We present advances on extending morphology PDEs and active contours to arbitrary graphs by developing difference schemes and geometric approximations of gradient and curvature, with theoretical results on their convergence in probability and asymptotic error bounds. We also use finite elements to generalize active contour models on graphs and reduce the problem from a PDE to a sparse nonlinear system. For both approaches we provide experimental results for image segmentation and graph clustering.

This presentation is part of Minisymposium “MS48 - Recent Advances in Mathematical Morphology: Algebraic and PDE-based Approaches”
organized by: Martin Welk (Private University for Health Sciences, Medical Informatics and Technology (UMIT)) , Michael Breuss (Brandenburg University of Technology) .

Authors:

Petros Maragos (National Technical University of Athens)

Christos Sakaridis (ETH Zürich)

Kimon Drakopoulos (University of Southern California)

Nikos Kolotouros (University of Pennsylvania)

Keywords:

active contours, graph clustering, image segmentation, partial differential equation models