BYU

Abstract by Nickolas Callor

Personal Infomation


Presenter's Name

Nickolas Callor

Co-Presenters

None

Degree Level

Doctorate

Co-Authors

Jason Heath
Gregory Conner

Abstract Infomation


Department

Mathematics

Faculty Advisor

Gregory Conner

Title

Persistence Value Analysis, with Applications

Abstract

We present the results of research to create a new topological tool for applying persistent homology to scientific categorization problems, which we tentatively refer to as persistence value analysis, or PVA. PVA refines the standard method of applying persistent homology to a problem by extracting a specific conclusion about the object of study rather than merely presenting the result of a computing the persistence of the object. 

In addition to presenting PVA as a mathematical object, we demonstrate one application to the problem of segmenting a digital X-ray scan of a 3-dimensional porous medium filled with fluid into meaningful segments for distinguishing the pore space from the enclosing material.