Summary:
Introduce methods to approximate the radii of conical frustums along rays as described in [MipNerf](https://arxiv.org/abs/2103.13415):
- Two new attributes are added to ImplicitronRayBundle: bins and radii. Bins is of size n_pts_per_ray + 1. It allows us to manipulate easily and n_pts_per_ray intervals. For example we need the intervals coordinates in the radii computation for \(t_{\mu}, t_{\delta}\). Radii are used to store the radii of the conical frustums.
- Add 3 new methods to compute the radii:
- approximate_conical_frustum_as_gaussians: It computes the mean along the ray direction, the variance of the
conical frustum with respect to t and variance of the conical frustum with respect to its radius. This
implementation follows the stable computation defined in the paper.
- compute_3d_diagonal_covariance_gaussian: Will leverage the two previously computed variances to find the
diagonal covariance of the Gaussian.
- conical_frustum_to_gaussian: Mix everything together to compute the means and the diagonal covariances along
the ray of the Gaussians.
- In AbstractMaskRaySampler, introduces the attribute `cast_ray_bundle_as_cone`. If False it won't change the previous behaviour of the RaySampler. However if True, the samplers will sample `n_pts_per_ray +1` instead of `n_pts_per_ray`. This points are then used to set the bins attribute of ImplicitronRayBundle. The support of HeterogeneousRayBundle has not been added since the current code does not allow it. A safeguard has been added to avoid a silent bug in the future.
Reviewed By: shapovalov
Differential Revision: D45269190
fbshipit-source-id: bf22fad12d71d55392f054e3f680013aa0d59b78
29b8ebd802