SDLKF: Signed Distance Linear Kernel Function for surface reconstruction

Abstract

In this paper, we introduce a novel explicit representation for surface reconstruction from multi-view images, named Signed Distance Linear Kernel Function (SDLFK), which simultaneously allows fast rendering and accurate surface reconstruction. The key insight is to use linear kernels to fit the Signed Distance Function (SDF) which has an analytic solution for volume rendering instead of numeric approximation. Specifically, the linear kernel function is defined within ellipsoids and calculated as the signed distance to the principal plane. For each ellipsoid intersected by rays, the expected depth and transmittance can be calculated through volume rendering with a closed-form solution. This procedure allows seamless switching between soft and hard surfaces, where the former facilitates optimization and the latter ensures precise reconstruction. Our evaluations demonstrate that our method improves the detailed geometry compared to state-of-the-art methods while maintaining fast and high-fidelity rendering.