Stochastic Signed Distance Processes

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AI Summary

This work addresses the strong reliance on silhouette supervision and inadequate uncertainty quantification in multi-view surface reconstruction by proposing the Stochastic Signed Distance Process (SSDP). SSDP models the signed distance field (SDF) along rays as a stochastic process and introduces a first-hitting-time distribution to enable probabilistic volume rendering. By deriving the first-hitting probability over sampling intervals via Bayesian filtering, the method establishes a differentiable probabilistic rendering framework, of which NeuS emerges as a special case. Evaluated on the DTU and MobileBrick datasets, the approach significantly outperforms existing baselines, achieving superior reconstruction accuracy and more reliable uncertainty estimates—all without requiring silhouette supervision.

Abstract

Multi-view surface reconstruction is a core problem in computer vision. One prominent line of work represents the surface implicitly as a signed distance field (SDF), optimizing it based on the photometric loss between rendered and observed pixel colors. These approaches typically employ SDF-based volume rendering to obtain a differentiable relaxation of discontinuous visibility along rays, thereby reducing reliance on silhouette supervision. In this paper, we reformulate SDF-based volume rendering as probabilistic surface rendering, where each pixel color is modeled as a mixture distribution induced by the random first ray-surface intersection. To this end, we introduce Stochastic Signed Distance Processes (SSDP), which model the SDF along each ray as a stochastic process, inducing a first-passage-time distribution for each ray. We then derive the first-passage probability for each sampling interval based on Bayesian filtering, together with its practical approximation for parallel rendering. We further show that NeuS, an existing SDF-based volume rendering method, arises as a special case of our formulation. Experiments on the DTU and MobileBrick datasets demonstrate that our method outperforms baselines in both surface reconstruction and uncertainty quantification, supporting the effectiveness of our first-passage formulation. Our code is available at https://github.com/skmhrk1209/SSDP.

Problem

• multi-view surface reconstruction
• signed distance field
• volume rendering
• first-passage time
• uncertainty quantification

Innovation

• Stochastic Signed Distance Processes
• first-passage-time distribution
• probabilistic surface rendering
• Bayesian filtering
• implicit surface reconstruction