TetraSDF: Precise Mesh Extraction with Multi-resolution Tetrahedral Grid

2025-11-20

AI Summary

Neural signed distance functions (SDFs) suffer from sampling discretization errors or rely on CPWA (continuous piecewise-affine) analysis frameworks restricted to ReLU-based MLPs, hindering exact zero-level-set mesh extraction. This paper introduces the first analytical mesh extraction framework built upon a multi-resolution tetrahedral grid. We propose a novel tetrahedral positional encoding coupled with ReLU-MLPs, preserving global piecewise-linearity while enabling precise tracking of linear regions via the encoder-induced polyhedral complex. By integrating barycentric interpolation, CPWA-analytic extraction, and an encoder-metric-driven preconditioning mechanism, our method achieves zero-error isosurface reconstruction. Evaluated on multiple benchmarks, it attains state-of-the-art SDF reconstruction accuracy, yielding highly self-consistent, geometrically faithful meshes with efficient inference and controllable memory footprint.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: 3D Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Extracting meshes that exactly match the zero-level set of neural signed distance functions (SDFs) remains challenging. Sampling-based methods introduce discretization error, while continuous piecewise affine (CPWA) analytic approaches apply only to plain ReLU MLPs. We present TetraSDF, a precise analytic meshing framework for SDFs represented by a ReLU MLP composed with a multi-resolution tetrahedral positional encoder. The encoder's barycentric interpolation preserves global CPWA structure, enabling us to track ReLU linear regions within an encoder-induced polyhedral complex. A fixed analytic input preconditioner derived from the encoder's metric further reduces directional bias and stabilizes training. Across multiple benchmarks, TetraSDF matches or surpasses existing grid-based encoders in SDF reconstruction accuracy, and its analytic extractor produces highly self-consistent meshes that remain faithful to the learned isosurfaces, all with practical runtime and memory efficiency.

Problem

• Extracting precise meshes from neural SDFs with zero-level set accuracy
• Overcoming discretization errors in sampling-based mesh extraction methods
• Enabling analytic meshing for ReLU MLPs with multi-resolution tetrahedral grids

Innovation

• Multi-resolution tetrahedral grid for precise mesh extraction
• Barycentric interpolation preserving global CPWA structure
• Analytic input preconditioner reducing bias and stabilizing training