Explainable Binary Classification of Separable Shape Ensembles

TL;DR

This paper introduces a novel formalism for shape analysis in large image segmentation ensembles, enabling explainable binary classification with interpretable features and efficient discrepancy detection.

Contribution

It presents a new approach combining eigenspace approximations and shape tensors for interpretable classification of large curve ensembles in images.

Findings

Effective binary classification using shape tensors and maximum mean discrepancy.

Detects subtle discrepancies in image pairs without labeled data.

Operates efficiently on thousands of curves in seconds.

Abstract

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.