Shape extraction from Gaussian primitives

Determine a principled procedure for extracting 3D shape (e.g., depth or surfaces) directly from the 3D Gaussian primitives used in Gaussian Splatting, replacing heuristic rules and enabling reliable, multi-view-consistent reconstruction.

Background

Gaussian Splatting represents scenes with 3D Gaussian primitives and achieves real-time novel view synthesis, but these primitives do not inherently define a surface. Prior shape reconstruction methods built on Gaussian Splatting have relied on heuristic depth or surface extraction, which reduces cross-view consistency and makes optimization sensitive to floaters.

The paper proposes a theoretical grounding by treating Gaussian primitives as stochastic solids, aiming to supply a canonical geometry field and volumetric attenuation model. The abstract explicitly notes that shape extraction from Gaussian primitives is an open problem, motivating the development of their geometry-grounded approach.