Automatic classification of deformable shapes

• URL: http://arxiv.org/abs/2211.02530v1
• Date: Fri, 4 Nov 2022 15:44:56 GMT
• Title: Automatic classification of deformable shapes
• Authors: Hossein Dabirian and Radmir Sultamuratov and James Herring and Carlos El Tallawi and William Zoghbi and Andreas Mang and Robert Azencott
• Abstract summary: Let $mathcalD$ be a dataset of smooth 3D-surfaces, partitioned into disjoint classes $mathitCL_j$, $j= 1, ldots, k$. We show how optimized diffeomorphic registration applied to large numbers of pairs $S,S' in mathcalD$ to implement automatic classification on $mathcalD$. We generate classifiers invariant by rigid motions in $mathbbR3$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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