Level-set methods for TDA on spatial data

In this talk, I will give a brief introduction to level-set methods for image analysis. I will then describe an application of level-sets to the construction of filtrations for persistent homology computations. I will present several case studies with various spatial data sets using this construction, including applications to voting, analyzing urban street patterns, and spiderwebs. I will conclude by discussing the types of data which I might imagine such methods to be suitable for analyzing and suggesting a few potential future applications of level-set based computations.