A Bayesian approach to nonlinear diffusion based on a Laplacian prior for ideal image gradient

We study the relationships between diffusivity functions in a nonlinear diffusion scheme and probabilities of edge presence under a marginal prior on ideal, noise-free image gradient. In particular we impose a Laplacian-shaped prior for the ideal gradient and we define the diffusivity function expli...

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Bibliographic Details
Published inIEEE/SP 13th Workshop on Statistical Signal Processing, 2005 pp. 477 - 482
Main Authors Pizurica, A., Vanhame, I., Sahli, H., Philips, W., Katartzis, A.
Format Conference Proceeding
LanguageEnglish
Published IEEE 2005
Subjects
Bayesian methods
Filtering
Image processing
Informatics
Information processing
Iris
Laplace equations
Shape control
Signal processing
Smoothing methods
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Summary:We study the relationships between diffusivity functions in a nonlinear diffusion scheme and probabilities of edge presence under a marginal prior on ideal, noise-free image gradient. In particular we impose a Laplacian-shaped prior for the ideal gradient and we define the diffusivity function explicitly in terms of edge probabilities under this prior. The resulting diffusivity function has no free parameters to optimize. Our results demonstrate that the new diffusivity function, automatically, i.e., without any parameter adjustments, satisfies the well accepted criteria for the goodness of edge-stopping functions. Our results also offer a new and interesting interpretation of some widely used diffusivity functions, which are now compared to edge-stopping functions under a marginal prior for the ideal image gradient
ISBN:9780780394032
0780394038
ISSN:2373-0803
2693-3551
DOI:10.1109/SSP.2005.1628642