Persistent Homology for images
Persistent homology has been widely applied to point clouds and simplicial complex. Here, it is applied to images, combined with machine learning to learn geometric features, or through a more theoretical point of view, to study the dual relationship between the most common cubical complexes built from images.
The Impact of Changes in Resolution on the Persistent Homology of Images
with T. Heiss, S. Tymochko, B. Story, H. Bui, B. Bleile and V. Robins, IEEE Big Data workshop: Applications of Topological Data Analysis to 'Big Data', 2021
The Persistent Homology of Dual Digital Image Constructions
with T. Heiss, K. Maggs, B. Bleile and V. Robins, Springer special issue Women in Mathematics, 2021
Duality in Persistent Homology of Images
with T. Heiss, K. Maggs, B. Bleile and V. Robins, Extended abstract
SoCG YRF 2020
A Topological “Reading” Lesson: Classification of MNIST using TDA
with G. Tauzin, 2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA), Boca Raton, FL, USA, 2019
From Trees to Barcodes and Back Again
By defining an equivalence class on the space of barcodes, one can identify the classes to the symmetric group. This opens the door to a more combinatorics and geometric group theory point of view of this space, and its relation to the space of trees is captivating.