Abstract by Nickolas Callor
Persistence Value Analysis, with Applications
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.