SDFoam: Signed-Distance Foam for explicit surface reconstruction

2025-12-18

AI Summary

Existing NeRF and 3D Gaussian Splatting (3DGS) methods achieve high-quality novel view synthesis but suffer from low mesh reconstruction accuracy and topological instability. To address this, we propose a joint optimization framework integrating implicit signed distance functions (SDFs) with explicit Voronoi diagrams. Our key innovation is a novel coupling mechanism wherein the SDF guides Voronoi cell faces toward the zero-level set, enforced via ray tracing and Eikonal equation regularization. This enables high-fidelity, topologically consistent surface reconstruction while preserving real-time rendering performance. Experiments demonstrate substantial improvements: significant reduction in Chamfer distance; PSNR and SSIM competitive with RadiantFoam; reduced floating-point noise; enhanced topological integrity; and maintained training efficiency.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

Neural radiance fields (NeRF) have driven impressive progress in view synthesis by using ray-traced volumetric rendering. Splatting-based methods such as 3D Gaussian Splatting (3DGS) provide faster rendering by rasterizing 3D primitives. RadiantFoam (RF) brought ray tracing back, achieving throughput comparable to Gaussian Splatting by organizing radiance with an explicit Voronoi Diagram (VD). Yet, all the mentioned methods still struggle with precise mesh reconstruction. We address this gap by jointly learning an explicit VD with an implicit Signed Distance Field (SDF). The scene is optimized via ray tracing and regularized by an Eikonal objective. The SDF introduces metric-consistent isosurfaces, which, in turn, bias near-surface Voronoi cell faces to align with the zero level set. The resulting model produces crisper, view-consistent surfaces with fewer floaters and improved topology, while preserving photometric quality and maintaining training speed on par with RadiantFoam. Across diverse scenes, our hybrid implicit-explicit formulation, which we name SDFoam, substantially improves mesh reconstruction accuracy (Chamfer distance) with comparable appearance (PSNR, SSIM), without sacrificing efficiency.

Problem

• Improves mesh reconstruction accuracy from neural radiance fields
• Combines explicit Voronoi diagram with implicit signed distance field
• Reduces artifacts like floaters while preserving rendering efficiency

Innovation

• Hybrid implicit-explicit formulation with Signed Distance Field
• Ray tracing optimization regularized by Eikonal objective
• Voronoi cell faces aligned to zero level set