Flat Norm Decomposition and Computation

The first goal of this work is to compute the multiscale flat norm on irregular graphs. By computing a local quadratic minimum, weights necessary for a discretization of the flat norm can be computed on irregular graphs in 2 and 3 dimensional space. This allows us to compute various geometry dependent quantities such as mean curvature, perimeter, and distances between shapes defined by subsets on graphs. The code for this project was written in Python and uses an efficient implementation of the min-cut max-flow algorithm. In addition to shape classification and signal denoising, we plan to apply this work to gravitational wave observation data to attempt to classify different glitches.