Reproduce “Neural Surface Maps” on OpenResearch

About this paper

Luca Morreale, Noam Aigerman, Vladimir Kim, Niloy J. Mitra

Neural surface maps represent each surface as a differentiable function from a two-dimensional domain to three-dimensional space. The authors optimize coordinate remappings over fixed surface representations for distortion optimization. In a reported animal comparison, their method achieves median symmetric Dirichlet distortion of 8.56 and 0.03% triangle flips, versus 10,669 and 49.86% for Mandad et al.; bijectivity is not guaranteed.

Key insights

• Neural networks' inherent differentiability and composability are well-suited for encoding and optimizing complex surface maps, transforming traditionally combinatorial geometry problems into continuous, differentiable ones.
• By optimizing an internal neural map (h) that re-parameterizes a canonical domain, map properties can be manipulated and optimized without altering the underlying 3D geometry of the surface.
• This framework unifies various geometry processing tasks, from parameterization to surface correspondence across collections, under a single, modular, and scalable differentiable pipeline.

Summary by alphaXiv.