A Bayesian formulation of edge-stopping functions in nonlinear diffusion

We propose a novel, Bayesian formulation of the edge-stopping (diffusivity) function in a nonlinear diffusion scheme in terms of edge probability under a marginal prior on noise-free gradient. This formulation differs from the existing probabilistic diffusion approaches that give stochastic formulations for the conductivity but not for the diffusivity function of the gradient. In particular, we impose a Laplacian prior for the ideal gradient, but the proposed formulation is general and can be used with other marginal distributions. We also make links to related works that treat correspondences between nonlinear diffusion and wavelet shrinkage

[1]  Konstantinos N. Plataniotis,et al.  Distance measures for color image retrieval , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[2]  Simon R. Arridge,et al.  Multi-Spectral Probabilistic Diffusion Using Bayesian Classification , 1997, Scale-Space.

[3]  Hamid Krim,et al.  Towards Bridging Scale-Space and Multiscale Frame Analyses , 2001 .

[4]  Aleksandra Pizurica,et al.  Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising , 2006, IEEE Transactions on Image Processing.

[5]  Pierre Moulin,et al.  Analysis of Multiresolution Image Denoising Schemes Using Generalized Gaussian and Complexity Priors , 1999, IEEE Trans. Inf. Theory.

[6]  A. Ben Hamza,et al.  Image denoising: a nonlinear robust statistical approach , 2001, IEEE Trans. Signal Process..

[7]  Stan Z. Li,et al.  Close-Form Solution and Parameter Selection for Convex Minimization-Based Edge-Preserving Smoothing , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Guillermo Sapiro,et al.  Robust anisotropic diffusion , 1998, IEEE Trans. Image Process..

[9]  Thomas Brox,et al.  On the Equivalence of Soft Wavelet Shrinkage, Total Variation Diffusion, Total Variation Regularization, and SIDEs , 2004, SIAM J. Numer. Anal..

[10]  Edward H. Adelson,et al.  Noise removal via Bayesian wavelet coring , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[11]  Hamid Krim,et al.  Smart nonlinear diffusion: a probabilistic approach , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Bin Yu,et al.  Wavelet thresholding via MDL for natural images , 2000, IEEE Trans. Inf. Theory.

[14]  Adhemar Bultheel,et al.  Empirical Bayes Approach to Improve Wavelet Thresholding for Image Noise Reduction , 2001 .

[15]  Joachim Weickert,et al.  Correspondences between Wavelet Shrinkage and Nonlinear Diffusion , 2003, Scale-Space.

[16]  Joachim Weickert,et al.  Anisotropic diffusion in image processing , 1996 .

[17]  S. Mallat A wavelet tour of signal processing , 1998 .