Coupled quasi-harmonic bases

TL;DR

This paper introduces a method to construct common approximate eigenbases for multiple shapes using joint diagonalization, improving shape analysis tasks like editing, pose transfer, and correspondence.

Contribution

It proposes a novel approach to generate compatible eigenbases across shapes, addressing limitations of independent Laplacian eigenbases in multi-shape applications.

Findings

Enhanced shape correspondence accuracy

Improved shape editing and pose transfer results

Demonstrated benefits on multiple shape analysis tasks

Abstract

The use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state-of-the-art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using classical tools from harmonic analysis on manifolds. However, many applications involving multiple shapes are obstacled by the fact that Laplacian eigenbases computed independently on different shapes are often incompatible with each other. In this paper, we propose the construction of common approximate eigenbases for multiple shapes using approximate joint diagonalization algorithms. We illustrate the benefits of the proposed approach on tasks from shape editing, pose transfer, correspondence, and similarity.