Voting for Distortion Points in Geometric Processing

TL;DR

This paper introduces an automatic voting-based method to detect distortion points on meshes, improving the quality of mesh parameterizations and related applications by robustly identifying key vertices with concentrated distortion.

Contribution

A novel voting strategy for automatic detection of distortion points on meshes, enhancing robustness over existing methods in geometric processing tasks.

Findings

Successfully detects distortion points on various meshes

Improves mesh parameterization quality

Outperforms state-of-the-art methods in robustness

Abstract

Low isometric distortion is often required for mesh parameterizations. A configuration of some vertices, where the distortion is concentrated, provides a way to mitigate isometric distortion, but determining the number and placement of these vertices is non-trivial. We call these vertices distortion points. We present a novel and automatic method to detect distortion points using a voting strategy. Our method integrates two components: candidate generation and candidate voting. Given a closed triangular mesh, we generate candidate distortion points by executing a three-step procedure repeatedly: (1) randomly cut an input to a disk topology; (2) compute a low conformal distortion parameterization; and (3) detect the distortion points. Finally, we count the candidate points and generate the final distortion points by voting. We demonstrate that our algorithm succeeds when employed on various closed meshes with a genus of zero or higher. The distortion points generated by our method are utilized in three applications, including planar parameterization, semi-automatic landmark correspondence, and isotropic remeshing. Compared to other state-of-the-art methods, our method demonstrates stronger practical robustness in distortion point detection.