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Automatic classification of deformable shapes

arXiv 2211.02530 ↗First posted 4 Nov 2022cs.CV cs.LG math.OCcited by 0

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Abstract (arXiv)

Let D be a dataset of smooth 3D-surfaces, partitioned into disjoint classes mathitCLj, j= 1, ldots, 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 mathitCLj by diffeomorphic interpolation of smooth surfaces between pairs S,S' ∈ mathitCLj. We also implement small random perturbations of surfaces S∈ mathitCLj by random flows of smooth diffeomorphisms Ft:ℝ3 → ℝ3. Finally, we test our automatic classification methods on a cardiology data base of discretized mitral valve surfaces.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 23 of its 92 references that are in the map. First posted on arXiv 4 Nov 2022.

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References · 23

  1. 2015Recent Advances in Convolutional Neural Networkscited by 360
  2. 2017Quicksilver: Fast Predictive Image Registration - a Deep Learning Approachcited by 113
  3. 2018Learning a Probabilistic Model for Diffeomorphic Registrationcited by 62
  4. 2022Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flowcited by 38
  5. 2022Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical frameworkcited by 18
  6. 2021ResNet-LDDMM: Advancing the LDDMM Framework using Deep Residual Networkscited by 13
  7. 2022Landmark-free Statistical Shape Modeling via Neural Flow Deformationscited by 11
  8. 2017A Lagrangian Gauss-Newton-Krylov Solver for Mass- and Intensity-Preserving Diffeomorphic Image Registrationcited by 10
  9. 2018CLAIRE: A distributed-memory solver for constrained large deformation diffeomorphic image registrationcited by 8
  10. 2022Deep Learning for Medical Image Registration: A Comprehensive Reviewcited by 8
  11. 2014An inexact Newton-Krylov algorithm for constrained diffeomorphic image registrationcited by 6
  12. 2020Fast GPU 3D Diffeomorphic Image Registrationcited by 6
11 more
  1. 2021Metamorphic image registration using a semi-Lagrangian schemecited by 6
  2. 2021Residual Networks as Flows of Velocity Fields for Diffeomorphic Time Series Alignmentcited by 4
  3. 2016A Semi-Lagrangian two-level preconditioned Newton-Krylov solver for constrained diffeomorphic image registrationcited by 3
  4. 2016Distributed-memory large deformation diffeomorphic 3D image registrationcited by 3
  5. 2020Multi-Node Multi-GPU Diffeomorphic Image Registration for Large-Scale Imaging Problemscited by 3
  6. 2022Shape spaces: From geometry to biological plausibilitycited by 3
  7. 2022CLAIRE -- Parallelized Diffeomorphic Image Registration for Large-Scale Biomedical Imaging Applicationscited by 3
  8. 2018Metric Registration of Curves and Surfaces using Optimal Controlcited by 2
  9. 2018Image Registration and Predictive Modeling: Learning the Metric on the Space of Diffeomorphismscited by 1
  10. 2020Mechanistic Modeling of Longitudinal Shape Changes: equations of motion and inverse problemscited by 1
  11. 2020Diffeomorphic Shape Matching by Operator Splitting in 3D Cardiology Imagingcited by 1

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