arXiv subjects

Bea Bleile

Publications and source records attributed to Bea Bleile.

5 recordsLinked to original sources

arXiv2026

Persistent Homology as a Morphological Signature of Fibrin Networks

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 patients with oesophageal cancer undergoing intended curative surgery. Investigation of clot structure brings new knowledge about blood coagulation, risk of bleeding, and thrombosis in this group of patients. Images of fibrin network formation in the collected blood samples were captured by confocal microscopy and three-dimensional z-stacks were analysed. Each z-stack was cropped to a centre region for analysis, the validity of which is assessed in detail. Overall, we found no significant differences in fibrin network topology across the perioperative period, and no consistent differences in network structure between the standard and intervention groups.

q-bio.OT↗

arXiv2021

The Impact of Changes in Resolution on the Persistent Homology of Images

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. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown.

cs.CG↗

arXiv2021

The Persistent Homology of Dual Digital Image Constructions

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 constructions (corresponding to direct and indirect digital adjacencies) can give different results for the same image. The two constructions are almost dual to each other, and we use this relationship to extend and modify the cubical complexes to become dual filtered cell complexes. We derive a general relationship between the persistent homology of two dual filtered cell complexes, and also establish how various modifications to a filtered complex change the persistence diagram. Applying these results to images, we derive a method to transform the persistence diagram computed using one type of cubical complex into a persistence diagram for the other construction. This means software for computing persistent homology from images can now be easily adapted to produce results for either of the two cubical complex constructions without additional low-level code implementation.

math.AT↗

arXiv2020

Duality in Persistent Homology of Images

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 barcodes between the two different (dual) topological models of pixel connectivity.

math.AT↗

arXiv2008

Batalin-Vilkovisky Integrals in Finite Dimensions

The Batalin-Vilkovisky method (BV) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological Perturbation Theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangian system with symmetries. Localization (illustrated in terms of Duistermaat-Heckman localization) as well as anomalous symmetries are discussed in the framework of BV.

math-ph↗