Information about the distances Correa computes between polygons.

Wasserstein between peristence diagrams

Given a pair of persistence diagrams $D_1, D_2$, the $p$-Wasserstein distance between them is defined as $$W_p(D_1,D_2) = \left ( \min_{f} \sum_{x_i \in D_1} || x_i - f(x_i) ||^p\right)^{1/p},$$ where we have balanced the size of the diagrams with ghost points.

Frechet

Max Ellipse

Min Ellipse

Least Square Ellipse

Willmore