The field of mathematical morphology offers well-studied techniques for image processing
and is applicable for studies ranging from materials science to ecological pattern formation …

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 …

Persistent homology, an algebraic method for discerning structure in abstract data, relies on
the construction of a sequence of nested topological spaces known as a filtration. Two …

Topological data analysis (TDA) is a rising branch in modern applied mathematics. It
extracts topological structures as features of a given space and uses these features to …

Abstract Topological Data Analysis (TDA), a fast-growing research topic in applied topology,
uses techniques in algebraic topology to capture features from data. Its importance has been …

Topological data analysis (TDA) is field that started only two decades ago and has already
shown promise both in theory and in applications. The goal of TDA is to quantify the shape …