  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.
