Topological Object Data Analysis Methods with an Application to Medical Imaging

We apply ideas from algebraic topology to study distributions on object spaces. We present a framework for using persistence landscapes to vectorize persistence diagrams as in Bubenik(2015)[3] and Patrangenaru et al.(2018)[13]. We apply these methods to analyze data from The Cancer Imaging Archive (TCIA), using a technique developed earlier for regular types of digital images. The aim of this study is a comparison of brain images of CPTAC Glioblastoma patients with similar images from clinically normal individuals. Result shows persistence landscape may capture topological features distinguishing the two groups.