# Automatic classification of deformable shapes

arXiv: https://arxiv.org/abs/2211.02530 · HTML: https://mlsanity.com/paper/2211.02530/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 92 references that are in the map.
- First posted on arXiv 4 Nov 2022.

## Builds on (most cited first, 23 of 23)

- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach](https://mlsanity.com/paper/1703.10908/) (2017)
- [Learning a Probabilistic Model for Diffeomorphic Registration](https://mlsanity.com/paper/1812.07460/) (2018)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [ResNet-LDDMM: Advancing the LDDMM Framework using Deep Residual Networks](https://mlsanity.com/paper/2102.07951/) (2021)
- [Landmark-free Statistical Shape Modeling via Neural Flow Deformations](https://mlsanity.com/paper/2209.06861/) (2022)
- [A Lagrangian Gauss-Newton-Krylov Solver for Mass- and Intensity-Preserving Diffeomorphic Image Registration](https://mlsanity.com/paper/1703.04446/) (2017)
- [CLAIRE: A distributed-memory solver for constrained large deformation diffeomorphic image registration](https://mlsanity.com/paper/1808.04487/) (2018)
- [Deep Learning for Medical Image Registration: A Comprehensive Review](https://mlsanity.com/paper/2204.11341/) (2022)
- [Metamorphic image registration using a semi-Lagrangian scheme](https://mlsanity.com/paper/2106.08817/) (2021)
- [An inexact Newton-Krylov algorithm for constrained diffeomorphic image registration](https://mlsanity.com/paper/1408.6299/) (2014)
- [Fast GPU 3D Diffeomorphic Image Registration](https://mlsanity.com/paper/2004.08893/) (2020)
- [Residual Networks as Flows of Velocity Fields for Diffeomorphic Time Series Alignment](https://mlsanity.com/paper/2106.11911/) (2021)
- [A Semi-Lagrangian two-level preconditioned Newton-Krylov solver for constrained diffeomorphic image registration](https://mlsanity.com/paper/1604.02153/) (2016)
- [Distributed-memory large deformation diffeomorphic 3D image registration](https://mlsanity.com/paper/1608.03630/) (2016)
- [Multi-Node Multi-GPU Diffeomorphic Image Registration for Large-Scale Imaging Problems](https://mlsanity.com/paper/2008.12820/) (2020)
- [Shape spaces: From geometry to biological plausibility](https://mlsanity.com/paper/2205.01237/) (2022)
- [CLAIRE -- Parallelized Diffeomorphic Image Registration for Large-Scale Biomedical Imaging Applications](https://mlsanity.com/paper/2209.08189/) (2022)
- [Metric Registration of Curves and Surfaces using Optimal Control](https://mlsanity.com/paper/1809.06422/) (2018)
- [Image Registration and Predictive Modeling: Learning the Metric on the Space of Diffeomorphisms](https://mlsanity.com/paper/1808.04439/) (2018)
- [Mechanistic Modeling of Longitudinal Shape Changes: equations of motion and inverse problems](https://mlsanity.com/paper/2003.05512/) (2020)
- [Diffeomorphic Shape Matching by Operator Splitting in 3D Cardiology Imaging](https://mlsanity.com/paper/2011.10165/) (2020)

## 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.