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Zero
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import numpy as np
def _sample_points_in_box3d(bbox_vertices, num_samples):
"""
Sample points in a axis-aligned 3D bounding box\n
- bbox_vertices: the vertices of the bounding box in the form: [[x0, y0, z0], [x1, y1, z1], ...]\n
- num_samples: the number of samples to use\n
Return:\n
- points: the sampled points in the form: [[x0, y0, z0], [x1, y1, z1], ...]
"""
# Compute the bounding box size
bbox_size = np.max(bbox_vertices, axis=0) - np.min(bbox_vertices, axis=0)
# Sample points in the bounding box
points = np.random.rand(num_samples, 3) * bbox_size + np.min(bbox_vertices, axis=0)
return points
def _apply_forward_transformations(points, transformations):
"""
Apply forward transformations to the points\n
- points: the points in the form: [[x0, y0, z0], [x1, y1, z1], ...]\n
- transformations: list of transformations to apply\n
Return:\n
- points_transformed: the transformed points in the form: [[x0, y0, z0], [x1, y1, z1], ...]
"""
if len(transformations) == 0:
return points
# To homogeneous coordinates
points_transformed = np.concatenate([points, np.ones((points.shape[0], 1))], axis=1)
# Apply the transformations one by one in order
for transformation in transformations:
if transformation["type"] == "translation":
points_transformed = np.matmul(
transformation["matrix"], points_transformed.T
).T
elif transformation["type"] == "rotation":
axis_origin = np.append(transformation["rotation_axis_origin"], 0)
points_recentered = points_transformed - axis_origin
points_rotated = np.matmul(transformation["matrix"], points_recentered.T).T
points_transformed = points_rotated + axis_origin
elif transformation["type"] == "plucker":
points_transformed = np.matmul(
transformation["matrix"], points_transformed.T
).T
else:
raise ValueError(f"Unknown transformation type: {transformation['type']}")
return points_transformed[..., :3]
def _apply_backward_transformations(points, transformations):
"""
Apply backward transformations to the points\n
- points: the points in the form: [[x0, y0, z0], [x1, y1, z1], ...]\n
- transformations: list of transformations to apply\n
- The inverse of the transformations are applied in reverse order\n
Return:\n
- points_transformed: the transformed points in the form: [[x0, y0, z0], [x1, y1, z1], ...]
Reference: https://mathematica.stackexchange.com/questions/106257/how-do-i-get-the-inverse-of-a-homogeneous-transformation-matrix
"""
if len(transformations) == 0:
return points
# To homogeneous coordinates
points_transformed = np.concatenate([points, np.ones((points.shape[0], 1))], axis=1)
# Apply the transformations one by one in reverse order
for transformation in transformations[::-1]:
inv_transformation = np.eye(4)
inv_transformation[:3, :3] = transformation["matrix"][:3, :3].T
inv_transformation[:3, 3] = -np.matmul(
transformation["matrix"][:3, :3].T, transformation["matrix"][:3, 3]
)
if transformation["type"] == "translation":
points_transformed = np.matmul(inv_transformation, points_transformed.T).T
elif transformation["type"] == "rotation":
axis_origin = np.append(transformation["rotation_axis_origin"], 0)
points_recentered = points_transformed - axis_origin
points_rotated = np.matmul(inv_transformation, points_recentered.T).T
points_transformed = points_rotated + axis_origin
elif transformation["type"] == "plucker":
points_transformed = np.matmul(inv_transformation, points_transformed.T).T
else:
raise ValueError(f"Unknown transformation type: {transformation['type']}")
return points_transformed[..., :3]
def _count_points_in_box3d(points, bbox_vertices):
"""
Count the number of points in a 3D bounding box\n
- points: the points in the form: [[x0, y0, z0], [x1, y1, z1], ...]\n
- bbox_vertices: the vertices of the bounding box in the form: [[x0, y0, z0], [x1, y1, z1], ...]\n
- The bbox is assumed to be axis-aligned\n
Return:\n
- num_points_in_bbox: the number of points in the bounding box
"""
# Count the number of points in the bounding box
num_points_in_bbox = np.sum(
np.all(points >= np.min(bbox_vertices, axis=0), axis=1)
& np.all(points <= np.max(bbox_vertices, axis=0), axis=1)
)
return num_points_in_bbox
def iou_aabb(bbox1_vertices, bbox2_verices):
"""
Compute the IoU between two axis-aligned bounding boxes\n
- bbox1_vertices: the vertices of the first bounding box in the form: [[x0, y0, z0], [x1, y1, z1], ...]\n
- bbox2_vertices: the vertices of the second bounding box in the form: [[x0, y0, z0], [x1, y1, z1], ...]\n
Return:\n
- iou: the IoU between the two bounding boxes
"""
# Compute the intersection and union of the two bounding boxes
min_bbox = np.maximum(np.min(bbox1_vertices, axis=0), np.min(bbox2_verices, axis=0))
max_bbox = np.minimum(np.max(bbox1_vertices, axis=0), np.max(bbox2_verices, axis=0))
intersection = np.prod(np.clip(max_bbox - min_bbox, a_min=0, a_max=None))
union = (
np.prod(np.max(bbox1_vertices, axis=0) - np.min(bbox1_vertices, axis=0))
+ np.prod(np.max(bbox2_verices, axis=0) - np.min(bbox2_verices, axis=0))
- intersection
)
# Compute the IoU
iou = intersection / union if union > 0 else 0
return iou
def sampling_iou(
bbox1_vertices,
bbox2_vertices,
bbox1_transformations,
bbox2_transformations,
num_samples=10000,
):
"""
Compute the IoU between two bounding boxes\n
- bbox1_vertices: the vertices of the first bounding box\n
- bbox2_vertices: the vertices of the second bounding box\n
- bbox1_transformations: list of transformations applied to the first bounding box\n
- bbox2_transformations: list of transformations applied to the second bounding box\n
- num_samples (optional): the number of samples to use per bounding box\n
Return:\n
- iou: the IoU between the two bounding boxes after applying the transformations
"""
# if no transformations are applied, use the axis-aligned bounding box IoU
if len(bbox1_transformations) == 0 and len(bbox2_transformations) == 0:
return iou_aabb(bbox1_vertices, bbox2_vertices)
# Volume of the two bounding boxes
bbox1_volume = np.prod(
np.max(bbox1_vertices, axis=0) - np.min(bbox1_vertices, axis=0)
)
bbox2_volume = np.prod(
np.max(bbox2_vertices, axis=0) - np.min(bbox2_vertices, axis=0)
)
# Sample points in the two bounding boxes
bbox1_points = _sample_points_in_box3d(bbox1_vertices, num_samples)
bbox2_points = _sample_points_in_box3d(bbox2_vertices, num_samples)
# Transform the points
forward_bbox1_points = _apply_forward_transformations(
bbox1_points, bbox1_transformations
)
forward_bbox2_points = _apply_forward_transformations(
bbox2_points, bbox2_transformations
)
# Transform the forward points to the other box's rest pose frame
forward_bbox1_points_in_rest_bbox2_frame = _apply_backward_transformations(
forward_bbox1_points, bbox2_transformations
)
forward_bbox2_points_in_rest_bbox1_frame = _apply_backward_transformations(
forward_bbox2_points, bbox1_transformations
)
# Count the number of points in the other bounding box
num_bbox1_points_in_bbox2 = _count_points_in_box3d(
forward_bbox1_points_in_rest_bbox2_frame, bbox2_vertices
)
num_bbox2_points_in_bbox1 = _count_points_in_box3d(
forward_bbox2_points_in_rest_bbox1_frame, bbox1_vertices
)
# Compute the IoU
intersect = (
bbox1_volume * num_bbox1_points_in_bbox2
+ bbox2_volume * num_bbox2_points_in_bbox1
) / 2
union = bbox1_volume * num_samples + bbox2_volume * num_samples - intersect
iou = intersect / union
return iou
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