A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance

Weickert, Joachim ; Scharr, Hanno

2000_04.pdf - Published

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URL: http://ub-madoc.bib.uni-mannheim.de/1837
URN: urn:nbn:de:bsz:180-madoc-18377
Document Type: Working paper
Year of publication: 2000
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Informatik > Technical Reports
Subject: 004 Computer science, internet
Classification: MSC: 68U10 ,
Subject headings (SWD): Bildverarbeitung , Anisotrope Diffusion , Skalenraum , Rotationsinvarianz , Finite-Differenzen-Methode
Keywords (English): image processing , anisotropic diffusion , scale-spaces , rotation invariance , filter design , finite differences , analytical solutions
Abstract: For strongly directed anisotropic processes such as coherence-enhancing diffusion filtering it is crucial to use numerical schemes with highly accurate directional behavior. We show that this is not possible in a satisfactory way when discretizations are limited to 3 x 3 stencils. As a consequence, we investigate a novel algorithm based on 5 x 5 stencils. It utilizes recently discovered differentiation filters with optimized rotation invariance. By juxtaposing it with several common algorithms we demonstrate its superior behavior with respect to the following properties: rotation invariance, avoidance of blurring artifacts (dissipativity), and accuracy. The latter one is evaluated by deriving an analytical solution for coherence-enhancing diffusion filtering of images with circular symmetry. Furthermore, we show that the new scheme is 3 to 4 times more efficient than explicit schemes on 3 x 3 stencils. It does not require to solve linear systems of equations, and it can be easily implemented in any dimension.
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