Assignment Flows and Nonlocal PDEs on Graphs

Authors: Dmitrij Sitenko, Bastian Boll, Christoph Schnoerr Abstract: This paper employs nonlocal operators and the corresponding calculus in order to show that assignment flows for image labeling can be represented by a nonlocal PDEs on the underlying graph. In addition, for the homogeneous Dirichlet condition, a tangent space parametrization and geometric integration can be used to solve the PDE numerically. The PDE reveals a nonlocal balance law that governs the spatially distributed dynamic mass assignment to labels. Numerical experiments illustrate the theoretical results.