Marching Neurons: Accurate Surface Extraction for Neural Implicit Shapes

2025-09-25

AI Summary

Traditional implicit surface extraction methods (e.g., Marching Cubes) suffer from geometric distortion and loss of fine details due to fixed voxel resolution. To address this, we propose an analytical surface tracing method tailored for neural implicit functions—such as signed distance function (SDF) networks—that leverages the spatial partitioning induced by neuron activations. Our approach employs a depth-first traversal strategy that enables discretization-free, sampling-free, and parallel surface extraction. By directly analyzing the internal geometric structure encoded in the network, it bypasses explicit spatial decomposition while preserving real-time performance and significantly improving reconstruction accuracy. Experiments demonstrate that our method consistently reconstructs high-fidelity triangle meshes across diverse neural architectures and complex topologies, achieving superior detail preservation without compromising computational efficiency.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: 3D Computer Vision
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Accurate surface geometry representation is crucial in 3D visual computing. Explicit representations, such as polygonal meshes, and implicit representations, like signed distance functions, each have distinct advantages, making efficient conversions between them increasingly important. Conventional surface extraction methods for implicit representations, such as the widely used Marching Cubes algorithm, rely on spatial decomposition and sampling, leading to inaccuracies due to fixed and limited resolution. We introduce a novel approach for analytically extracting surfaces from neural implicit functions. Our method operates natively in parallel and can navigate large neural architectures. By leveraging the fact that each neuron partitions the domain, we develop a depth-first traversal strategy to efficiently track the encoded surface. The resulting meshes faithfully capture the full geometric information from the network without ad-hoc spatial discretization, achieving unprecedented accuracy across diverse shapes and network architectures while maintaining competitive speed.

Problem

• Conventional surface extraction methods suffer from fixed resolution limitations
• Existing algorithms like Marching Cubes cause inaccuracies due to spatial sampling
• Efficient conversion between implicit and explicit 3D representations remains challenging

Innovation

• Analytical surface extraction from neural implicit functions
• Depth-first traversal strategy tracking encoded surfaces
• Native parallel processing for large neural architectures