Flexible Isosurface Extraction for Gradient-Based Mesh Optimization

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