A non-convex PDE scale space

Authors:
Markus Grasmair;Frank Lenzen;Andreas Obereder;Otmar Scherzer;Matthias Fuchs
Affiliations:
Department of Computer Science, University of Innsbruck, Innsbruck, Austria;Department of Computer Science, University of Innsbruck, Innsbruck, Austria;Department of Computer Science, University of Innsbruck, Innsbruck, Austria;Department of Computer Science, University of Innsbruck, Innsbruck, Austria;Department of Computer Science, University of Innsbruck, Innsbruck, Austria
Venue:
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Year:
2005

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Abstract

For image filtering applications, it has been observed recently that both diffusion filtering and associated regularization models provide similar filtering properties. The comparison has been performed for regularization functionals with convex penalization functional. In this paper we discuss the relation between non-convex regularization functionals and associated time dependent diffusion filtering techniques (in particular the Mean Curvature Flow equation). Here, the general idea is to approximate an evolution process by a sequence of minimizers of iteratively convexified energy (regularization) functionals.