Structured Representation for Non-Planar Regions

Develop a structured representation for non-planar surface regions in scenes that integrates with the GSPlane framework for Gaussian Splatting, enabling Gaussians associated with curved or irregular surfaces to be re-parameterized and optimized under appropriate non-planar constraints.

Background

GSPlane introduces a structured representation for planar regions by re-parameterizing Gaussian centers as normalized combinations of three non-collinear basis points defining each plane. This enforces geometric consistency for planar Gaussians during training and enables mesh layout refinement that produces topologically coherent, low-vertex meshes in planar areas.

Despite these advances for planes, GSPlane does not provide an analogous structured parameterization for non-planar regions. Extending the approach beyond planes to handle curved or irregular surfaces is identified as an open challenge, which would broaden the applicability of structured constraints and improve mesh quality across the entire scene.