Automatic classification of deformable shapes

TL;DR

This paper presents a method for automatic classification of deformable 3D shapes using optimized diffeomorphic registration to generate invariant feature vectors, with applications demonstrated on cardiac mitral valve surfaces.

Contribution

It introduces a novel approach combining diffeomorphic registration, surface interpolation, and random perturbations to improve shape classification accuracy.

Findings

Effective classification of deformable shapes achieved

Enhanced class representation via surface interpolation

Robustness tested on cardiac mitral valve data

Abstract

Let $\mathcal{D}$ be a dataset of smooth 3D-surfaces, partitioned into disjoint classes $\mathit{CL}_j$, $j= 1, \ldots, k$. We show how optimized diffeomorphic registration applied to large numbers of pairs $S,S' \in \mathcal{D}$ can provide descriptive feature vectors to implement automatic classification on $\mathcal{D}$, and generate classifiers invariant by rigid motions in $\mathbb{R}^3$. To enhance accuracy of automatic classification, we enrich the smallest classes $\mathit{CL}_j$ by diffeomorphic interpolation of smooth surfaces between pairs $S,S' \in \mathit{CL}_j$. We also implement small random perturbations of surfaces $S\in \mathit{CL}_j$ by random flows of smooth diffeomorphisms $F_t:\mathbb{R}^3 \to \mathbb{R}^3$. Finally, we test our automatic classification methods on a cardiology data base of discretized mitral valve surfaces.