Geometry Field Splatting with Gaussian Surfels

TL;DR

This paper introduces a novel differentiable rendering method for geometry fields using Gaussian surfels, improving 3D surface reconstruction quality by addressing discontinuities and better modeling specular reflections.

Contribution

It presents an efficient, nearly exact differentiable rendering algorithm for Gaussian surfels, and introduces techniques to ensure color continuity and better handle specular surfaces.

Findings

Improved 3D surface reconstruction quality on standard datasets.

Developed a differentiable rendering algorithm removing previous approximations.

Enhanced modeling of specular reflections using spherical harmonics encoded reflection vectors.

Abstract

Geometric reconstruction of opaque surfaces from images is a longstanding challenge in computer vision, with renewed interest from volumetric view synthesis algorithms using radiance fields. We leverage the geometry field proposed in recent work for stochastic opaque surfaces, which can then be converted to volume densities. We adapt Gaussian kernels or surfels to splat the geometry field rather than the volume, enabling precise reconstruction of opaque solids. Our first contribution is to derive an efficient and almost exact differentiable rendering algorithm for geometry fields parameterized by Gaussian surfels, while removing current approximations involving Taylor series and no self-attenuation. Next, we address the discontinuous loss landscape when surfels cluster near geometry, showing how to guarantee that the rendered color is a continuous function of the colors of the kernels, irrespective of ordering. Finally, we use latent representations with spherical harmonics encoded reflection vectors rather than spherical harmonics encoded colors to better address specular surfaces. We demonstrate significant improvement in the quality of reconstructed 3D surfaces on widely-used datasets.