Modeling 3DGS primitives with dual registration and rendering roles

Determine how a 3D Gaussian Splatting primitive should be modeled for registration when its covariance is also optimized by photometric error for rendering.

Background

The paper discusses uncertainty-weighted registration methods such as Generalized ICP, in which point-cloud covariances can be derived from RGB-D sensor uncertainty estimates. In 3D Gaussian Splatting SLAM, however, the Gaussian covariance may simultaneously serve as a rendering parameter optimized by photometric error and as a metric uncertainty used for geometric registration.

The unresolved issue concerns how to represent or model the primitive in this dual-purpose setting. The paper addresses the issue through a dual-covariance parameterization, but the broader modeling question is explicitly identified as remaining open in the related-work discussion.