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Uniform discritization of SO(3) via random rotation matrices #28

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merged 16 commits into from
Apr 3, 2022
Merged

Uniform discritization of SO(3) via random rotation matrices #28

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eda1512
Random rotations
Mar 28, 2022
ca187c8
np.dot was the wrong operator. This is too, but its closer to the cor…
Mar 28, 2022
f4b7d13
Implemented random version (correctly)
Mar 29, 2022
cbd542f
Format code with black
deepsource-autofix[bot] Mar 29, 2022
319d860
Removed healpy import
Mar 29, 2022
1bb8c31
Merge branch 'itr_ref_grid_so3' of github.com:compSPI/reconstructSPI …
Mar 29, 2022
c9d0335
Untested geomstats implementation
Mar 29, 2022
c315164
Geomstats import
Mar 29, 2022
69c6058
Format code with black
deepsource-autofix[bot] Mar 29, 2022
e7a649a
Fixed rotations to include negatives to cover entire space
Mar 30, 2022
b74ad6d
Merge branch 'dev' of github.com:compSPI/reconstructSPI into itr_ref_…
Mar 31, 2022
e353f0f
Geomstats is a pip package
Apr 2, 2022
701891e
Import changes. verifying with black.
Apr 2, 2022
d51f0bc
Updated docstring
Apr 2, 2022
b251e5c
Trying pre-commit to see if it fixes the imports
Apr 2, 2022
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deepsource-autofix[bot] Apr 2, 2022
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1 change: 1 addition & 0 deletions environment.yml
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Expand Up @@ -15,4 +15,5 @@ dependencies:
- pytorch
- pip :
- git+https://github.com/compSPI/simSPI.git
- geomstats

6 changes: 5 additions & 1 deletion reconstructSPI/iterative_refinement/expectation_maximization.py
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Expand Up @@ -2,6 +2,7 @@

import numpy as np
from simSPI.transfer import eval_ctf
from geomstats.geometry import special_orthogonal


class IterativeRefinement:
Expand Down Expand Up @@ -290,7 +291,10 @@ def grid_SO3_uniform(n_rotations):
Array describing rotations.
Shape (n_rotations, 3, 3)
"""
rots = np.ones((n_rotations, 3, 3))
geom = special_orthogonal.SpecialOrthogonal(3, "matrix")
rots = geom.random_uniform(n_rotations)
negatives = np.tile(np.random.randint(2, size=n_rotations) * 2 - 1, (3, 3, 1)).T
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I think you are negating every second rotation. A bit opaque in how the tiling works, so I would put a note in the docstring, or the variable name indicating how you are scaling each rotation by +1 or -1, with one random number per rotation.

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I'll add a note to the docstring. The reason for this is that geomstats only rotates on a half-sphere. So, I invert the rotations randomly in order to cover the entire sphere (I validated the functionality in a jupyter notebook and am happy to post images confirming this behaviour)

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@geoffwoollard geoffwoollard Apr 2, 2022 •
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Yes I recall this. Great work! Put as much as you can of that in the docstring and tests so that it doesn't go to waste.

The test has to be better than checking for the shape. For sure orthonormality

  • orthogonality: each R.dot(R.T) is close np.eye(3)
  • normality: np.linalg.det(R) is close 1

And I think something for uniformity would be great. If you can come up with some heuristic, would be a nice start. Doesn't have to be rigorous, just protest against a bad fail case. Some ideas (that work with large # of rotations)

  • project to the three coordinates used to plot on sphere. Check roughly same amount above/below, through the three axes (up/down; left/right; front/back)
  • convert to some encoding (Euler angles???) and check stats on those encoding (I think two Euler angles (ZYZ or ZXZ) are uniform and one is not)
  • integrate with an even function (e.g. x2 + y2 + z2) that should be double the integration on half. If the function is odd (e.g. x3 + y3 + z3) it should integrate to roughly one.
    • even: (axis_3_vectors[half_idx]**2).sum() is close 2*axis_3_vectors.sum()
    • odd: (axis_3_vectors[half_idx]**3).sum() is close 0

Made issue here for ref: #39

rots[:] *= negatives
return rots

@staticmethod
Expand Down