HodgeNet: learning spectral geometry on triangle meshes

Fig. 1. Mesh segmentation results on the full-resolution MIT animation dataset. Each mesh in the dataset contains 20,000 faces (10,000 vertices). We show an example ground truth segmentation in the bottom-left. In contrast to previous works, which downsample each mesh by more than 10×, we efficiently process dense meshes both at train and test time.

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.