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Weighted Umeyama.

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Summary:
1. Introduced weights to Umeyama implementation. This will be needed for weighted ePnP but is useful on its own.
2. Refactored to use the same code for the Pointclouds mask and passed weights.
3. Added test cases with random weights.
4. Fixed a bug in tests that calls the function with 0 points (fails randomly in Pytorch 1.3, will be fixed in the next release: https://github.com/pytorch/pytorch/issues/31421 ).

Reviewed By: gkioxari

Differential Revision: D20070293

fbshipit-source-id: e9f549507ef6dcaa0688a0f17342e6d7a9a4336c
This commit is contained in:
Roman Shapovalov 2020-04-03 02:57:01 -07:00 committed by Facebook GitHub Bot
parent e5b1d6d3a3
commit e37085d999
6 changed files with 278 additions and 50 deletions
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68
pytorch3d/ops/points_alignment.py
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@ -1,16 +1,18 @@
#!/usr/bin/env python3
# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
import warnings
from typing import Tuple, Union
from typing import List, Optional, Tuple, Union
import torch
from pytorch3d.structures.pointclouds import Pointclouds
from pytorch3d.structures import utils as strutil
from pytorch3d.ops import utils as oputil
def corresponding_points_alignment(
X: Union[torch.Tensor, Pointclouds],
Y: Union[torch.Tensor, Pointclouds],
weights: Union[torch.Tensor, List[torch.Tensor], None] = None,
estimate_scale: bool = False,
allow_reflection: bool = False,
eps: float = 1e-8,
@ -28,9 +30,14 @@ def corresponding_points_alignment(
Args:
X: Batch of `d`-dimensional points of shape `(minibatch, num_point, d)`
or a `Pointclouds` object.
or a `Pointclouds` object.
Y: Batch of `d`-dimensional points of shape `(minibatch, num_point, d)`
or a `Pointclouds` object.
or a `Pointclouds` object.
weights: Batch of non-negative weights of
shape `(minibatch, num_point)` or list of `minibatch` 1-dimensional
tensors that may have different shapes; in that case, the length of
i-th tensor should be equal to the number of points in X_i and Y_i.
Passing `None` means uniform weights.
estimate_scale: If `True`, also estimates a scaling component `s`
of the transformation. Otherwise assumes an identity
scale and returns a tensor of ones.
@ -59,25 +66,45 @@ def corresponding_points_alignment(
"Point sets X and Y have to have the same \
number of batches, points and dimensions."
)
if weights is not None:
if isinstance(weights, list):
if any(np != w.shape[0] for np, w in zip(num_points, weights)):
raise ValueError(
"number of weights should equal to the "
+ "number of points in the point cloud."
)
weights = [w[..., None] for w in weights]
weights = strutil.list_to_padded(weights)[..., 0]
if Xt.shape[:2] != weights.shape:
raise ValueError(
"weights should have the same first two dimensions as X."
)
b, n, dim = Xt.shape
# compute the centroids of the point sets
Xmu = Xt.sum(1) / torch.clamp(num_points[:, None], 1)
Ymu = Yt.sum(1) / torch.clamp(num_points[:, None], 1)
# mean-center the point sets
Xc = Xt - Xmu[:, None]
Yc = Yt - Ymu[:, None]
if (num_points < Xt.shape[1]).any() or (num_points < Yt.shape[1]).any():
# in case we got Pointclouds as input, mask the unused entries in Xc, Yc
mask = (
torch.arange(n, dtype=torch.int64, device=Xc.device)[None]
torch.arange(n, dtype=torch.int64, device=Xt.device)[None]
< num_points[:, None]
).type_as(Xc)
Xc *= mask[:, :, None]
Yc *= mask[:, :, None]
).type_as(Xt)
weights = mask if weights is None else mask * weights.type_as(Xt)
# compute the centroids of the point sets
Xmu = oputil.wmean(Xt, weights, eps=eps)
Ymu = oputil.wmean(Yt, weights, eps=eps)
# mean-center the point sets
Xc = Xt - Xmu
Yc = Yt - Ymu
total_weight = torch.clamp(num_points, 1)
# special handling for heterogeneous point clouds and/or input weights
if weights is not None:
Xc *= weights[:, :, None]
Yc *= weights[:, :, None]
total_weight = torch.clamp(weights.sum(1), eps)
if (num_points < (dim + 1)).any():
warnings.warn(
@ -87,7 +114,7 @@ def corresponding_points_alignment(
# compute the covariance XYcov between the point sets Xc, Yc
XYcov = torch.bmm(Xc.transpose(2, 1), Yc)
XYcov = XYcov / torch.clamp(num_points[:, None, None], 1)
XYcov = XYcov / total_weight[:, None, None]
# decompose the covariance matrix XYcov
U, S, V = torch.svd(XYcov)
@ -111,17 +138,16 @@ def corresponding_points_alignment(
if estimate_scale:
# estimate the scaling component of the transformation
trace_ES = (torch.diagonal(E, dim1=1, dim2=2) * S).sum(1)
Xcov = (Xc * Xc).sum((1, 2)) / torch.clamp(num_points, 1)
Xcov = (Xc * Xc).sum((1, 2)) / total_weight
# the scaling component
s = trace_ES / torch.clamp(Xcov, eps)
# translation component
T = Ymu - s[:, None] * torch.bmm(Xmu[:, None], R)[:, 0, :]
T = Ymu[:, 0, :] - s[:, None] * torch.bmm(Xmu, R)[:, 0, :]
else:
# translation component
T = Ymu - torch.bmm(Xmu[:, None], R)[:, 0]
T = Ymu[:, 0, :] - torch.bmm(Xmu, R)[:, 0, :]
# unit scaling since we do not estimate scale
s = T.new_ones(b)

44
pytorch3d/ops/utils.py Normal file
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@ -0,0 +1,44 @@
# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
from typing import Optional, Tuple, Union
import torch
def wmean(
x: torch.Tensor,
weight: Optional[torch.Tensor] = None,
dim: Union[int, Tuple[int]] = -2,
keepdim: bool = True,
eps: float = 1e-9,
) -> torch.Tensor:
"""
Finds the mean of the input tensor across the specified dimension.
If the `weight` argument is provided, computes weighted mean.
Args:
x: tensor of shape `(*, D)`, where D is assumed to be spatial;
weights: if given, non-negative tensor of shape `(*,)`. It must be
broadcastable to `x.shape[:-1]`. Note that the weights for
the last (spatial) dimension are assumed same;
dim: dimension(s) in `x` to average over;
keepdim: tells whether to keep the resulting singleton dimension.
eps: minumum clamping value in the denominator.
Returns:
the mean tensor:
* if `weights` is None => `mean(x, dim)`,
* otherwise => `sum(x*w, dim) / max{sum(w, dim), eps}`.
"""
args = dict(dim=dim, keepdim=keepdim)
if weight is None:
return x.mean(**args)
if any(
xd != wd and xd != 1 and wd != 1
for xd, wd in zip(x.shape[-2::-1], weight.shape[::-1])
):
raise ValueError("wmean: weights are not compatible with the tensor")
return (
(x * weight[..., None]).sum(**args)
/ weight[..., None].sum(**args).clamp(eps)
)

1
tests/bm_points_alignment.py
View File

@ -16,6 +16,7 @@ def bm_corresponding_points_alignment() -> None:
"dim": [3, 20],
"estimate_scale": [True, False],
"n_points": [100, 10000],
"random_weights": [False, True],
"use_pointclouds": [False],
}

11
tests/common_testing.py
View File

@ -1,5 +1,6 @@
# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
from typing import Optional
import unittest
@ -35,13 +36,15 @@ class TestCaseMixin(unittest.TestCase):
*,
rtol: float = 1e-05,
atol: float = 1e-08,
equal_nan: bool = False
equal_nan: bool = False,
msg: Optional[str] = None,
) -> None:
"""
Verify that two tensors or arrays are the same shape and close.
Args:
input, other: two tensors or two arrays.
rtol, atol, equal_nan: as for torch.allclose.
msg: message in case the assertion is violated.
Note:
Optional arguments here are all keyword-only, to avoid confusion
with msg arguments on other assert functions.
@ -54,5 +57,7 @@ class TestCaseMixin(unittest.TestCase):
input, other, rtol=rtol, atol=atol, equal_nan=equal_nan
)
else:
close = np.allclose(input, other, rtol=rtol, atol=atol, equal_nan=equal_nan)
self.assertTrue(close)
close = np.allclose(
input, other, rtol=rtol, atol=atol, equal_nan=equal_nan
)
self.assertTrue(close, msg)

75
tests/test_ops_utils.py Normal file
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@ -0,0 +1,75 @@
# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
import unittest
import numpy as np
import torch
from common_testing import TestCaseMixin
from pytorch3d.ops import utils as oputil
class TestOpsUtils(TestCaseMixin, unittest.TestCase):
def setUp(self) -> None:
super().setUp()
torch.manual_seed(42)
np.random.seed(42)
def test_wmean(self):
device = torch.device("cuda:0")
n_points = 20
x = torch.rand(n_points, 3, device=device)
weight = torch.rand(n_points, device=device)
x_np = x.cpu().data.numpy()
weight_np = weight.cpu().data.numpy()
# test unweighted
mean = oputil.wmean(x, keepdim=False)
mean_gt = np.average(x_np, axis=-2)
self.assertClose(mean.cpu().data.numpy(), mean_gt)
# test weighted
mean = oputil.wmean(x, weight=weight, keepdim=False)
mean_gt = np.average(x_np, axis=-2, weights=weight_np)
self.assertClose(mean.cpu().data.numpy(), mean_gt)
# test keepdim
mean = oputil.wmean(x, weight=weight, keepdim=True)
self.assertClose(mean[0].cpu().data.numpy(), mean_gt)
# test binary weigths
mean = oputil.wmean(x, weight=weight > 0.5, keepdim=False)
mean_gt = np.average(x_np, axis=-2, weights=weight_np > 0.5)
self.assertClose(mean.cpu().data.numpy(), mean_gt)
# test broadcasting
x = torch.rand(10, n_points, 3, device=device)
x_np = x.cpu().data.numpy()
mean = oputil.wmean(x, weight=weight, keepdim=False)
mean_gt = np.average(x_np, axis=-2, weights=weight_np)
self.assertClose(mean.cpu().data.numpy(), mean_gt)
weight = weight[None, None, :].repeat(3, 1, 1)
mean = oputil.wmean(x, weight=weight, keepdim=False)
self.assertClose(mean[0].cpu().data.numpy(), mean_gt)
# test failing broadcasting
weight = torch.rand(x.shape[0], device=device)
with self.assertRaises(ValueError) as context:
oputil.wmean(x, weight=weight, keepdim=False)
self.assertTrue("weights are not compatible" in str(context.exception))
# test dim
weight = torch.rand(x.shape[0], n_points, device=device)
weight_np = np.tile(
weight[:, :, None].cpu().data.numpy(),
(1, 1, x_np.shape[-1]),
)
mean = oputil.wmean(x, dim=0, weight=weight, keepdim=False)
mean_gt = np.average(x_np, axis=0, weights=weight_np)
self.assertClose(mean.cpu().data.numpy(), mean_gt)
# test dim tuple
mean = oputil.wmean(x, dim=(0, 1), weight=weight, keepdim=False)
mean_gt = np.average(x_np, axis=(0, 1), weights=weight_np)
self.assertClose(mean.cpu().data.numpy(), mean_gt)

129
tests/test_points_alignment.py
View File

@ -6,6 +6,8 @@ import numpy as np
import unittest
import torch
from common_testing import TestCaseMixin
from pytorch3d.ops import points_alignment
from pytorch3d.structures.pointclouds import Pointclouds
from pytorch3d.transforms import rotation_conversions
@ -35,7 +37,7 @@ def _apply_pcl_transformation(X, R, T, s=None):
return X_t
class TestCorrespondingPointsAlignment(unittest.TestCase):
class TestCorrespondingPointsAlignment(TestCaseMixin, unittest.TestCase):
def setUp(self) -> None:
super().setUp()
torch.manual_seed(42)
@ -171,6 +173,7 @@ class TestCorrespondingPointsAlignment(unittest.TestCase):
estimate_scale=False,
allow_reflection=False,
reflect=False,
random_weights=False,
):
device = torch.device("cuda:0")
@ -198,12 +201,27 @@ class TestCorrespondingPointsAlignment(unittest.TestCase):
# point cloud X
X_t = _apply_pcl_transformation(X, R, T, s=s)
weights = None
if random_weights:
template = X.points_padded() if use_pointclouds else X
weights = torch.rand_like(template[:, :, 0])
weights = weights / weights.sum(dim=1, keepdim=True)
# zero out some weights as zero weights are a common use case
# this guarantees there are no zero weight
weights *= (weights * template.size()[1] > 0.3).to(weights)
if use_pointclouds: # convert to List[Tensor]
weights = [
w[:npts]
for w, npts in zip(weights, X.num_points_per_cloud())
]
torch.cuda.synchronize()
def run_corresponding_points_alignment():
points_alignment.corresponding_points_alignment(
X,
X_t,
weights,
allow_reflection=allow_reflection,
estimate_scale=estimate_scale,
)
@ -230,26 +248,28 @@ class TestCorrespondingPointsAlignment(unittest.TestCase):
"""
# run this for several different point cloud sizes
for n_points in (100, 3, 2, 1, 0):
for n_points in (100, 3, 2, 1):
# run this for several different dimensionalities
for dim in torch.arange(2, 10):
for dim in range(2, 10):
# switches whether we should use the Pointclouds inputs
use_point_clouds_cases = (
(True, False) if dim == 3 and n_points > 3 else (False,)
)
for use_pointclouds in use_point_clouds_cases:
for estimate_scale in (False, True):
for reflect in (False, True):
for allow_reflection in (False, True):
self._test_single_corresponding_points_alignment(
batch_size=10,
n_points=n_points,
dim=int(dim),
use_pointclouds=use_pointclouds,
estimate_scale=estimate_scale,
reflect=reflect,
allow_reflection=allow_reflection,
)
for random_weights in (False, True,):
for use_pointclouds in use_point_clouds_cases:
for estimate_scale in (False, True):
for reflect in (False, True):
for allow_reflection in (False, True):
self._test_single_corresponding_points_alignment(
batch_size=10,
n_points=n_points,
dim=dim,
use_pointclouds=use_pointclouds,
estimate_scale=estimate_scale,
reflect=reflect,
allow_reflection=allow_reflection,
random_weights=random_weights,
)
def _test_single_corresponding_points_alignment(
self,
@ -260,6 +280,7 @@ class TestCorrespondingPointsAlignment(unittest.TestCase):
estimate_scale=False,
reflect=False,
allow_reflection=False,
random_weights=False,
):
"""
Executes a single test for `corresponding_points_alignment` for a
@ -294,6 +315,20 @@ class TestCorrespondingPointsAlignment(unittest.TestCase):
)
R = torch.bmm(M, R)
weights = None
if random_weights:
template = X.points_padded() if use_pointclouds else X
weights = torch.rand_like(template[:, :, 0])
weights = weights / weights.sum(dim=1, keepdim=True)
# zero out some weights as zero weights are a common use case
# this guarantees there are no zero weight
weights *= (weights * template.size()[1] > 0.3).to(weights)
if use_pointclouds: # convert to List[Tensor]
weights = [
w[:npts]
for w, npts in zip(weights, X.num_points_per_cloud())
]
# apply the generated transformation to the generated
# point cloud X
X_t = _apply_pcl_transformation(X, R, T, s=s)
@ -302,6 +337,7 @@ class TestCorrespondingPointsAlignment(unittest.TestCase):
R_est, T_est, s_est = points_alignment.corresponding_points_alignment(
X,
X_t,
weights,
allow_reflection=allow_reflection,
estimate_scale=estimate_scale,
)
@ -313,9 +349,40 @@ class TestCorrespondingPointsAlignment(unittest.TestCase):
f"use_pointclouds={use_pointclouds}, "
f"estimate_scale={estimate_scale}, "
f"reflect={reflect}, "
f"allow_reflection={allow_reflection}."
f"allow_reflection={allow_reflection},"
f"random_weights={random_weights}."
)
# if we test the weighted case, check that weights help with noise
if random_weights and not use_pointclouds and n_points >= (dim + 10):
# add noise to 20% points with smallest weight
X_noisy = X_t.clone()
_, mink_idx = torch.topk(-weights, int(n_points * 0.2), dim=1)
mink_idx = mink_idx[:, :, None].expand(-1, -1, X_t.shape[-1])
X_noisy.scatter_add_(
1, mink_idx, 0.3 * torch.randn_like(mink_idx, dtype=X_t.dtype)
)
def align_and_get_mse(weights_):
R_n, T_n, s_n = points_alignment.corresponding_points_alignment(
X_noisy,
X_t,
weights_,
allow_reflection=allow_reflection,
estimate_scale=estimate_scale,
)
X_t_est = _apply_pcl_transformation(X_noisy, R_n, T_n, s=s_n)
return (
((X_t_est - X_t) * weights[..., None]) ** 2
).sum(dim=(1, 2)) / weights.sum(dim=-1)
# check that using weights leads to lower weighted_MSE(X_noisy, X_t)
self.assertTrue(
torch.all(align_and_get_mse(weights) <= align_and_get_mse(None))
)
if reflect and not allow_reflection:
# check that all rotations have det=1
self._assert_all_close(
@ -325,34 +392,44 @@ class TestCorrespondingPointsAlignment(unittest.TestCase):
)
else:
# mask out inputs with too few non-degenerate points for assertions
w = (
torch.ones_like(R_est[:, 0, 0])
if weights is None or n_points >= dim + 10
else (weights > 0.0).all(dim=1).to(R_est)
)
# check that the estimated tranformation is the same
# as the ground truth
if n_points >= (dim + 1):
# the checks on transforms apply only when
# the problem setup is unambiguous
self._assert_all_close(R_est, R, assert_error_message)
self._assert_all_close(T_est, T, assert_error_message)
self._assert_all_close(s_est, s, assert_error_message)
msg = assert_error_message
self._assert_all_close(R_est, R, msg, w[:, None, None], atol=1e-5)
self._assert_all_close(T_est, T, msg, w[:, None])
self._assert_all_close(s_est, s, msg, w)
# check that the orthonormal part of the
# transformation has a correct determinant (+1/-1)
desired_det = R_est.new_ones(batch_size)
if reflect:
desired_det *= -1.0
self._assert_all_close(
torch.det(R_est), desired_det, assert_error_message
)
self._assert_all_close(torch.det(R_est), desired_det, msg, w)
# check that the transformed point cloud
# X matches X_t
X_t_est = _apply_pcl_transformation(X, R_est, T_est, s=s_est)
self._assert_all_close(
X_t, X_t_est, assert_error_message, atol=1e-5
X_t, X_t_est, assert_error_message, w[:, None, None], atol=1e-5
)
def _assert_all_close(self, a_, b_, err_message, atol=1e-6):
def _assert_all_close(self, a_, b_, err_message, weights=None, atol=1e-6):
if isinstance(a_, Pointclouds):
a_ = a_.points_packed()
if isinstance(b_, Pointclouds):
b_ = b_.points_packed()
self.assertTrue(torch.allclose(a_, b_, atol=atol), err_message)
if weights is None:
self.assertClose(a_, b_, atol=atol, msg=err_message)
else:
self.assertClose(
a_ * weights, b_ * weights, atol=atol, msg=err_message
)