TetraSDF: Precise Mesh Extraction with Multi-resolution Tetrahedral Grid

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.