Abstract

In this paper, novel statistical and topological data analyses of 2D images are developed. One considers methodologies based on the Region Covariance Descriptor (RCD) and Topological Data Analysis (TDA) rooted in the simplicial as well as cubical persistent homologies. These methods provide statistical methods for data from populations of complex data objects that are elements of non-Euclidean spaces. The 2D image data considered consist of pictures of two leaves—A and B—from the same tree, twenty of each leaf, from different perspectives. The novel statistical procedures developed are used for correctly determining that leaf A images and leaf B images are in fact those of different leaves and for the development of classification techniques. A key finding is that TDA using cubical homology yields the best testing and classification procedures while essentially requiring no image processing unlike the competing methods developed which require extensive image processing.

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant DMS - 2311059

Keywords and Phrases

Cubical homologies; Distance based-methods; Region covariance descriptor based-methods; Topological data analysis

International Standard Serial Number (ISSN)

1559-8616; 1559-8608

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2025 Springer, All rights reserved.

Publication Date

01 Sep 2025

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