Automatic classification of deformable shapes

2022/11/04 by Hossein Dabirian, Dabirian, Hossein, Radmir Sultamuratov +11
Computer Science · Engineering · #37C05 #3D Shape Modeling and Analysis #49K15 #49M05 #62H30 #65K10 #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Image Processing and 3D Reconstruction #Machine Learning (cs.LG) #Medical Image Segmentation Techniques #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2211.02530

openalex publication_date 2022/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 ℝ³. 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:ℝ³ → ℝ³. Finally, we test our automatic classification methods on a cardiology data base of discretized mitral valve surfaces.

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