Vic Patrangenaru
Florida State University, Tallahassee, USA

We consider statistical and topological data analysis of 2D and 3D image data. We first consider methodologies for 2D image data based on the Region Covariance Descriptor (RCD) and Topological Data Analysis (TDA) rooted in the simplicial as well cubical persistent homologies. Our 2D example concerns images of leaf data which consist of pictures of two leaves-A and B- from the same tree, twenty of each leaf, from different perspectives. The novel statistical procedures introduce are used for first correctly determining that leaf A images and leaf B images are in fact those of different leaves as for the develop of classification techniques. Next, we collected a total of 52 clamshells from the same species, and placed seven mathematical landmarks on them, that were matched across the data. The 3D surfaces of those shells were reconstructed, using Metashape Software (Agisoft). The 3D projective shape space has a Lie group structure. A two sample test for Veronese-Whitney mean 3D projective shapes for comparing two groups of shells, based on their size, was using a test statistic for mean change on a Lie group. Joint work with A. Algahtani, R. L. Paige.

[1] M. Crane, V. Patrangenaru, Random Change on a Lie Group and Mean Glaucomatous Projective Shape Change Detection From Stereo Pair Images, Journal of Multivariate Analysis, 102, 225-237 (2011)
[2] A. Dixon, V. Patrangenaru, C. Shen, An Introduction to Topological Object Data Analysis, BSG Proceedings, 28, 52--68, (2021)
http://www.mathem.pub.ro/proc/bsgp-28/K28-di-ZKN76.pdf
[3] V. Patrangenaru, P. Bubenik, R.Paige and D. Osborne, Challenges in Topological Object Data Analysis, Sankhya A: The Indian Journal of Statistics, 81, 244--271 (2019)
[4] M. Qiu, R. Paige, V. Patrangenaru, A nonparametric approach to 3D projective shape analysis from digital camera images - II, Journal of Applied Statistics, 46, 2677--2699 (2019)