HodgeNet: Learning Spectral Geometry on Triangle Meshes

Dmitriy Smirnov; Justin Solomon

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arXiv · 2104.12826

HodgeNet: Learning Spectral Geometry on Triangle Meshes

Dmitriy Smirnov·Justin Solomon

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Abstract

Constrained by the limitations of learning toolkits engineered for other applications, such as those in image processing, many mesh-based learning algorithms employ data flows that would be atypical from the perspective of conventional geometry processing. As an alternative, we present a technique for learning from meshes built from standard geometry processing modules and operations. We show that low-order eigenvalue/eigenvector computation from operators parameterized using discrete exterior calculus is amenable to efficient approximate backpropagation, yielding spectral per-element or per-mesh features with similar formulas to classical descriptors like the heat/wave kernel signatures. Our model uses few parameters, generalizes to high-resolution meshes, and exhibits performance and time complexity on par with past work.

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BibTeX RIS

Dmitriy Smirnov, Justin Solomon. 2021-04-26. HodgeNet: Learning Spectral Geometry on Triangle Meshes. https://arxiv.org/abs/2104.12826

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