Not normalising control points by X.std()

Summary:
davnov134 found that the algorithm crashes if X is an axis-aligned plane. This is because I implemented scaling control points by `X.std()` as a poor man’s version of PCA whitening.
I checked that it does not bring consistent improvements, so let’s get rid of it.

The algorithm still results in slightly higher errors on the axis aligned planes but at least it does not crash. As a next step, I will experiment with detecting a planar case and using 3-point barycentric coordinates rather than 4-points.

Reviewed By: davnov134

Differential Revision: D21179968

fbshipit-source-id: 1f002fce5541934486b51808be0e910324977222

Author: shapovalov

pytorch3d/ops/__init__.py

@@ -6,6 +6,7 @@
 from .knn import knn_gather, knn_points
 from .mesh_face_areas_normals import mesh_face_areas_normals
 from .packed_to_padded import packed_to_padded, padded_to_packed
+from .perspective_n_points import efficient_pnp
 from .points_alignment import corresponding_points_alignment, iterative_closest_point
 from .points_normals import (
     estimate_pointcloud_local_coord_frames,

pytorch3d/ops/perspective_n_points.py

@@ -34,11 +34,10 @@ def _define_control_points(x, weight, storage_opts=None):
     """
     storage_opts = storage_opts or {}
     x_mean = oputil.wmean(x, weight)
-    x_std = oputil.wmean((x - x_mean) ** 2, weight) ** 0.5
     c_world = F.pad(torch.eye(3, **storage_opts), (0, 0, 0, 1), value=0.0).expand_as(
         x[:, :4, :]
     )
-    return c_world * x_std + x_mean
+    return c_world + x_mean
 
 
 def _compute_alphas(x, c_world):