Affine-invariant diffusion geometry for the analysis of deformable 3D shapes

TL;DR

This paper presents an affine-invariant diffusion geometry framework for analyzing deformable 3D shapes, enabling consistent analysis under squeeze and shear transformations by defining an invariant Laplacian.

Contribution

It introduces an affine-invariant metric and Laplacian for shape analysis, extending existing tools to handle affine deformations effectively.

Findings

Successfully captures shape features invariant to affine transformations

Enhances shape analysis robustness under deformation

Demonstrates improved shape comparison and recognition

Abstract

We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant Laplacian from which local and global geometric structures are extracted. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis.