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

2025-05-07

AI Summary

In gradient-based isosurface optimization, tightly coupling tetrahedral mesh topology with signed distance fields (SDFs) remains challenging, often yielding non-watertight or self-intersecting meshes. To address this, we propose TetWeave—a joint optimization framework for differentiable isosurface extraction. Its core innovation lies in dynamically constructing Delaunay tetrahedral meshes while co-optimizing vertex positions and an orientation-aware signed distance field (OSDF), guaranteeing watertight, 2-manifold, and self-intersection-free adaptive meshes. TetWeave incorporates error-driven resampling and surface fairness constraints, achieving memory complexity approximately linear in the number of output vertices. Experiments demonstrate state-of-the-art performance across multi-view reconstruction, mesh compression, and geometric texture synthesis—significantly outperforming fixed-resolution implicit representations.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning with Manifolds
• Computer Vision: 3D Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• Optimizes tetrahedral grid placement for mesh reconstruction
• Ensures watertight, manifold meshes without intersections
• Enables adaptive resampling for high reconstruction accuracy

Innovation

• On-the-fly Delaunay tetrahedral grid construction
• Joint optimization of grid and directional distance
• Adaptive resampling for high reconstruction accuracy