HodgeNet: Learning Spectral Geometry on Triangle Meshes

04/26/2021
by   Dmitriy Smirnov, et al.
0

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.

READ FULL TEXT
research
07/04/2022

Generalized Spectral Coarsening

Many computational algorithms applied to geometry operate on discrete re...
research
01/23/2022

Differential Geometry in Neural Implicits

We introduce a neural implicit framework that bridges discrete different...
research
01/31/2023

A cut finite element method for the heat equation on overlapping meshes: L^2-analysis for dG(0) mesh movement

We present a cut finite element method for the heat equation on two over...
research
05/04/2020

Neural Subdivision

This paper introduces Neural Subdivision, a novel framework for data-dri...
research
10/08/2022

Developable Quad Meshes

There are different ways to capture the property of a surface being deve...
research
06/01/2021

Integer Coordinates for Intrinsic Geometry Processing

In this work, we present a general, efficient, and provably robust repre...
research
10/18/2018

An Iterative Parallel Algorithm for Computing Geodesic Distances on Triangular Meshes

The computation of geodesic distances is an important research topic in ...

Please sign up or login with your details

Forgot password? Click here to reset