Efficient surrogate for Wasserstein-barycenter interpolation

Find a computationally cheap surrogate for Wasserstein-barycenter interpolation when constructing resampled Gaussian splats, replacing the costly optimization required to compute barycenters of Gaussian distributions while supporting interpolation of splat rotations.

Background

The resampling method uses a precomputed dictionary of Gaussian-splat decompositions and currently selects the closest dictionary entry. The authors discuss possible interpolation strategies for opacity and rotation. For rotations, they identify the Wasserstein barycenter as a principled option because the barycenter of Gaussian distributions remains Gaussian, but computing it requires solving an optimization problem during resampling, which is considered too costly in practice.

The unresolved task is therefore to develop a cheaper approximation or surrogate for Wasserstein-barycenter computation that could make more consistent rotation interpolation practical within the dictionary-based resampling pipeline.