Reversible Harmonic Maps between Discrete Surfaces

TL;DR

This paper introduces a novel method for computing reversible harmonic maps directly between triangle meshes, improving accuracy and feature preservation across diverse geometries without relying on intermediate domains.

Contribution

It presents a new approach that optimizes for harmonicity and reversibility, handling various input types and geometries, outperforming existing methods in conformal distortion.

Findings

Lower conformal distortion than state-of-the-art methods

Successfully maps key features of input shapes

Applicable to diverse geometries and input data types

Abstract

Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can sometimes be computed between nearly-isometric meshes, the more general case of meshes with diverse geometries remains challenging. We propose a novel approach for direct map computation between triangle meshes without mapping to an intermediate domain, which optimizes for the harmonicity and reversibility of the forward and backward maps. Our method is general both in the information it can receive as input, e.g. point landmarks, a dense map or a functional map, and in the diversity of the geometries to which it can be applied. We demonstrate that our maps exhibit lower conformal distortion than the state-of-the-art, while succeeding in correctly mapping key features of the input shapes.