We start with a simple introduction to topological data analysis where the most popular tool is called a persistence diagram. Briefly, a persistence diagram is a multiset of points in the plane descri
We propose a flexible algorithm for feature detection and hypothesis testing in images with ultra-low signal-to-noise ratio using cubical persistent homology. Our main application is in the identifica
Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data a
A common computational problem is to compute topological information about a real surface defined by a system of polynomial equations. Our software, called polyTop, leverages numerical algebraic geome
