Geometry Field Splatting with Gaussian Surfels
This addresses the problem of accurate 3D surface reconstruction from images for computer vision applications, representing an incremental advancement over existing volumetric methods.
The paper tackles the challenge of geometric reconstruction of opaque surfaces from images by adapting Gaussian kernels to splat geometry fields instead of volumes, enabling precise reconstruction of opaque solids. They demonstrate significant improvement in reconstructed 3D surface quality on widely-used datasets.
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.