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Fix returning a proper rotation in levelling; supporting batches and default centroid

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Summary:
`get_rotation_to_best_fit_xy` is useful to expose externally, however there was a bug (which we probably did not care about for our use case): it could return a rotation matrix with det(R) == −1.
The diff fixes that, and also makes centroid optional (it can be computed from points).

Reviewed By: bottler

Differential Revision: D39926791

fbshipit-source-id: 5120c7892815b829f3ddcc23e93d4a5ec0ca0013
This commit is contained in:
Roman Shapovalov
2022-09-29 11:56:14 -07:00
committed by Facebook GitHub Bot
parent de98c9cc2f
commit 74bbd6fd76
2 changed files with 45 additions and 10 deletions
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26
pytorch3d/implicitron/tools/circle_fitting.py
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@@ -12,22 +12,30 @@ from typing import Optional
import torch
def _get_rotation_to_best_fit_xy(
points: torch.Tensor, centroid: torch.Tensor
def get_rotation_to_best_fit_xy(
points: torch.Tensor, centroid: Optional[torch.Tensor] = None
) -> torch.Tensor:
"""
Returns a rotation r such that points @ r has a best fit plane
Returns a rotation R such that `points @ R` has a best fit plane
parallel to the xy plane
Args:
points: (N, 3) tensor of points in 3D
centroid: (3,) their centroid
points: (*, N, 3) tensor of points in 3D
centroid: (*, 1, 3), (3,) or scalar: their centroid
Returns:
(3,3) tensor rotation matrix
(*, 3, 3) tensor rotation matrix
"""
points_centered = points - centroid[None]
return torch.linalg.eigh(points_centered.t() @ points_centered)[1][:, [1, 2, 0]]
if centroid is None:
centroid = points.mean(dim=-2, keepdim=True)
points_centered = points - centroid
_, evec = torch.linalg.eigh(points_centered.transpose(-1, -2) @ points_centered)
# in general, evec can form either right- or left-handed basis,
# but we need the former to have a proper rotation (not reflection)
return torch.cat(
(evec[..., 1:], torch.cross(evec[..., 1], evec[..., 2])[..., None]), dim=-1
)
def _signed_area(path: torch.Tensor) -> torch.Tensor:
@@ -191,7 +199,7 @@ def fit_circle_in_3d(
Circle3D object
"""
centroid = points.mean(0)
r = _get_rotation_to_best_fit_xy(points, centroid)
r = get_rotation_to_best_fit_xy(points, centroid)
normal = r[:, 2]
rotated_points = (points - centroid) @ r
result_2d = fit_circle_in_2d(