Automatic classification of deformable shapes

11/04/2022

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by   Hossein Dabirian, et al.

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