def point_mesh_face_distance(meshes: Meshes, pcls: Pointclouds):
"""
Computes the distance between a pointcloud and a mesh within a batch.
Given a pair `(mesh, pcl)` in the batch, we define the distance to be the
sum of two distances, namely `point_face(mesh, pcl) + face_point(mesh, pcl)`
`point_face(mesh, pcl)`: Computes the squared distance of each point p in pcl
to the closest triangular face in mesh and averages across all points in pcl
`face_point(mesh, pcl)`: Computes the squared distance of each triangular face in
mesh to the closest point in pcl and averages across all faces in mesh.
The above distance functions are applied for all `(mesh, pcl)` pairs in the batch
and then averaged across the batch.
Args:
meshes: A Meshes data structure containing N meshes
pcls: A Pointclouds data structure containing N pointclouds
Returns:
loss: The `point_face(mesh, pcl) + face_point(mesh, pcl)` distance
between all `(mesh, pcl)` in a batch averaged across the batch.
"""
if len(meshes) != len(pcls):
raise ValueError("meshes and pointclouds must be equal sized batches")
N = len(meshes)
# packed representation for pointclouds
points = pcls.points_packed() # (P, 3)
points_first_idx = pcls.cloud_to_packed_first_idx()
max_points = pcls.num_points_per_cloud().max().item()
# packed representation for faces
verts_packed = meshes.verts_packed()
faces_packed = meshes.faces_packed()
tris = verts_packed[faces_packed] # (T, 3, 3)
tris_first_idx = meshes.mesh_to_faces_packed_first_idx()
max_tris = meshes.num_faces_per_mesh().max().item()
# point to face distance: shape (P,)
point_to_face = point_face_distance(points, points_first_idx, tris,
tris_first_idx, max_points)
# weight each example by the inverse of number of points in the example
point_to_cloud_idx = pcls.packed_to_cloud_idx() # (sum(P_i),)
num_points_per_cloud = pcls.num_points_per_cloud() # (N,)
weights_p = num_points_per_cloud.gather(0, point_to_cloud_idx)
weights_p = 1.0 / weights_p.float()
point_to_face = point_to_face * weights_p
point_dist = point_to_face.sum() / N
# face to point distance: shape (T,)
face_to_point = face_point_distance(points, points_first_idx, tris,
tris_first_idx, max_tris)
# weight each example by the inverse of number of faces in the example
tri_to_mesh_idx = meshes.faces_packed_to_mesh_idx() # (sum(T_n),)
num_tris_per_mesh = meshes.num_faces_per_mesh() # (N, )
weights_t = num_tris_per_mesh.gather(0, tri_to_mesh_idx)
weights_t = 1.0 / weights_t.float()
face_to_point = face_to_point * weights_t
face_dist = face_to_point.sum() / N
return point_dist + face_dist
def point_mesh_edge_distance(meshes: Meshes, pcls: Pointclouds):
"""
Computes the distance between a pointcloud and a mesh within a batch.
Given a pair `(mesh, pcl)` in the batch, we define the distance to be the
sum of two distances, namely `point_edge(mesh, pcl) + edge_point(mesh, pcl)`
`point_edge(mesh, pcl)`: Computes the squared distance of each point p in pcl
to the closest edge segment in mesh and averages across all points in pcl
`edge_point(mesh, pcl)`: Computes the squared distance of each edge segment in mesh
to the closest point in pcl and averages across all edges in mesh.
The above distance functions are applied for all `(mesh, pcl)` pairs in the batch
and then averaged across the batch.
Args:
meshes: A Meshes data structure containing N meshes
pcls: A Pointclouds data structure containing N pointclouds
Returns:
loss: The `point_edge(mesh, pcl) + edge_point(mesh, pcl)` distance
between all `(mesh, pcl)` in a batch averaged across the batch.
"""
if len(meshes) != len(pcls):
raise ValueError("meshes and pointclouds must be equal sized batches")
N = len(meshes)
# packed representation for pointclouds
points = pcls.points_packed() # (P, 3)
points_first_idx = pcls.cloud_to_packed_first_idx()
max_points = pcls.num_points_per_cloud().max().item()
# packed representation for edges
verts_packed = meshes.verts_packed()
edges_packed = meshes.edges_packed()
segms = verts_packed[edges_packed] # (S, 2, 3)
segms_first_idx = meshes.mesh_to_edges_packed_first_idx()
max_segms = meshes.num_edges_per_mesh().max().item()
# point to edge distance: shape (P,)
point_to_edge = point_edge_distance(points, points_first_idx, segms,
segms_first_idx, max_points)
# weight each example by the inverse of number of points in the example
point_to_cloud_idx = pcls.packed_to_cloud_idx() # (sum(P_i), )
num_points_per_cloud = pcls.num_points_per_cloud() # (N,)
weights_p = num_points_per_cloud.gather(0, point_to_cloud_idx)
weights_p = 1.0 / weights_p.float()
point_to_edge = point_to_edge * weights_p
point_dist = point_to_edge.sum() / N
# edge to edge distance: shape (S,)
edge_to_point = edge_point_distance(points, points_first_idx, segms,
segms_first_idx, max_segms)
# weight each example by the inverse of number of edges in the example
segm_to_mesh_idx = meshes.edges_packed_to_mesh_idx() # (sum(S_n),)
num_segms_per_mesh = meshes.num_edges_per_mesh() # (N,)
weights_s = num_segms_per_mesh.gather(0, segm_to_mesh_idx)
weights_s = 1.0 / weights_s.float()
edge_to_point = edge_to_point * weights_s
edge_dist = edge_to_point.sum() / N
return point_dist + edge_dist
