Classification of Deformable Smooth Shapes Through Geodesic Flows of Diffeomorphisms

Hossein Dabirian; Radmir Sultamuratov; James Herring; Carlos El Tallawi; William Zoghbi; Andreas Mang; Robert Azencott

doi:10.1007/s10851-024-01211-z

Classification of Deformable Smooth Shapes Through Geodesic Flows of Diffeomorphisms

Hossein Dabirian, Radmir Sultamuratov, James Herring, Carlos El Tallawi, William Zoghbi, Andreas Mang, Robert Azencott

Research output: Contribution to journal › Article › peer-review

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^′), 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 the accuracy of shape 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 classification methods on a cardiology database of discretized mitral valve surfaces.

Original language	English (US)
Pages (from-to)	1033-1059
Number of pages	27
Journal	Journal of Mathematical Imaging and Vision
Volume	66
Issue number	6
DOIs	https://doi.org/10.1007/s10851-024-01211-z
State	Published - Dec 2024

Keywords

Classification of deformable smooth shapes
Data augmentation
Diffeomorphic shape matching
Random forests

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Condensed Matter Physics
Computer Vision and Pattern Recognition
Geometry and Topology
Applied Mathematics

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10.1007/s10851-024-01211-z

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abstract = "Let D be a dataset of smooth 3D surfaces, partitioned into disjoint classes CLj, j=1,…,k. We show how optimized diffeomorphic registration applied to large numbers of pairs (S,S′), 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 the accuracy of shape classification, we enrich the smallest classes CLj by diffeomorphic interpolation of smooth surfaces between pairs S,S′∈CLj. We also implement small random perturbations of surfaces S∈CLj by random flows of smooth diffeomorphisms Ft:R3→R3. Finally, we test our classification methods on a cardiology database of discretized mitral valve surfaces.",

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AU - Sultamuratov, Radmir

AU - Herring, James

AU - El Tallawi, Carlos

AU - Zoghbi, William

AU - Mang, Andreas

AU - Azencott, Robert

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

PY - 2024/12

Y1 - 2024/12

N2 - Let D be a dataset of smooth 3D surfaces, partitioned into disjoint classes CLj, j=1,…,k. We show how optimized diffeomorphic registration applied to large numbers of pairs (S,S′), 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 the accuracy of shape classification, we enrich the smallest classes CLj by diffeomorphic interpolation of smooth surfaces between pairs S,S′∈CLj. We also implement small random perturbations of surfaces S∈CLj by random flows of smooth diffeomorphisms Ft:R3→R3. Finally, we test our classification methods on a cardiology database of discretized mitral valve surfaces.

AB - Let D be a dataset of smooth 3D surfaces, partitioned into disjoint classes CLj, j=1,…,k. We show how optimized diffeomorphic registration applied to large numbers of pairs (S,S′), 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 the accuracy of shape classification, we enrich the smallest classes CLj by diffeomorphic interpolation of smooth surfaces between pairs S,S′∈CLj. We also implement small random perturbations of surfaces S∈CLj by random flows of smooth diffeomorphisms Ft:R3→R3. Finally, we test our classification methods on a cardiology database of discretized mitral valve surfaces.

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KW - Data augmentation

KW - Diffeomorphic shape matching

KW - Random forests

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Classification of Deformable Smooth Shapes Through Geodesic Flows of Diffeomorphisms

Abstract

Keywords

ASJC Scopus subject areas

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