Learning Joint Surface Atlases

TL;DR

This paper introduces a novel method for learning continuous, topologically flexible surface atlases with bidirectional mappings, improving surface representation and applications like texture transfer and correspondence estimation.

Contribution

It proposes learning a continuous 2D domain with arbitrary topology and consistent bidirectional mappings, enhancing surface representations over prior fixed-domain methods.

Findings

Improved surface representation quality over baselines

Enhanced consistency in shape collections

Better performance in texture transfer and correspondence tasks

Abstract

This paper describes new techniques for learning atlas-like representations of 3D surfaces, i.e. homeomorphic transformations from a 2D domain to surfaces. Compared to prior work, we propose two major contributions. First, instead of mapping a fixed 2D domain, such as a set of square patches, to the surface, we learn a continuous 2D domain with arbitrary topology by optimizing a point sampling distribution represented as a mixture of Gaussians. Second, we learn consistent mappings in both directions: charts, from the 3D surface to 2D domain, and parametrizations, their inverse. We demonstrate that this improves the quality of the learned surface representation, as well as its consistency in a collection of related shapes. It thus leads to improvements for applications such as correspondence estimation, texture transfer, and consistent UV mapping. As an additional technical contribution, we outline that, while incorporating normal consistency has clear benefits, it leads to issues in the optimization, and that these issues can be mitigated using a simple repulsive regularization. We demonstrate that our contributions provide better surface representation than existing baselines.