TetraSDF: Precise Mesh Extraction with Multi-resolution Tetrahedral Grid
This addresses the problem of precise mesh extraction for 3D reconstruction and graphics applications, offering an incremental improvement over existing methods by extending analytic approaches to more complex neural networks.
The paper tackles the challenge of extracting meshes that exactly match the zero-level set of neural signed distance functions (SDFs) by introducing TetraSDF, a precise analytic meshing framework that uses a multi-resolution tetrahedral positional encoder. It matches or surpasses existing grid-based encoders in SDF reconstruction accuracy and produces highly self-consistent meshes with practical runtime and memory efficiency.
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.