TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization

TL;DR

TetWeave introduces a flexible, on-the-fly tetrahedral grid method for isosurface extraction that produces high-quality, adaptive meshes with minimal memory, suitable for various computer graphics and vision tasks.

Contribution

It presents a novel approach combining Delaunay tetrahedral grids with gradient-based optimization for improved isosurface extraction.

Findings

Produces watertight, two-manifold, intersection-free meshes

Achieves near-linear memory scaling with mesh size

Effective in multi-view 3D reconstruction and mesh compression

Abstract

We introduce TetWeave, a novel isosurface representation for gradient-based mesh optimization that jointly optimizes the placement of a tetrahedral grid used for Marching Tetrahedra and a novel directional signed distance at each point. TetWeave constructs tetrahedral grids on-the-fly via Delaunay triangulation, enabling increased flexibility compared to predefined grids. The extracted meshes are guaranteed to be watertight, two-manifold and intersection-free. The flexibility of TetWeave enables a resampling strategy that places new points where reconstruction error is high and allows to encourage mesh fairness without compromising on reconstruction error. This leads to high-quality, adaptive meshes that require minimal memory usage and few parameters to optimize. Consequently, TetWeave exhibits near-linear memory scaling relative to the vertex count of the output mesh - a substantial improvement over predefined grids. We demonstrate the applicability of TetWeave to a broad range of challenging tasks in computer graphics and vision, such as multi-view 3D reconstruction, mesh compression and geometric texture generation.