Stability and local feature enhancement of higher order nonlinear diffusion filtering

Authors:
Stephan Didas;Joachim Weickert;Bernhard Burgeth
Affiliations:
Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany
Venue:
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Year:
2005

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Abstract

This paper discusses the extension of nonlinear diffusion filters to higher derivative orders. While such processes can be useful in practice, their theoretical properties are only partly understood so far. We establish important results concerning L2-stability and forward-backward diffusion properties which are related to well-posedness questions. Stability in the L2-norm is proven for nonlinear diffusion filtering of arbitrary order. In the case of fourth order filtering, a qualitative description of the filtering behaviour in terms of forward and backward diffusion is given and compared to second order nonlinear diffusion. This description shows that curvature enhancement is possible with of fourth order nonlinear diffusion in contrast to second order filters where only edges can be enhanced.