ { "front_dir": [ 0.3, -0.1, -1 ], "label": "a black stop light", "left_dir": [ -1, 0, -0.3 ] }, { "front_dir": [ -0.2, -0.1, -1 ], "label": "a yellow light on a traffic signal", "left_dir": [ -1, 0.1, 0.2 ] } ]
A
To solve this problem, we first detect the front directions of a black stop light and a yellow light on a traffic signal. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a black stop light is (0.3, -0.1, -1.0). The front direction of a yellow light on a traffic signal is (-0.2, -0.1, -1.0). The cosine similarity between the two front directions is 0.90, corresponding to an angle of 25.84. The angle is small, meaning that the two objects are facing same or similar directions. Therefore, the final answer is A. same or similar directions.
A. same or similar directions.
multi_object_same_direction
003956104a6b7d0d.jpg
00397b268766bea0_0e5d
Consider the real-world 3D orientations of the objects. What is the relationship between the orientations of a white laptop and a silver laptop with a black keyboard, parallel of perpendicular to each other?
parallel
perpendicular
null
null
[ { "bbox_3d": [ 0, 1.1, 6.5 ], "label": "a white laptop" }, { "bbox_3d": [ 0.5, 0.9, 2.9 ], "label": "a silver laptop with a black keyboard" } ]
[ { "front_dir": [ 0.8, -0.1, -0.6 ], "label": "a white laptop", "left_dir": [ -0.7, 0, -0.8 ] }, { "front_dir": [ -0.9, 0, -0.5 ], "label": "a silver laptop with a black keyboard", "left_dir": [ -0.5, 0, 0.9 ] } ]
B
To solve this problem, we first detect the front directions of a white laptop and a silver laptop with a black keyboard. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is closer to 0 or 180, than to 90 degrees, then the two objects are parallel to each other. Otherwise, the two objects are perpendicular to each other. The front direction of a white laptop is (0.8, -0.1, -0.6). The front direction of a silver laptop with a black keyboard is (-0.9, -0.0, -0.5). The cosine similarity between the two front directions is -0.31, corresponding to an angle of 108.12. The angle is closer to 90, than to 0 or 180 degrees, meaning that the two objects are perpendicular to each other. Therefore, the final answer is B. perpendicular.
B. perpendicular.
multi_object_parallel
00397b268766bea0.jpg
0039df5da0090751_5940
Consider the real-world 3D locations and orientations of the objects. Which object is a brown van with a bike rack facing towards, a car with a woman standing next to it or the a dock with a boat?
a car with a woman standing next to it
a dock with a boat
null
null
[ { "bbox_3d": [ 4.4, 2.5, 11 ], "label": "a brown van with a bike rack" }, { "bbox_3d": [ 4.5, 2.9, 16.7 ], "label": "a car with a woman standing next to it" }, { "bbox_3d": [ 1.6, 1.2, 10.6 ], "label": "a dock with a boat" } ]
[ { "front_dir": [ 0.1, 0.1, 1 ], "label": "a brown van with a bike rack", "left_dir": [ 1, 0, -0.2 ] }, { "front_dir": [ 0.7, -0.1, -0.7 ], "label": "a car with a woman standing next to it", "left_dir": [ -0.7, -0.1, -0.7 ] }, { "front_dir": [ -0.1, 0, -1 ], "label": "a dock with a boat", "left_dir": [ -1, 0, 0.1 ] } ]
A
To solve this problem, we first detect the 3D location of a brown van with a bike rack, a car with a woman standing next to it, and a dock with a boat. Then we compute the cosine similarities between the front direction of a brown van with a bike rack and the vectors from a brown van with a bike rack to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a brown van with a bike rack is facing towards. The 3D location of a brown van with a bike rack is (4.4, 2.5, 11.0). The 3D location of a car with a woman standing next to it is (4.5, 2.9, 16.7). The 3D location of a dock with a boat is (1.6, 1.2, 10.6). The front direction of a brown van with a bike rack is (0.1, 0.1, 1.0). First we consider if a brown van with a bike rack is facing towards the a car with a woman standing next to it. The vector from a brown van with a bike rack to a car with a woman standing next to it is (0.1, 0.4, 5.7). The cosine similarity between the front direction and the vector is 0.99, corresponding to an angle of 7.71 degrees. First we consider if a brown van with a bike rack is facing towards the a dock with a boat. The vector from a brown van with a bike rack to a dock with a boat is (-2.8, -1.2, -0.4). The cosine similarity between the front direction and the vector is -0.30, corresponding to an angle of 107.57 degrees. We find that the angle between the front direction and a car with a woman standing next to it is smaller. Therefore, the final answer is A. a car with a woman standing next to it.
A. a car with a woman standing next to it.
multi_object_facing
0039df5da0090751.jpg
003a17ee9d38e7c6_b8eb
Consider the real-world 3D locations of the objects. Which is closer to a projector with a gray case, a man wearing a black shirt or a woman with blonde hair?
a man wearing a black shirt
a woman with blonde hair
null
null
[ { "bbox_3d": [ 2.4, 2.2, 5.3 ], "label": "a projector with a gray case" }, { "bbox_3d": [ -0.2, 1.1, 4.1 ], "label": "a man wearing a black shirt" }, { "bbox_3d": [ -1.8, 1.1, 4.6 ], "label": "a woman with blonde hair" } ]
[]
A
To solve this problem, we first detect the 3D location of a projector with a gray case, a man wearing a black shirt, and a woman with blonde hair. Then we compute the L2 distances between a projector with a gray case and a man wearing a black shirt, and between a projector with a gray case and a woman with blonde hair. The object that is closer to a projector with a gray case is the one with a smaller distance. The 3D location of a projector with a gray case is (2.4, 2.2, 5.3). The 3D location of a man wearing a black shirt is (-0.2, 1.1, 4.1). The 3D location of a woman with blonde hair is (-1.8, 1.1, 4.6). The L2 distance between a projector with a gray case and a man wearing a black shirt is 3.007036285846187. The L2 distance between a projector with a gray case and a woman with blonde hair is 4.382768996549432. Between the two distances, the distance between a projector with a gray case and a man wearing a black shirt is smaller. Therefore, the final answer is A. a man wearing a black shirt.
A. a man wearing a black shirt.
multi_object_closer_to
003a17ee9d38e7c6.jpg
003a61dc573e6fdb_8093
Consider the real-world 3D orientations of the objects. Are a silver car parked on the street and a red car facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ -2.1, 0.6, 6.4 ], "label": "a silver car parked on the street" }, { "bbox_3d": [ 2.5, 0.8, 8.3 ], "label": "a red car" } ]
[ { "front_dir": [ 0.8, 0, 0.7 ], "label": "a silver car parked on the street", "left_dir": [ 0.7, 0.1, -0.8 ] }, { "front_dir": [ -0.7, 0, -0.7 ], "label": "a red car", "left_dir": [ -0.7, 0, 0.7 ] } ]
B
To solve this problem, we first detect the front directions of a silver car parked on the street and a red car. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a silver car parked on the street is (0.8, 0.0, 0.7). The front direction of a red car is (-0.7, 0.0, -0.7). The cosine similarity between the two front directions is -1.00, corresponding to an angle of 176.99. The angle is large, meaning that the two objects are facing very different directions. Therefore, the final answer is B. very different directions.
B. very different directions.
multi_object_same_direction
003a61dc573e6fdb.jpg
003a61dc573e6fdb_572c
Consider the real-world 3D locations and orientations of the objects. Which object is a black bicycle with a white frame facing towards, a man in a white shirt talking on a cell phone or the a man wearing a plaid shirt?
a man in a white shirt talking on a cell phone
a man wearing a plaid shirt
null
null
[ { "bbox_3d": [ 1, 0.6, 2.7 ], "label": "a black bicycle with a white frame" }, { "bbox_3d": [ 2.5, 1.2, 14.5 ], "label": "a man in a white shirt talking on a cell phone" }, { "bbox_3d": [ -0.5, 1.1, 4.1 ], "label": "a man wearing a plaid shirt" } ]
[ { "front_dir": [ -1, 0, 0.3 ], "label": "a black bicycle with a white frame", "left_dir": [ 0.2, 0.2, 0.9 ] }, { "front_dir": [ -0.7, 0, -0.7 ], "label": "a man in a white shirt talking on a cell phone", "left_dir": [ -0.7, 0.1, 0.7 ] } ]
B
To solve this problem, we first detect the 3D location of a black bicycle with a white frame, a man in a white shirt talking on a cell phone, and a man wearing a plaid shirt. Then we compute the cosine similarities between the front direction of a black bicycle with a white frame and the vectors from a black bicycle with a white frame to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a black bicycle with a white frame is facing towards. The 3D location of a black bicycle with a white frame is (1.0, 0.6, 2.7). The 3D location of a man in a white shirt talking on a cell phone is (2.5, 1.2, 14.5). The 3D location of a man wearing a plaid shirt is (-0.5, 1.1, 4.1). The front direction of a black bicycle with a white frame is (-1.0, -0.0, 0.3). First we consider if a black bicycle with a white frame is facing towards the a man in a white shirt talking on a cell phone. The vector from a black bicycle with a white frame to a man in a white shirt talking on a cell phone is (1.5, 0.6, 11.8). The cosine similarity between the front direction and the vector is 0.13, corresponding to an angle of 82.41 degrees. First we consider if a black bicycle with a white frame is facing towards the a man wearing a plaid shirt. The vector from a black bicycle with a white frame to a man wearing a plaid shirt is (-1.5, 0.6, 1.4). The cosine similarity between the front direction and the vector is 0.83, corresponding to an angle of 34.02 degrees. We find that the angle between the front direction and a man wearing a plaid shirt is smaller. Therefore, the final answer is B. a man wearing a plaid shirt.
B. a man wearing a plaid shirt.
multi_object_facing
003a61dc573e6fdb.jpg
003acaad7b338303_01cf
Consider the real-world 3D orientations of the objects. What is the relationship between the orientations of a wooden cabinet with a glass top and a wooden chair with a red cushion, parallel of perpendicular to each other?
parallel
perpendicular
null
null
[ { "bbox_3d": [ 0.6, 0.8, 4.2 ], "label": "a wooden cabinet with a glass top" }, { "bbox_3d": [ -0.7, 1.1, 5.3 ], "label": "a wooden chair with a red cushion" } ]
[ { "front_dir": [ -0.9, 0, -0.5 ], "label": "a wooden cabinet with a glass top", "left_dir": [ -0.5, 0.2, 0.8 ] }, { "front_dir": [ 1, -0.1, 0.2 ], "label": "a wooden chair with a red cushion", "left_dir": [ 0.2, -0.1, -1 ] } ]
A
To solve this problem, we first detect the front directions of a wooden cabinet with a glass top and a wooden chair with a red cushion. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is closer to 0 or 180, than to 90 degrees, then the two objects are parallel to each other. Otherwise, the two objects are perpendicular to each other. The front direction of a wooden cabinet with a glass top is (-0.9, -0.0, -0.5). The front direction of a wooden chair with a red cushion is (1.0, -0.1, 0.2). The cosine similarity between the two front directions is -0.94, corresponding to an angle of 159.73. The angle is closer to 0 or 180, than to 90 degrees, meaning that the two objects are parallel to each other. Therefore, the final answer is A. parallel.
A. parallel.
multi_object_parallel
003acaad7b338303.jpg
003acaad7b338303_b928
Consider the real-world 3D orientations of the objects. Are a wooden chair with a brown seat and a wooden cabinet with a sink in it facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ -1.2, 1.5, 6.5 ], "label": "a wooden chair with a brown seat" }, { "bbox_3d": [ 0.8, 1.7, 4.2 ], "label": "a wooden cabinet with a sink in it" } ]
[ { "front_dir": [ 0.3, -0.1, -1 ], "label": "a wooden chair with a brown seat", "left_dir": [ -1, 0.1, -0.3 ] }, { "front_dir": [ -0.1, -0.2, -1 ], "label": "a wooden cabinet with a sink in it", "left_dir": [ -1, 0.1, 0.1 ] } ]
A
To solve this problem, we first detect the front directions of a wooden chair with a brown seat and a wooden cabinet with a sink in it. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a wooden chair with a brown seat is (0.3, -0.1, -1.0). The front direction of a wooden cabinet with a sink in it is (-0.1, -0.2, -1.0). The cosine similarity between the two front directions is 0.93, corresponding to an angle of 21.71. The angle is small, meaning that the two objects are facing same or similar directions. Therefore, the final answer is A. same or similar directions.
A. same or similar directions.
multi_object_same_direction
003acaad7b338303.jpg
003bc827f96b6440_315d
Consider the real-world 3D locations of the objects. Which object has a lower location?
a brick chimney
a green hedge
null
null
[ { "bbox_3d": [ 3.3, 12.7, 21.3 ], "label": "a brick chimney" }, { "bbox_3d": [ 6.2, 5.9, 18.7 ], "label": "a green hedge" } ]
[]
B
To solve this problem, we first estimate the 3D heights of the two objects. The object with a larger height value is at a higher location. The object with a smaller height value is at a lower location. The 3D height of a brick chimney is 15.9. The 3D height of a green hedge is 11.7. The 3D height of a brick chimney is larger, meaning that the location of a brick chimney is higher. In other words, the location of a green hedge is lower. Therefore, the answer is B. a brick chimney.
B. a brick chimney
height_higher
003bc827f96b6440.jpg
003cd2790a0978ef_9728
Consider the real-world 3D locations and orientations of the objects. Which object is a car facing towards, a black car or the a wooden plank?
a black car
a wooden plank
null
null
[ { "bbox_3d": [ -1.5, 0.8, 13.3 ], "label": "a car" }, { "bbox_3d": [ 1.2, 1.4, 12.4 ], "label": "a black car" }, { "bbox_3d": [ -0.2, 0.5, 9.2 ], "label": "a wooden plank" } ]
[ { "front_dir": [ -0.1, 0.2, -1 ], "label": "a car", "left_dir": [ -1, -0.1, 0.1 ] }, { "front_dir": [ -1, 0, 0 ], "label": "a black car", "left_dir": [ 0, 0, 1 ] } ]
B
To solve this problem, we first detect the 3D location of a car, a black car, and a wooden plank. Then we compute the cosine similarities between the front direction of a car and the vectors from a car to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a car is facing towards. The 3D location of a car is (-1.5, 0.8, 13.3). The 3D location of a black car is (1.2, 1.4, 12.4). The 3D location of a wooden plank is (-0.2, 0.5, 9.2). The front direction of a car is (-0.1, 0.2, -1.0). First we consider if a car is facing towards the a black car. The vector from a car to a black car is (2.8, 0.6, -0.9). The cosine similarity between the front direction and the vector is 0.21, corresponding to an angle of 77.77 degrees. First we consider if a car is facing towards the a wooden plank. The vector from a car to a wooden plank is (1.4, -0.3, -4.1). The cosine similarity between the front direction and the vector is 0.87, corresponding to an angle of 29.48 degrees. We find that the angle between the front direction and a wooden plank is smaller. Therefore, the final answer is B. a wooden plank.
B. a wooden plank.
multi_object_facing
003cd2790a0978ef.jpg
003d6b5212e607fe_642f
Consider the real-world 3D locations and orientations of the objects. Which object is a laptop computer facing towards, a table with a red tablecloth and a sign on it or the a laptop computer?
a table with a red tablecloth and a sign on it
a laptop computer
null
null
[ { "bbox_3d": [ 0.7, 0.8, 1.7 ], "label": "a laptop computer" }, { "bbox_3d": [ 0.2, 0.5, 1.1 ], "label": "a table with a red tablecloth and a sign on it" }, { "bbox_3d": [ 0.1, 0.8, 1.7 ], "label": "a laptop computer" } ]
[ { "front_dir": [ -0.3, -0.1, -1 ], "label": "a laptop computer", "left_dir": [ -0.9, -0.1, 0.3 ] }, { "front_dir": [ 0, -0.2, -1 ], "label": "a laptop computer", "left_dir": [ -1, 0, 0 ] } ]
A
To solve this problem, we first detect the 3D location of a laptop computer, a table with a red tablecloth and a sign on it, and a laptop computer. Then we compute the cosine similarities between the front direction of a laptop computer and the vectors from a laptop computer to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a laptop computer is facing towards. The 3D location of a laptop computer is (0.7, 0.8, 1.7). The 3D location of a table with a red tablecloth and a sign on it is (0.2, 0.5, 1.1). The 3D location of a laptop computer is (0.1, 0.8, 1.7). The front direction of a laptop computer is (-0.3, -0.1, -1.0). First we consider if a laptop computer is facing towards the a table with a red tablecloth and a sign on it. The vector from a laptop computer to a table with a red tablecloth and a sign on it is (-0.5, -0.3, -0.6). The cosine similarity between the front direction and the vector is 0.88, corresponding to an angle of 28.09 degrees. First we consider if a laptop computer is facing towards the a laptop computer. The vector from a laptop computer to a laptop computer is (-0.6, 0.0, -0.0). The cosine similarity between the front direction and the vector is 0.30, corresponding to an angle of 72.53 degrees. We find that the angle between the front direction and a table with a red tablecloth and a sign on it is smaller. Therefore, the final answer is A. a table with a red tablecloth and a sign on it.
A. a table with a red tablecloth and a sign on it.
multi_object_facing
003d6b5212e607fe.jpg
003e015da41306d8_9c89
Consider the real-world 3D location of the objects. Which object is further away from the camera?
a crowd of people
a person wearing a white shirt
null
null
[ { "bbox_3d": [ -2.3, 0.9, 17.7 ], "label": "a crowd of people" }, { "bbox_3d": [ 4.8, 2.1, 27.2 ], "label": "a person wearing a white shirt" } ]
[]
B
To solve this problem, we first estimate the 3D locations of a crowd of people and a person wearing a white shirt. Then we estimate the L2 distances from the camera to the two objects. The object with a smaller L2 distance is the one that is closer to the camera. The 3D location of a crowd of people is (-2.3, 0.9, 17.7). The 3D location of a person wearing a white shirt is (4.8, 2.1, 27.2). The L2 distance from the camera to a crowd of people is 17.84. The L2 distance from the camera to a person wearing a white shirt is 27.69. The distance to a person wearing a white shirt is larger. Therefore, the answer is B. a person wearing a white shirt.
B. a person wearing a white shirt.
location_closer_to_camera
003e015da41306d8.jpg
003e739bd9052df1_226e
Consider the real-world 3D locations of the objects. Is a street corner with a curb directly underneath a long wooden pole?
yes
no
null
null
[ { "bbox_3d": [ 4.2, 4.2, 30.4 ], "label": "a long wooden pole" }, { "bbox_3d": [ -0.2, 0.4, 19.7 ], "label": "a street corner with a curb" } ]
[]
B
To solve this problem, we first determine the 3D locations of a long wooden pole and a street corner with a curb. Then we compute the vector pointing from a street corner with a curb to a long wooden pole, as well as the up direction of a street corner with a curb. We estimate the cosine similarity between the vector and the up direction, which leads to the angle between the two directions. If the angle is small, then a long wooden pole is directly above a street corner with a curb. Otherwise, then a long wooden pole is not directly above a street corner with a curb. To solve the question, we first determine if a long wooden pole is directly above a street corner with a curb. The 3D location of a long wooden pole is (4.2, 4.2, 30.4). The 3D location of a street corner with a curb is (-0.2, 0.4, 19.7). The vector from a street corner with a curb to a long wooden pole is hence (4.4, 3.8, 10.7). The up direction of a street corner with a curb is (0.0, 1.0, 0.0). The cosine similarity between the vector and the up direction is 0.32, corresponding to an angle of 71 degrees. The angle between the vector and the up direction is large, meaning that a long wooden pole is not directly above a street corner with a curb. In other words, a street corner with a curb is not directly underneath a long wooden pole. Therefore, the answer is B. no.
B. no.
location_above
003e739bd9052df1.jpg
003f09a845bd1f65_bac9
Consider the real-world 3D locations and orientations of the objects. Which side of a wooden kitchen cabinet with a drawer is facing a man wearing a brown sweater?
front
left
back
right
[ { "bbox_3d": [ -3.7, 0.8, 8.3 ], "label": "a wooden kitchen cabinet with a drawer" }, { "bbox_3d": [ -0.7, 1.7, 5.2 ], "label": "a man wearing a brown sweater" } ]
[ { "front_dir": [ 0.5, 0, -0.9 ], "label": "a wooden kitchen cabinet with a drawer", "left_dir": [ -0.9, 0.1, -0.5 ] } ]
A
To solve this problem, we first detect the 3D locations of a wooden kitchen cabinet with a drawer and a man wearing a brown sweater. Then we compute the vector pointing from a wooden kitchen cabinet with a drawer to a man wearing a brown sweater. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a wooden kitchen cabinet with a drawer, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a wooden kitchen cabinet with a drawer that is facing a man wearing a brown sweater corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The 3D location of a wooden kitchen cabinet with a drawer is (-3.7, 0.8, 8.3). The 3D location of a man wearing a brown sweater is (-0.7, 1.7, 5.2). The vector from a wooden kitchen cabinet with a drawer to a man wearing a brown sweater is hence (3.1, 0.9, -3.2). The left direction of a wooden kitchen cabinet with a drawer is (-0.9, 0.1, -0.5). The cosine similarity between the vector pointing to a man wearing a brown sweater and the left direction is -0.24, corresponding to an angle of 104.12 degrees. Thus the angle between the vector pointing to a man wearing a brown sweater and the right direction is 75.88 degrees. The front direction of a wooden kitchen cabinet with a drawer is (0.5, 0.0, -0.9). The cosine similarity between the vector pointing to a man wearing a brown sweater and the front direction is 0.94, corresponding to an angle of 19.43 degrees. Thus the angle between the vector pointing to a man wearing a brown sweater and the back direction is 160.57 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 19.43 degrees. Thus the front side of a wooden kitchen cabinet with a drawer is facing the a man wearing a brown sweater. Therefore, the final answer is A. front.
A. front.
multi_object_viewpoint_towards_object
003f09a845bd1f65.jpg
003f2728d2f8847e_56c6
Consider the real-world 3D locations of the objects. Which is closer to a green and white sign, a truck or an orange and black sign?
a truck
an orange and black sign
null
null
[ { "bbox_3d": [ 5.6, 1.2, 14.1 ], "label": "a green and white sign" }, { "bbox_3d": [ 3.4, 1.3, 25.5 ], "label": "a truck" }, { "bbox_3d": [ 2, 1, 7.6 ], "label": "an orange and black sign" } ]
[]
B
To solve this problem, we first detect the 3D location of a green and white sign, a truck, and an orange and black sign. Then we compute the L2 distances between a green and white sign and a truck, and between a green and white sign and an orange and black sign. The object that is closer to a green and white sign is the one with a smaller distance. The 3D location of a green and white sign is (5.6, 1.2, 14.1). The 3D location of a truck is (3.4, 1.3, 25.5). The 3D location of an orange and black sign is (2.0, 1.0, 7.6). The L2 distance between a green and white sign and a truck is 11.57723384644125. The L2 distance between a green and white sign and an orange and black sign is 7.393962117164113. Between the two distances, the distance between a green and white sign and an orange and black sign is smaller. Therefore, the final answer is B. an orange and black sign.
B. an orange and black sign.
multi_object_closer_to
003f2728d2f8847e.jpg
003f511905b3d29b_4734
Consider the real-world 3D locations and orientations of the objects. If I stand at a chair with a metal frame's position facing where it is facing, is a round wooden table in front of me or behind me?
in front of
behind
null
null
[ { "bbox_3d": [ 0.1, 0.2, 1.6 ], "label": "a round wooden table" }, { "bbox_3d": [ 0.3, 0.4, 1.7 ], "label": "a chair with a metal frame" } ]
[ { "front_dir": [ -0.6, 0, -0.8 ], "label": "a chair with a metal frame", "left_dir": [ -0.8, 0.1, 0.6 ] } ]
A
To solve this problem, we first determine the 3D locations of a round wooden table and a chair with a metal frame. Then we estimate the vector pointing from a chair with a metal frame to a round wooden table, as well as the front direction of a chair with a metal frame. Next we compute the cosine similarities between the vector and the front direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a round wooden table is in front of a chair with a metal frame. Otherwise, a round wooden table is behind a chair with a metal frame. The 3D location of a round wooden table is (0.1, 0.2, 1.6). The 3D location of a chair with a metal frame is (0.3, 0.4, 1.7). The vector from a chair with a metal frame to a round wooden table is hence (-0.3, -0.1, -0.1). The front direction of a chair with a metal frame is (-0.6, -0.0, -0.8). The cosine similarity between the vector and the front direction is 0.75, corresponding to an angle of 41.37 degrees. The angle is smaller than 90 degrees, meaning that a round wooden table is in front of a chair with a metal frame. Therefore, the final answer is A. in front of.
A. in front of.
orientation_in_front_of
003f511905b3d29b.jpg
003f77cad7bff90c_76d4
Consider the real-world 3D orientations of the objects. What is the relationship between the orientations of a green armchair with a red cushion and a brown wooden bench, parallel of perpendicular to each other?
parallel
perpendicular
null
null
[ { "bbox_3d": [ 4.2, 1.6, 16 ], "label": "a green armchair with a red cushion" }, { "bbox_3d": [ 1.7, 0.4, 6.7 ], "label": "a brown wooden bench" } ]
[ { "front_dir": [ -1, 0.1, 0.2 ], "label": "a green armchair with a red cushion", "left_dir": [ 0.2, 0.3, 0.9 ] }, { "front_dir": [ -0.2, 0, -1 ], "label": "a brown wooden bench", "left_dir": [ -1, 0.1, 0.2 ] } ]
B
To solve this problem, we first detect the front directions of a green armchair with a red cushion and a brown wooden bench. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is closer to 0 or 180, than to 90 degrees, then the two objects are parallel to each other. Otherwise, the two objects are perpendicular to each other. The front direction of a green armchair with a red cushion is (-1.0, 0.1, 0.2). The front direction of a brown wooden bench is (-0.2, 0.0, -1.0). The cosine similarity between the two front directions is 0.01, corresponding to an angle of 89.57. The angle is closer to 90, than to 0 or 180 degrees, meaning that the two objects are perpendicular to each other. Therefore, the final answer is B. perpendicular.
B. perpendicular.
multi_object_parallel
003f77cad7bff90c.jpg
0040576a77b68092_b5cc
Consider the real-world 3D locations and orientations of the objects. Which side of a blue and white plane is facing the camera?
front
left
back
right
[ { "bbox_3d": [ -14.3, 1.9, 50.4 ], "label": "a blue and white plane" } ]
[ { "front_dir": [ -0.9, 0.1, -0.3 ], "label": "a blue and white plane", "left_dir": [ -0.3, 0.1, 0.9 ] } ]
D
To solve this problem, we first estimate the 3D location of a blue and white plane. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a blue and white plane, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a blue and white plane that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a blue and white plane is (-14.3, 1.9, 50.4). The vector from a blue and white plane to camera is hence (14.3, -1.9, -50.4). The left direction of a blue and white plane is (-0.3, 0.1, 0.9). The cosine similarity between the vector pointing to camera and the left direction is -1.00, corresponding to an angle of 174.73 degrees. Thus the angle between the vector pointing to camera and the right direction is 5.27 degrees. The front direction of a blue and white plane is (-0.9, 0.1, -0.3). The cosine similarity between the vector pointing to camera and the front direction is 0.08, corresponding to an angle of 85.69 degrees. Thus the angle between the vector pointing to camera and the back direction is 94.31 degrees. Among the four directions, the smallest angle is the right direction, with an angle of 5.27 degrees. Thus the right side of a blue and white plane is facing the camera. Therefore, the final answer is D. right.
D. right.
orientation_viewpoint
0040576a77b68092.jpg
0040b6af697eaf8c_2b70
Consider the real-world 3D location of the objects. Which object is further away from the camera?
a white helmet with a black chin strap
a person is holding a white helmet
null
null
[ { "bbox_3d": [ 0, 0.4, 0.7 ], "label": "a white helmet with a black chin strap" }, { "bbox_3d": [ 0, 0.5, 1 ], "label": "a person is holding a white helmet" } ]
[]
B
To solve this problem, we first estimate the 3D locations of a white helmet with a black chin strap and a person is holding a white helmet. Then we estimate the L2 distances from the camera to the two objects. The object with a smaller L2 distance is the one that is closer to the camera. The 3D location of a white helmet with a black chin strap is (-0.0, 0.4, 0.7). The 3D location of a person is holding a white helmet is (-0.0, 0.5, 1.0). The L2 distance from the camera to a white helmet with a black chin strap is 0.80. The L2 distance from the camera to a person is holding a white helmet is 1.09. The distance to a person is holding a white helmet is larger. Therefore, the answer is B. a person is holding a white helmet.
B. a person is holding a white helmet.
location_closer_to_camera
0040b6af697eaf8c.jpg
00411797643d8b96_9b4f
Consider the real-world 3D locations of the objects. Are the a white dog with a brown nose and the a black and white dog next to each other or far away from each other?
next to each other
far away from each other
null
null
[ { "bbox_3d": [ -0.1, 0.2, 1.6 ], "label": "a white dog with a brown nose" }, { "bbox_3d": [ 0.1, 0.2, 1.5 ], "label": "a black and white dog" } ]
[]
A
To solve this problem, we first estimate the 3D locations of a white dog with a brown nose and a black and white dog. Then we can compute the L2 distance between the two objects. Next we estimate the rough sizes of the two objects. If the distance between the two objects is smaller or roughly the same as the object sizes, then the two objects are next to each other. Otherwise, the two objects are far away from each other. The 3D location of a white dog with a brown nose is (-0.1, 0.2, 1.6). The 3D location of a black and white dog is (0.1, 0.2, 1.5). The L2 distance between the two objects is 0.23. The size of the a white dog with a brown nose is roughly 0.30. The size of the a black and white dog is roughly 0.44. The distance between the two objects is smaller or roughly the same as the object sizes, meaning that they are next to each other. Therefore, the answer is A. next to each other.
A. next to each other.
location_next_to
00411797643d8b96.jpg
0041638e183368dc_6dc5
Consider the real-world 3D orientations of the objects. Are a white laptop with a blue screen and a laptop with a white case facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ -2.5, 1, 3.6 ], "label": "a white laptop with a blue screen" }, { "bbox_3d": [ -3.3, 0.9, 6.7 ], "label": "a laptop with a white case" } ]
[ { "front_dir": [ 0.5, -0.2, -0.8 ], "label": "a white laptop with a blue screen", "left_dir": [ -0.8, 0.2, -0.6 ] }, { "front_dir": [ 0.5, 0.1, -0.9 ], "label": "a laptop with a white case", "left_dir": [ -0.9, 0.2, -0.5 ] } ]
A
To solve this problem, we first detect the front directions of a white laptop with a blue screen and a laptop with a white case. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a white laptop with a blue screen is (0.5, -0.2, -0.8). The front direction of a laptop with a white case is (0.5, 0.1, -0.9). The cosine similarity between the two front directions is 0.97, corresponding to an angle of 13.32. The angle is small, meaning that the two objects are facing same or similar directions. Therefore, the final answer is A. same or similar directions.
A. same or similar directions.
multi_object_same_direction
0041638e183368dc.jpg
00416c9bae78b025_ff01
Consider the real-world 3D location of the objects. Which object is further away from the camera?
a man in a yellow shirt is standing next to a bicycle
a red bicycle with a black seat
null
null
[ { "bbox_3d": [ 1.6, 1.7, 4.6 ], "label": "a man in a yellow shirt is standing next to a bicycle" }, { "bbox_3d": [ -2.6, 1.4, 8.6 ], "label": "a red bicycle with a black seat" } ]
[]
B
To solve this problem, we first estimate the 3D locations of a man in a yellow shirt is standing next to a bicycle and a red bicycle with a black seat. Then we estimate the L2 distances from the camera to the two objects. The object with a smaller L2 distance is the one that is closer to the camera. The 3D location of a man in a yellow shirt is standing next to a bicycle is (1.6, 1.7, 4.6). The 3D location of a red bicycle with a black seat is (-2.6, 1.4, 8.6). The L2 distance from the camera to a man in a yellow shirt is standing next to a bicycle is 5.17. The L2 distance from the camera to a red bicycle with a black seat is 9.08. The distance to a red bicycle with a black seat is larger. Therefore, the answer is B. a red bicycle with a black seat.
B. a red bicycle with a black seat.
location_closer_to_camera
00416c9bae78b025.jpg
0041bb65f5eb7a26_98c8
Consider the real-world 3D orientations of the objects. What is the relationship between the orientations of a white car and a white car with a red and black racing team logo, parallel of perpendicular to each other?
parallel
perpendicular
null
null
[ { "bbox_3d": [ 3.6, 0.7, 6.2 ], "label": "a white car" }, { "bbox_3d": [ 1.9, 0.7, 3.2 ], "label": "a white car with a red and black racing team logo" } ]
[ { "front_dir": [ -0.9, 0, 0.4 ], "label": "a white car", "left_dir": [ 0.4, 0.1, 0.9 ] }, { "front_dir": [ -0.9, 0, 0.4 ], "label": "a white car with a red and black racing team logo", "left_dir": [ 0.4, -0.1, 0.9 ] } ]
A
To solve this problem, we first detect the front directions of a white car and a white car with a red and black racing team logo. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is closer to 0 or 180, than to 90 degrees, then the two objects are parallel to each other. Otherwise, the two objects are perpendicular to each other. The front direction of a white car is (-0.9, -0.0, 0.4). The front direction of a white car with a red and black racing team logo is (-0.9, -0.0, 0.4). The cosine similarity between the two front directions is 1.00, corresponding to an angle of 1.70. The angle is closer to 0 or 180, than to 90 degrees, meaning that the two objects are parallel to each other. Therefore, the final answer is A. parallel.
A. parallel.
multi_object_parallel
0041bb65f5eb7a26.jpg
0041e6917dc5e5d8_619a
Consider the real-world 3D locations of the objects. Is a purple knitted hat directly above a woman in a purple hat?
yes
no
null
null
[ { "bbox_3d": [ -0.1, 1.2, 1.5 ], "label": "a purple knitted hat" }, { "bbox_3d": [ 0.1, 0.7, 1.5 ], "label": "a woman in a purple hat" } ]
[]
A
To solve this problem, we first determine the 3D locations of a purple knitted hat and a woman in a purple hat. Then we compute the vector pointing from a woman in a purple hat to a purple knitted hat, as well as the up direction of a woman in a purple hat. We estimate the cosine similarity between the vector and the up direction, which leads to the angle between the two directions. If the angle is small, then a purple knitted hat is directly above a woman in a purple hat. Otherwise, then a purple knitted hat is not directly above a woman in a purple hat. The 3D location of a purple knitted hat is (-0.1, 1.2, 1.5). The 3D location of a woman in a purple hat is (0.1, 0.7, 1.5). The vector from a woman in a purple hat to a purple knitted hat is hence (-0.2, 0.5, -0.1). The up direction of a woman in a purple hat is (0.0, 1.0, 0.0). The cosine similarity between the vector and the up direction is 0.95, corresponding to an angle of 17 degrees. The angle between the vector and the up direction is small, meaning that a purple knitted hat is directly above a woman in a purple hat. Therefore, the answer is A. yes.
A. yes.
location_above
0041e6917dc5e5d8.jpg
004240c13e727699_2152
Consider the real-world 3D locations and orientations of the objects. Which side of a white cabinet with a black handle is facing the camera?
front
left
back
right
[ { "bbox_3d": [ 1.5, 1.4, 4.4 ], "label": "a white cabinet with a black handle" } ]
[ { "front_dir": [ -0.2, -0.1, -1 ], "label": "a white cabinet with a black handle", "left_dir": [ -1, 0.1, 0.2 ] } ]
A
To solve this problem, we first estimate the 3D location of a white cabinet with a black handle. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a white cabinet with a black handle, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a white cabinet with a black handle that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a white cabinet with a black handle is (1.5, 1.4, 4.4). The vector from a white cabinet with a black handle to camera is hence (-1.5, -1.4, -4.4). The left direction of a white cabinet with a black handle is (-1.0, 0.1, 0.2). The cosine similarity between the vector pointing to camera and the left direction is 0.05, corresponding to an angle of 87.04 degrees. Thus the angle between the vector pointing to camera and the right direction is 92.96 degrees. The front direction of a white cabinet with a black handle is (-0.2, -0.1, -1.0). The cosine similarity between the vector pointing to camera and the front direction is 0.99, corresponding to an angle of 9.75 degrees. Thus the angle between the vector pointing to camera and the back direction is 170.25 degrees. Among the four directions, the smallest angle is the front direction, with an angle of 9.75 degrees. Thus the front side of a white cabinet with a black handle is facing the camera. Therefore, the final answer is A. front.
A. front.
orientation_viewpoint
004240c13e727699.jpg
00435745b14a50d9_0eef
Consider the real-world 3D locations and orientations of the objects. If I stand at a black car with a chrome grill's position facing where it is facing, is a car with a blue hood in front of me or behind me?
in front of
behind
null
null
[ { "bbox_3d": [ -4.7, 0.4, 9.3 ], "label": "a car with a blue hood" }, { "bbox_3d": [ -0.9, 0.8, 1.5 ], "label": "a black car with a chrome grill" } ]
[ { "front_dir": [ 0.5, 0, 0.8 ], "label": "a car with a blue hood", "left_dir": [ 0.8, -0.2, -0.5 ] }, { "front_dir": [ 0.9, 0.1, -0.4 ], "label": "a black car with a chrome grill", "left_dir": [ -0.4, 0.3, -0.9 ] } ]
B
To solve this problem, we first determine the 3D locations of a car with a blue hood and a black car with a chrome grill. Then we estimate the vector pointing from a black car with a chrome grill to a car with a blue hood, as well as the front direction of a black car with a chrome grill. Next we compute the cosine similarities between the vector and the front direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a car with a blue hood is in front of a black car with a chrome grill. Otherwise, a car with a blue hood is behind a black car with a chrome grill. The 3D location of a car with a blue hood is (-4.7, 0.4, 9.3). The 3D location of a black car with a chrome grill is (-0.9, 0.8, 1.5). The vector from a black car with a chrome grill to a car with a blue hood is hence (-3.8, -0.4, 7.8). The front direction of a black car with a chrome grill is (0.9, 0.1, -0.4). The cosine similarity between the vector and the front direction is -0.77, corresponding to an angle of 139.96 degrees. The angle is smaller than 90 degrees, meaning that a car with a blue hood is behind a black car with a chrome grill. Therefore, the final answer is B. behind.
B. behind.
orientation_in_front_of
00435745b14a50d9.jpg
004362c113465601_1541
Consider the real-world 3D locations and orientations of the objects. If I stand at a red tractor with a blue hood's position facing where it is facing, is a spray of water coming from a red machine on the left or right of me?
on the left
on the right
null
null
[ { "bbox_3d": [ 1.7, 0.6, 16.2 ], "label": "a spray of water coming from a red machine" }, { "bbox_3d": [ 1.8, 0.7, 15.9 ], "label": "a red tractor with a blue hood" } ]
[ { "front_dir": [ -1, 0.1, 0 ], "label": "a red tractor with a blue hood", "left_dir": [ 0, -0.1, 1 ] } ]
A
To solve this problem, we first determine the 3D locations of a spray of water coming from a red machine and a red tractor with a blue hood. Then we estimate the vector pointing from a red tractor with a blue hood to a spray of water coming from a red machine, as well as the left direction of a red tractor with a blue hood. Next we compute the cosine similarities between the vector and the left direction, which leads to the angle between the vector and the fron direction. If the angle is smaller than 90 degrees, then a spray of water coming from a red machine is on the left of a red tractor with a blue hood. Otherwise, a spray of water coming from a red machine is behind a red tractor with a blue hood. The 3D location of a spray of water coming from a red machine is (1.7, 0.6, 16.2). The 3D location of a red tractor with a blue hood is (1.8, 0.7, 15.9). The vector from a red tractor with a blue hood to a spray of water coming from a red machine is hence (-0.1, -0.1, 0.3). The left direction of a red tractor with a blue hood is (0.0, -0.1, 1.0). The cosine similarity between the vector and the left direction is 0.95, corresponding to an angle of 18.79 degrees. The angle is smaller than 90 degrees, meaning that a spray of water coming from a red machine is on the left of a red tractor with a blue hood. Therefore, the final answer is A. on the left.
A. on the left.
orientation_on_the_left
004362c113465601.jpg
0043d748121f4a3b_302d
Consider the real-world 3D locations and orientations of the objects. Which side of a motorcycle with a chrome exhaust is facing a girl wearing a green shirt?
front
left
back
right
[ { "bbox_3d": [ 3.4, 1, 6.6 ], "label": "a motorcycle with a chrome exhaust" }, { "bbox_3d": [ 0.9, 1.3, 3 ], "label": "a girl wearing a green shirt" } ]
[ { "front_dir": [ -0.5, 0.1, 0.9 ], "label": "a motorcycle with a chrome exhaust", "left_dir": [ 0.9, 0.1, 0.5 ] } ]
D
To solve this problem, we first detect the 3D locations of a motorcycle with a chrome exhaust and a girl wearing a green shirt. Then we compute the vector pointing from a motorcycle with a chrome exhaust to a girl wearing a green shirt. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a motorcycle with a chrome exhaust, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a motorcycle with a chrome exhaust that is facing a girl wearing a green shirt corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The 3D location of a motorcycle with a chrome exhaust is (3.4, 1.0, 6.6). The 3D location of a girl wearing a green shirt is (0.9, 1.3, 3.0). The vector from a motorcycle with a chrome exhaust to a girl wearing a green shirt is hence (-2.5, 0.3, -3.6). The left direction of a motorcycle with a chrome exhaust is (0.9, 0.1, 0.5). The cosine similarity between the vector pointing to a girl wearing a green shirt and the left direction is -0.90, corresponding to an angle of 154.17 degrees. Thus the angle between the vector pointing to a girl wearing a green shirt and the right direction is 25.83 degrees. The front direction of a motorcycle with a chrome exhaust is (-0.5, 0.1, 0.9). The cosine similarity between the vector pointing to a girl wearing a green shirt and the front direction is -0.40, corresponding to an angle of 113.70 degrees. Thus the angle between the vector pointing to a girl wearing a green shirt and the back direction is 66.30 degrees. Among the four directions, the smallest angle is the right direction, with an angle of 25.83 degrees. Thus the right side of a motorcycle with a chrome exhaust is facing the a girl wearing a green shirt. Therefore, the final answer is D. right.
D. right.
multi_object_viewpoint_towards_object
0043d748121f4a3b.jpg
0043ea91600e3cb8_fd4e
Consider the real-world 3D locations and orientations of the objects. Which object is a black backpack facing towards, a white house with a dome or the a man wearing a black jacket and a helmet?
a white house with a dome
a man wearing a black jacket and a helmet
null
null
[ { "bbox_3d": [ 0.2, 0.5, 4 ], "label": "a black backpack" }, { "bbox_3d": [ -6.6, 17.4, 100.5 ], "label": "a white house with a dome" }, { "bbox_3d": [ 0.1, 2, 5.2 ], "label": "a man wearing a black jacket and a helmet" } ]
[ { "front_dir": [ 0, -0.2, 1 ], "label": "a black backpack", "left_dir": [ 1, 0, 0 ] } ]
A
To solve this problem, we first detect the 3D location of a black backpack, a white house with a dome, and a man wearing a black jacket and a helmet. Then we compute the cosine similarities between the front direction of a black backpack and the vectors from a black backpack to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a black backpack is facing towards. The 3D location of a black backpack is (0.2, 0.5, 4.0). The 3D location of a white house with a dome is (-6.6, 17.4, 100.5). The 3D location of a man wearing a black jacket and a helmet is (0.1, 2.0, 5.2). The front direction of a black backpack is (-0.0, -0.2, 1.0). First we consider if a black backpack is facing towards the a white house with a dome. The vector from a black backpack to a white house with a dome is (-6.8, 16.9, 96.5). The cosine similarity between the front direction and the vector is 0.93, corresponding to an angle of 21.40 degrees. First we consider if a black backpack is facing towards the a man wearing a black jacket and a helmet. The vector from a black backpack to a man wearing a black jacket and a helmet is (-0.1, 1.5, 1.2). The cosine similarity between the front direction and the vector is 0.45, corresponding to an angle of 63.26 degrees. We find that the angle between the front direction and a white house with a dome is smaller. Therefore, the final answer is A. a white house with a dome.
A. a white house with a dome.
multi_object_facing
0043ea91600e3cb8.jpg
00445b9419d205b5_57a6
Consider the real-world 3D orientations of the objects. What is the relationship between the orientations of a white plastic chair and a white plastic chair, parallel of perpendicular to each other?
parallel
perpendicular
null
null
[ { "bbox_3d": [ -0.2, 1.3, 3.3 ], "label": "a white plastic chair" }, { "bbox_3d": [ -0.4, 0.9, 2.9 ], "label": "a white plastic chair" } ]
[ { "front_dir": [ 0.2, 0.1, -1 ], "label": "a white plastic chair", "left_dir": [ -1, -0.1, -0.2 ] }, { "front_dir": [ 1, 0.1, 0.1 ], "label": "a white plastic chair", "left_dir": [ 0.1, 0.2, -1 ] } ]
B
To solve this problem, we first detect the front directions of a white plastic chair and a white plastic chair. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is closer to 0 or 180, than to 90 degrees, then the two objects are parallel to each other. Otherwise, the two objects are perpendicular to each other. The front direction of a white plastic chair is (0.2, 0.1, -1.0). The front direction of a white plastic chair is (1.0, 0.1, 0.1). The cosine similarity between the two front directions is 0.08, corresponding to an angle of 85.47. The angle is closer to 90, than to 0 or 180 degrees, meaning that the two objects are perpendicular to each other. Therefore, the final answer is B. perpendicular.
B. perpendicular.
multi_object_parallel
00445b9419d205b5.jpg
0045aa812f8af5f6_e9c1
Consider the real-world 3D orientations of the objects. Are a red car is parked in front of a building and a red car with a white stripe facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ -3.6, 1.1, 9.6 ], "label": "a red car is parked in front of a building" }, { "bbox_3d": [ 0, 1.4, 3.5 ], "label": "a red car with a white stripe" } ]
[ { "front_dir": [ -0.2, -0.1, -1 ], "label": "a red car is parked in front of a building", "left_dir": [ -1, 0, 0.2 ] }, { "front_dir": [ 0.1, 0, -1 ], "label": "a red car with a white stripe", "left_dir": [ -1, 0.1, -0.1 ] } ]
A
To solve this problem, we first detect the front directions of a red car is parked in front of a building and a red car with a white stripe. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a red car is parked in front of a building is (-0.2, -0.1, -1.0). The front direction of a red car with a white stripe is (0.1, -0.0, -1.0). The cosine similarity between the two front directions is 0.97, corresponding to an angle of 14.11. The angle is small, meaning that the two objects are facing same or similar directions. Therefore, the final answer is A. same or similar directions.
A. same or similar directions.
multi_object_same_direction
0045aa812f8af5f6.jpg
0046afb78d9b8f05_5778
Consider the real-world 3D locations of the objects. Is a man in white shirt playing guitar directly above a woman wearing a pink dress?
yes
no
null
null
[ { "bbox_3d": [ -5.9, 1.9, 16.2 ], "label": "a man in white shirt playing guitar" }, { "bbox_3d": [ -4.7, 0.9, 15.7 ], "label": "a woman wearing a pink dress" } ]
[]
B
To solve this problem, we first determine the 3D locations of a man in white shirt playing guitar and a woman wearing a pink dress. Then we compute the vector pointing from a woman wearing a pink dress to a man in white shirt playing guitar, as well as the up direction of a woman wearing a pink dress. We estimate the cosine similarity between the vector and the up direction, which leads to the angle between the two directions. If the angle is small, then a man in white shirt playing guitar is directly above a woman wearing a pink dress. Otherwise, then a man in white shirt playing guitar is not directly above a woman wearing a pink dress. The 3D location of a man in white shirt playing guitar is (-5.9, 1.9, 16.2). The 3D location of a woman wearing a pink dress is (-4.7, 0.9, 15.7). The vector from a woman wearing a pink dress to a man in white shirt playing guitar is hence (-1.2, 1.0, 0.5). The up direction of a woman wearing a pink dress is (0.0, 1.0, 0.0). The cosine similarity between the vector and the up direction is 0.61, corresponding to an angle of 52 degrees. The angle between the vector and the up direction is large, meaning that a man in white shirt playing guitar is not directly above a woman wearing a pink dress. Therefore, the answer is B. no.
B. no.
location_above
0046afb78d9b8f05.jpg
0046fdc86addea94_0a2c
Consider the real-world 3D locations and orientations of the objects. Which side of a wooden chair with a hole in the back is facing the camera?
front
left
back
right
[ { "bbox_3d": [ -1.6, 1.3, 5.5 ], "label": "a wooden chair with a hole in the back" } ]
[ { "front_dir": [ 1, -0.1, 0.2 ], "label": "a wooden chair with a hole in the back", "left_dir": [ 0.2, -0.2, -1 ] } ]
B
To solve this problem, we first estimate the 3D location of a wooden chair with a hole in the back. Then we obtain the vector pointing from the object to the camera. Now we compute the angles between the vector and the left, right, front, back directions. We first compute the left direction of a wooden chair with a hole in the back, which leads to the angle between left direction and the vector. Immediately we also get the angle between the right direction and the vector. Similarly we compute the angles between the vector and front, back directions. The side of a wooden chair with a hole in the back that is facing the camera corresponds to the direction with the smallest angle. Based on the four estimated angles, we can predict the final answer. The location of a wooden chair with a hole in the back is (-1.6, 1.3, 5.5). The vector from a wooden chair with a hole in the back to camera is hence (1.6, -1.3, -5.5). The left direction of a wooden chair with a hole in the back is (0.2, -0.2, -1.0). The cosine similarity between the vector pointing to camera and the left direction is 0.99, corresponding to an angle of 7.05 degrees. Thus the angle between the vector pointing to camera and the right direction is 172.95 degrees. The front direction of a wooden chair with a hole in the back is (1.0, -0.1, 0.2). The cosine similarity between the vector pointing to camera and the front direction is 0.11, corresponding to an angle of 83.61 degrees. Thus the angle between the vector pointing to camera and the back direction is 96.39 degrees. Among the four directions, the smallest angle is the left direction, with an angle of 7.05 degrees. Thus the left side of a wooden chair with a hole in the back is facing the camera. Therefore, the final answer is B. left.
B. left.
orientation_viewpoint
0046fdc86addea94.jpg
0046fdc86addea94_92b7
Consider the real-world 3D locations and orientations of the objects. Which object is a black laptop with a white apple logo facing towards, a black laptop with a wooden desk or the a wooden chair with a brown seat?
a black laptop with a wooden desk
a wooden chair with a brown seat
null
null
[ { "bbox_3d": [ -2.9, 2.9, 7.9 ], "label": "a black laptop with a white apple logo" }, { "bbox_3d": [ -0.3, 1.3, 1.9 ], "label": "a black laptop with a wooden desk" }, { "bbox_3d": [ 1, 1.4, 7.6 ], "label": "a wooden chair with a brown seat" } ]
[ { "front_dir": [ 0.4, -0.2, -0.9 ], "label": "a black laptop with a white apple logo", "left_dir": [ -0.9, 0.1, -0.4 ] }, { "front_dir": [ 0.2, -0.2, -1 ], "label": "a black laptop with a wooden desk", "left_dir": [ -1, 0.1, -0.2 ] }, { "front_dir": [ -0.1, -0.2, -1 ], "label": "a wooden chair with a brown seat", "left_dir": [ -1, 0.1, 0.1 ] } ]
A
To solve this problem, we first detect the 3D location of a black laptop with a white apple logo, a black laptop with a wooden desk, and a wooden chair with a brown seat. Then we compute the cosine similarities between the front direction of a black laptop with a white apple logo and the vectors from a black laptop with a white apple logo to the other two objects. We can estimate the angles from the cosine similarities, and the object with a smaller angle is the object that a black laptop with a white apple logo is facing towards. The 3D location of a black laptop with a white apple logo is (-2.9, 2.9, 7.9). The 3D location of a black laptop with a wooden desk is (-0.3, 1.3, 1.9). The 3D location of a wooden chair with a brown seat is (1.0, 1.4, 7.6). The front direction of a black laptop with a white apple logo is (0.4, -0.2, -0.9). First we consider if a black laptop with a white apple logo is facing towards the a black laptop with a wooden desk. The vector from a black laptop with a white apple logo to a black laptop with a wooden desk is (2.7, -1.6, -6.1). The cosine similarity between the front direction and the vector is 1.00, corresponding to an angle of 1.20 degrees. First we consider if a black laptop with a white apple logo is facing towards the a wooden chair with a brown seat. The vector from a black laptop with a white apple logo to a wooden chair with a brown seat is (4.0, -1.5, -0.3). The cosine similarity between the front direction and the vector is 0.52, corresponding to an angle of 58.44 degrees. We find that the angle between the front direction and a black laptop with a wooden desk is smaller. Therefore, the final answer is A. a black laptop with a wooden desk.
A. a black laptop with a wooden desk.
multi_object_facing
0046fdc86addea94.jpg
00475aff0e9b2b31_ac32
Consider the real-world 3D locations of the objects. Which is closer to a man in a yellow shirt and a white hat, a man in a white shirt playing a trumpet or a man in a blue hat and white shirt playing a trumpet?
a man in a white shirt playing a trumpet
a man in a blue hat and white shirt playing a trumpet
null
null
[ { "bbox_3d": [ 0, 1.2, 7.6 ], "label": "a man in a yellow shirt and a white hat" }, { "bbox_3d": [ 0.7, 0.8, 7.7 ], "label": "a man in a white shirt playing a trumpet" }, { "bbox_3d": [ 1.7, 1.1, 6.8 ], "label": "a man in a blue hat and white shirt playing a trumpet" } ]
[]
A
To solve this problem, we first detect the 3D location of a man in a yellow shirt and a white hat, a man in a white shirt playing a trumpet, and a man in a blue hat and white shirt playing a trumpet. Then we compute the L2 distances between a man in a yellow shirt and a white hat and a man in a white shirt playing a trumpet, and between a man in a yellow shirt and a white hat and a man in a blue hat and white shirt playing a trumpet. The object that is closer to a man in a yellow shirt and a white hat is the one with a smaller distance. The 3D location of a man in a yellow shirt and a white hat is (0.0, 1.2, 7.6). The 3D location of a man in a white shirt playing a trumpet is (0.7, 0.8, 7.7). The 3D location of a man in a blue hat and white shirt playing a trumpet is (1.7, 1.1, 6.8). The L2 distance between a man in a yellow shirt and a white hat and a man in a white shirt playing a trumpet is 0.768059437575004. The L2 distance between a man in a yellow shirt and a white hat and a man in a blue hat and white shirt playing a trumpet is 1.8556695184124166. Between the two distances, the distance between a man in a yellow shirt and a white hat and a man in a white shirt playing a trumpet is smaller. Therefore, the final answer is A. a man in a white shirt playing a trumpet.
A. a man in a white shirt playing a trumpet.
multi_object_closer_to
00475aff0e9b2b31.jpg
0047c66c4cd20efc_e27f
Consider the real-world 3D locations of the objects. Which is closer to a car with a white roof, a red car with the hood open or a red toy car in a shop window?
a red car with the hood open
a red toy car in a shop window
null
null
[ { "bbox_3d": [ 0.4, 0.7, 0.8 ], "label": "a car with a white roof" }, { "bbox_3d": [ 0.1, 0.1, 1 ], "label": "a red car with the hood open" }, { "bbox_3d": [ 0.2, 0.4, 1 ], "label": "a red toy car in a shop window" } ]
[]
B
To solve this problem, we first detect the 3D location of a car with a white roof, a red car with the hood open, and a red toy car in a shop window. Then we compute the L2 distances between a car with a white roof and a red car with the hood open, and between a car with a white roof and a red toy car in a shop window. The object that is closer to a car with a white roof is the one with a smaller distance. The 3D location of a car with a white roof is (0.4, 0.7, 0.8). The 3D location of a red car with the hood open is (0.1, 0.1, 1.0). The 3D location of a red toy car in a shop window is (0.2, 0.4, 1.0). The L2 distance between a car with a white roof and a red car with the hood open is 0.6788038886976165. The L2 distance between a car with a white roof and a red toy car in a shop window is 0.37699470042552496. Between the two distances, the distance between a car with a white roof and a red toy car in a shop window is smaller. Therefore, the final answer is B. a red toy car in a shop window.
B. a red toy car in a shop window.
multi_object_closer_to
0047c66c4cd20efc.jpg
0047fa2c7d9bfd25_a92d
Consider the real-world 3D orientations of the objects. Are a wooden chair with a white seat and a wooden chair with a black seat facing same or similar directions, or very different directions?
same or similar directions
very different directions
null
null
[ { "bbox_3d": [ -0.7, 0.4, 6.3 ], "label": "a wooden chair with a white seat" }, { "bbox_3d": [ -0.2, 0.7, 1.6 ], "label": "a wooden chair with a black seat" } ]
[ { "front_dir": [ 0.6, -0.1, -0.8 ], "label": "a wooden chair with a white seat", "left_dir": [ -0.8, -0.2, -0.6 ] }, { "front_dir": [ -0.9, 0, -0.5 ], "label": "a wooden chair with a black seat", "left_dir": [ -0.5, 0.2, 0.9 ] } ]
B
To solve this problem, we first detect the front directions of a wooden chair with a white seat and a wooden chair with a black seat. Then we compute the cosine similarities between the two front directions, and the angle between them. If the angle between the two front directions is small, then the two objects are facing same or similar directions. Otherwise, the two objects are facing very different directions. The front direction of a wooden chair with a white seat is (0.6, -0.1, -0.8). The front direction of a wooden chair with a black seat is (-0.9, 0.0, -0.5). The cosine similarity between the two front directions is -0.16, corresponding to an angle of 99.37. The angle is large, meaning that the two objects are facing very different directions. Therefore, the final answer is B. very different directions.
B. very different directions.
multi_object_same_direction
0047fa2c7d9bfd25.jpg