基於梯度的網格優化的彈性等值面提取

摘要

本研究考慮基於梯度的網格優化，通過將三維表面網格表示為標量場的等值面，逐步進行優化。這種方法在包括攝影測量、生成建模和反物理學等應用中越來越常見。現有的實現適應了經典的等值面提取算法，如Marching Cubes或Dual Contouring；這些技術旨在從固定的已知場中提取網格，在優化設置中，它們缺乏表示高質量保留特徵網格的自由度，或者受到數值不穩定性的影響。我們引入了FlexiCubes，這是一種專門設計用於根據幾何、視覺甚至物理目標優化未知網格的等值面表示。我們的主要見解是引入額外精心選擇的參數到表示中，這些參數允許對提取的網格幾何和連接進行局部靈活調整。這些參數與基礎標量場一起通過自動微分進行更新，用於優化下游任務。我們基於Dual Marching Cubes提出了提取方案以改善拓撲性質，並提出了擴展以選擇性生成四面體和階層自適應網格。廣泛的實驗驗證了FlexiCubes在合成基準和真實應用中的效果，表明它在網格質量和幾何保真度方面提供了顯著改進。

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.

基於梯度的網格優化的彈性等值面提取

Flexible Isosurface Extraction for Gradient-Based Mesh Optimization

摘要

Support