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# Copyright (c) 2023 Gray Lab
# Permission is hereby granted, free of charge, to any person obtaining a copy of this
# software and associated documentation files (the "Software"), to deal in the Software
# without restriction, including without limitation the rights to use, copy, modify, merge,
# publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons
# to whom the Software is furnished to do so, subject to the following conditions:
# # The above copyright notice and this permission notice shall be included in all copies or
# substantial portions of the Software.
# # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
# INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
# PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE
# FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
# OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
# DEALINGS IN THE SOFTWARE.
import os
import sys
import einops
import torch
root = os.path.abspath(".")
sys.path.insert(0, root) # Adds project's root directory
def mean_w_mask(a, mask, keepdim=True):
"""
Computes the mean of point cloud a accounting for the mask.
Args:
a: Input point cloud of shape [*, n, d]
mask: Input mask of shape [*, n] of boolean values
keepdim: whether to keep the dimension across which we're computing the mean
like normal pytorch mean
Returns:
Masked mean of a across dimension -2 (or n)
"""
mask = mask[..., None] # [*, n, 1]
num_elements = torch.sum(mask, dim=-2, keepdim=True) # [*, 1, 1]
num_elements = torch.where(
num_elements == 0, torch.tensor(1.0), num_elements
) # [*, 1, 1]
a_masked = torch.masked_fill(a, ~mask, 0.0) # [*, n, d]
mean = torch.sum(a_masked, dim=-2, keepdim=True) / num_elements # [*, 1, d]
mean = torch.masked_fill(mean, num_elements == 0, 0.0) # [*, 1, d]
if not keepdim:
mean = einops.rearrange(mean, "... () d -> ... d")
return mean
def kabsch_align_ind(mobile, target, mask=None, ret_both=False):
"""
Aligns mobile to target.
Args:
mobile: Torch tensor of shape [n, 3] -- Point Cloud to Align (source)
target: Torch tensor of shape [n, 3] -- Reference Point Cloud (target)
mask: Torch tensor of bools shape [n] -- if not None
ret_both: Whether to return both pointclouds or just the mobile
Returns:
mobile_aligned: mobile point cloud aligned to target, shape [n, 3]
"""
if mask is None:
mask = torch.ones(mobile.shape[:-1]).bool()
mobile, target = mobile[None, ...], target[None, ...] # [1, n, 3]
mobile_aligned = kabsch_align(mobile, target) # [1, n, 3]
if ret_both:
return mobile_aligned[0], target[0] # [n, 3]
return mobile_aligned[0] # [n, 3]
def kabsch_align(mobile, target, mask=None):
"""
Aligns mobile to target.
Args:
mobile: Torch tensor of shape [b, n, 3] -- Point Cloud to Align (source)
target: Torch tensor of shape [b, n, 3] -- Reference Point Cloud (target)
mask: Torch tensor of bools shape [b, n] -- if not None
Returns:
mobile_aligned: mobile point cloud aligned to target, shape [b, n, 3]
"""
if mask is None:
mask = torch.ones(mobile.shape[:-1]).bool() # [b, n] all True
mean_mobile = mean_w_mask(mobile, mask, keepdim=True)
mean_target = mean_w_mask(target, mask, keepdim=True)
mobile_centered = mobile - mean_mobile
target_ceneterd = target - mean_target
# These two operations make masked positions non-zero
mobile_centered = torch.masked_fill(
mobile_centered, ~mask[..., None], 0.0
) # Fill masked positions with 0
target_ceneterd = torch.masked_fill(
target_ceneterd, ~mask[..., None], 0.0
) # Fill masked positions with 0
R = _find_rot_alignment(mobile_centered, target_ceneterd, mask)
mobile_aligned = (
torch.matmul(
R,
mobile_centered.transpose(-2, -1),
).transpose(-2, -1)
+ mean_target
) # [b, n, 3]
mobile_aligned = torch.masked_fill(
mobile_aligned, ~mask[..., None], 0.0
) # Fill masked positions with 0
return mobile_aligned
# This function was adapted from GeoDock's code (MIT License)
# https://github.com/Graylab/GeoDock/blob/main/geodock/utils/metrics.py#L103
# We pulled out translation stuff, vecotrize it and added masks
def _find_rot_alignment(A, B, mask=None):
"""
Finds rotation that alignes two point clouds with zero center of mass.
The mask functionality is simple. Once we center the point clouds,
we zero-out the masked elements. Since the point clouds are centered,
the masked elements will coincide at the origin for all rotations,
so they do not affect the rotation found.
Args:
A: Torch tensor of shape [b, n, 3] -- point cloud to align (source) / mobile
B: Torch tensor of shape [b, n, 3] -- reference point cloud (target) / target
mask: Torch tensor of bools shape [b, n] -- if not None
Returns:
R: optimal rotations that best aligns A towards B, shape [b, 3, 3]
"""
if mask is None:
mask = torch.ones(A.shape[:-1]).bool() # [b, n] all True
# Confirm pointclouds are centered
sh = mean_w_mask(A, mask, keepdim=True).shape
assert torch.allclose(
mean_w_mask(A, mask, keepdim=True),
torch.zeros(sh, device=A.device),
atol=1e-4,
rtol=1e-4,
)
assert torch.allclose(
mean_w_mask(B, mask, keepdim=True),
torch.zeros(sh, device=B.device),
atol=1e-4,
rtol=1e-4,
)
assert A.shape == B.shape
mask = mask[..., None] # [b, n, 1]
A = torch.masked_fill(A, ~mask, 0.0)
B = torch.masked_fill(B, ~mask, 0.0)
# Covariance matrix and SVD
H = torch.matmul(A.transpose(-2, -1), B)
# To float32, batched SVD not implemented otherwise
U, S, Vt = torch.linalg.svd(
H.to(torch.float32), full_matrices=True
) # Breaks with mixed precision
R = torch.matmul(
Vt.transpose(-2, -1),
U.transpose(-2, -1),
) # [b, 3, 3]
# Handle the special reflection case
det_R = torch.linalg.det(R.to(torch.float32)) # [b], breaks with mixed precision
SS = torch.eye(3, device=R.device).repeat(A.shape[0], 1, 1) # Shape [b, 3, 3]
SS[:, -1, -1] = torch.where(
det_R < 0,
torch.tensor(-1.0, device=R.device),
torch.tensor(1.0, device=R.device),
) # [b, 3, 3]
R_aux = torch.matmul(Vt.transpose(-2, -1), SS)
R = torch.matmul(R_aux, U.transpose(-2, -1)) # [b, 3, 3]
return R
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