June 2021 Aggregated pairwise classification of elastic planar shapes
Min Ho Cho, Sebastian Kurtek, Steven N. MacEachern
Author Affiliations +
Ann. Appl. Stat. 15(2): 619-637 (June 2021). DOI: 10.1214/21-AOAS1452


The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to early formulations of the problem with an object to be classified described as a vector in a relatively low-dimensional Euclidean space. Statistical shape data have two main properties that suggest a need for a novel approach: (i) shapes are inherently infinite-dimensional with strong dependence among the positions of nearby points, and (ii) shape space is not Euclidean but is fundamentally curved. To accommodate these features of the data, we work with the square-root velocity function of the curves to provide a useful formal description of the shape, pass to tangent spaces of the manifold of shapes at projection points (which effectively separate shapes for pairwise classification in the training data) and use principal components within these tangent spaces to reduce dimensionality. We illustrate the impact of the projection point and choice of subspace on the misclassification rate with a novel method of combining pairwise classifiers.

Funding Statement

This research was partially supported by NSF DMS 1613110 (to SM), and NSF DMS 1613054, NSF CCF 1740761, NSF CCF 1839252 and NIH R37 CA214955 (to SK).


We thank Dr. Hamid Laga from Murdoch University and Dr. Xiang Bai from Huazhong University of Science and Technology for providing the outlines from the Flavia Plant Leaf and the animal datasets, respectively. We also thank the Editor, Associate Editor and two reviewers for their thoughtful comments, which significantly improved this manuscript.


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Min Ho Cho. Sebastian Kurtek. Steven N. MacEachern. "Aggregated pairwise classification of elastic planar shapes." Ann. Appl. Stat. 15 (2) 619 - 637, June 2021. https://doi.org/10.1214/21-AOAS1452


Received: 1 May 2020; Revised: 1 February 2021; Published: June 2021
First available in Project Euclid: 12 July 2021

MathSciNet: MR4298974
zbMATH: 1478.62161
Digital Object Identifier: 10.1214/21-AOAS1452

Keywords: Dimension reduction , LDA , pairwise classification , projection point , QDA , registration

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.15 • No. 2 • June 2021
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