numerical instability in compositing.norm_weighted_sum

[polarbart]

This PR fixes a numerical instability in norm_weighted_sum on cpu and cuda.

When points_idx only contains one point with a small weight (<1e-4) the gradient gets disproportionately large.

Reason:
For numerical stability the normalization scalar (the sum of the weights/alphas) is clipped at 1e-4. However, this clipping isn't applied to the weighted sum of the features in the numerator.
If the sum of the weights is small the numerator then has a large value which results in an unwanted large gradient.

Fix:
Just clip the normalization scalar for the denominator and not for the numerator.
This also ensures the numerical stability for which the clipping was originally intended.

Code example:

import torch
from pytorch3d.renderer.compositing import norm_weighted_sum

pointsidx = torch.zeros(1, 1, 1, 1, dtype=torch.int64)
alphas = torch.full((1, 1, 1, 1), 1e-10, requires_grad=True)
pt_clds = torch.ones(1, 1)

out = norm_weighted_sum(pointsidx, alphas, pt_clds)
out.sum().backward()
print(f'value:    {out.item()}')
print(f'gradient: {alphas.grad.item()}')

Results of current master:

value:    9.999999974752427e-07
gradient: 9999.990234375

Results with this branch:

value:    9.999999974752427e-07
gradient: 0.0

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[github-actions]

This PR is stale because it has been open 45 days with no activity. Remove stale label or comment or this will be closed in 10 days.

[github-actions]

This PR is stale because it has been open 45 days with no activity. Remove stale label or comment or this will be closed in 10 days.