基于梯度的网格优化的柔性等值面提取

摘要

本文考虑基于梯度的网格优化，通过将三维表面网格表示为标量场的等值面来进行迭代优化。这在包括摄影测量、生成建模和反物理学等应用中越来越常见。现有的实现采用了经典的等值面提取算法，如Marching Cubes或Dual Contouring；这些技术旨在从固定、已知的场中提取网格，在优化设置中缺乏表达高质量保持特征的网格的自由度，或者受到数值不稳定性的影响。我们引入了FlexiCubes，这是一种专门设计用于根据几何、视觉甚至物理目标优化未知网格的等值面表示。我们的主要见解是引入了额外精心选择的参数到表示中，允许对提取的网格几何和连接性进行局部灵活调整。这些参数会随着基础标量场一起通过自动微分进行更新，用于优化下游任务。我们基于Dual Marching Cubes设计了提取方案以改善拓扑特性，并提出了生成四面体和分层自适应网格的扩展。大量实验证实了FlexiCubes在合成基准和实际应用中的有效性，表明它在网格质量和几何保真度方面提供了显著改进。

English

This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry, generative modeling, and inverse physics. Existing implementations adapt classic isosurface extraction algorithms like Marching Cubes or Dual Contouring; these techniques were designed to extract meshes from fixed, known fields, and in the optimization setting they lack the degrees of freedom to represent high-quality feature-preserving meshes, or suffer from numerical instabilities. We introduce FlexiCubes, an isosurface representation specifically designed for optimizing an unknown mesh with respect to geometric, visual, or even physical objectives. Our main insight is to introduce additional carefully-chosen parameters into the representation, which allow local flexible adjustments to the extracted mesh geometry and connectivity. These parameters are updated along with the underlying scalar field via automatic differentiation when optimizing for a downstream task. We base our extraction scheme on Dual Marching Cubes for improved topological properties, and present extensions to optionally generate tetrahedral and hierarchically-adaptive meshes. Extensive experiments validate FlexiCubes on both synthetic benchmarks and real-world applications, showing that it offers significant improvements in mesh quality and geometric fidelity.

基于梯度的网格优化的柔性等值面提取

Flexible Isosurface Extraction for Gradient-Based Mesh Optimization

摘要

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