# Explainable Binary Classification of Separable Shape Ensembles

arXiv: https://arxiv.org/abs/2410.12994 · HTML: https://mlsanity.com/paper/2410.12994/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 92 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 10 of 10)

- [The varifold representation of non-oriented shapes for diffeomorphic registration](https://mlsanity.com/paper/1304.6108/) (2013)
- [A Purely Algebraic Justification of the Kabsch-Umeyama Algorithm](https://mlsanity.com/paper/1902.03138/) (2019)
- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [CLAIRE: A distributed-memory solver for constrained large deformation diffeomorphic image registration](https://mlsanity.com/paper/1808.04487/) (2018)
- [3D Shape Sequence of Human Comparison and Classification using Current and Varifolds](https://mlsanity.com/paper/2207.12485/) (2022)
- [Supervised deep learning of elastic SRV distances on the shape space of curves](https://mlsanity.com/paper/2101.04929/) (2021)
- [VariGrad: A Novel Feature Vector Architecture for Geometric Deep Learning on Unregistered Data](https://mlsanity.com/paper/2307.03553/) (2023)
- [Lipschitz and H"older Continuity in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2310.18078/) (2023)
- [Grassmannian Shape Representations for Aerodynamic Applications](https://mlsanity.com/paper/2201.04649/) (2022)
- [Separable Shape Tensors for Aerodynamic Design](https://mlsanity.com/paper/2208.04743/) (2022)

## Built on by (most cited first, 1 of 1)

- [A Riemannian View on Active Subspaces](https://mlsanity.com/paper/2607.25163/) (2026)

## Abstract (arXiv)

Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve ensembles facilitate inferences about important changes when comparing and contrasting images. We introduce novel pattern recognition formalisms combined with inference methods over large ensembles of segmented curves. Our formalism involves accurately approximating eigenspaces of composite integral operators to motivate discrete, dual representations of curves collocated at quadrature nodes. Approximations are projected onto underlying matrix manifolds and the resulting separable shape tensors constitute rigid-invariant decompositions of curves into generalized (linear) scale variations and complementary (nonlinear) undulations. With thousands of curves segmented from pairs of images, we demonstrate how data-driven features of separable shape tensors inform explainable binary classification utilizing a product maximum mean discrepancy; absent labeled data, building interpretable feature spaces in seconds without high performance computation, and detecting discrepancies below cursory visual inspections.