18 citations · 72 across the 13 of their papers we have counts for
13 papers
Persistent Homology as a Morphological Signature of Fibrin Networks
Thomas Burnett, Theresa Reinhold, Bea Bleile +5
We present an investigation of the applicability of topological data analysis (TDA) to the study of high-resolution confocal microscopy images of fibrin network structures from pat…
Realisation and Splitting for Poincaré Duality Pairs in Dimension Three
Beatrice Bleile
In earlier work we presented necessary conditions for a fundamental triple to be that of a 3-dimensional Poincaré duality pair with aspherical boundary components. We provide a con…
The Impact of Changes in Resolution on the Persistent Homology of Images
Teresa Heiss, Sarah Tymochko, Brittany Story +4
Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging.…
The Persistent Homology of Dual Digital Image Constructions
Bea Bleile, Adélie Garin, Teresa Heiss +2
To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructio…
Duality in Persistent Homology of Images
Adélie Garin, Teresa Heiss, Kelly Maggs +2
We derive the relationship between the persistent homology barcodes of two dual filtered CW complexes. Applied to greyscale digital images, we obtain an algorithm to convert barcod…
Poincaré duality complexes with highly connected universal cover
Beatrice Bleile, Imre Bokor, Jonathan A. Hillman
Turaev conjectured that the classification, realization and splitting results for Poincaré duality complexes of dimension (PD-complexes) generalize to PD-complexes…