Title: Guaranteed Bounding Meshes Extraction from Neural Implicit Surfaces via Neural Network Verification
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Neural Verification, Bounding Volume, Rendering, Simulation

Abstract: Geometric queries on neural implicit surfaces, such as ray tracing and collision detection, present a significant challenge since they require explicit spatial reasoning over neural networks. This work addresses this challenge by connecting these geometric queries to neural network verification problems. Inspired by the state-of-the-art neural verification tools, we propose a new framework utilizing linear bound propagation-based verifiers to solve these queries in real time, enabling applications such as real-time rendering and physics simulation with soundness guarantees. Instead of naively running neural network verifiers on-the-fly, we first classify a 3D input domain into multiple regions of interest, which can then assist in subsequent verifications. We achieve this objective by constructing explicit bounding volumes and then leveraging linear bounds generated by SOTA neural network verifiers to guide the generation of \emph{sound piecewise linear bounding meshes}. In this paper, we propose Guaranteed Inner-and-Outer Meshes (GIOM), which can serve as bounding volumes and merge seamlessly with existing explicit geometry processors to accelerate queries on neural implicits. As tight and \emph{sound} bounding meshes, GIOM enables accelerated neural SDF queries without sacrificing quality. With GIOM, we develop accelerated neural implicit ray casting, collision detection, and constructive solid geometry methods (CSG), achieving up to a 300\% speedup in real-time rendering, a 500\% speedup in physics simulation, and an optimization-free neural CSG procedure. 
Experiments show that GIOM significantly outperforms existing methods in the speed-quality trade‑off.