Title: MeshMoment: A Moment-Based Loss Function for 3D Learning on Meshes
Primary area: learning on graphs and other geometries & topologies
Keywords: 3D Meshes, Moment Loss, Geometric Loss

Abstract: In this paper, we address issues related to defining evaluation metrics and losses natively over meshes without resorting to intermediate representations. We demonstrate and discuss the pitfalls of commonly used intermediate representations - voxels and pointclouds - and propose a novel class of loss functions based on moments that can be calculated natively on meshes. The losses can be defined over both surfaces and volumes, and we investigate the vectorizability of computing moment losses and provide fully vectorized efficient implementations. We also expose their salient features which include differentiability, rigorous error bounds, and numerical stability. These loss functions can be applied towards various machine learning tasks like 3D reconstruction and Physics-Informed Neural Networks.

TL;DR: We proposed a loss function based on Geometric Moment to optimize machine learning tasks related to meshes