title: Flexible Isosurface Extraction for Gradient-Based Mesh Optimization
summary: 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.
paper_authors._id: 64d5a750505306fcd2a03332
paper_authors.name: Tianchang Shen
paper_authors._id: 64d5a750505306fcd2a03333
paper_authors.name: Jacob Munkberg
paper_authors._id: 64d5a750505306fcd2a03334
paper_authors.name: Jon Hasselgren
paper_authors._id: 64d5a750505306fcd2a03335
paper_authors.name: Kangxue Yin
paper_authors._id: 64d5a750505306fcd2a03336
paper_authors.name: Zian Wang
paper_authors._id: 64d5a750505306fcd2a03337
paper_authors.name: Wenzheng Chen
paper_authors._id: 64d5a750505306fcd2a03338
paper_authors.name: Zan Gojcic
paper_authors._id: 64d5a750505306fcd2a03339
paper_authors.name: Sanja Fidler
paper_authors._id: 64d5a750505306fcd2a0333a
paper_authors.name: Nicholas Sharp
paper_authors._id: 64d5a750505306fcd2a0333b
paper_authors.name: Jun Gao
paper_title: Flexible Isosurface Extraction for Gradient-Based Mesh Optimization
paper_summary: 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.
paper_ai_keywords: gradient-based mesh optimization isosurface scalar field Marching Cubes Dual Contouring FlexiCubes automatic differentiation Dual Marching Cubes tetrahedral meshes hierarchically-adaptive meshes