Abstract. The Perona-Malik model is an effective but ill-posed model for denoising digital images by anisotropic diffusion. Instead of complex regularizations, we propose a new continuous model which is well-posed and show that it is nevertheless effective for denoising. In addition, an extension of our model offers the possibility of inducing a convergence for the discretization. A comparison to the original Perona-Malik model is carried out using an human vision-centered quality index which shows the improvements of our model when it comes to denoising.

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Abstract. Perona-Malik diffusion is a well-known type of nonlinear diffusion that can be used for image segmentation and denoising. The process itself needs an parameter k to decide which edges will be retained and which can be blurred and a stopping time tS. Although there have been investigations on how to set these parameters, especially for regularized diffusion models, as well as different criteria for the optimal stopping time have been suggested, there is yet no quick and conclusive way to estimate both parameters -or to reduce the search space at least. In this paper, we show that Gaussian noise characteristics of an image and the diffusion parameters for an optimal optical result can be estimated based on the image histogram. We demonstrate the effectiveness of lazy learning in this area and develop a custom feature weighting algorithm.

SUMMARYWe present a massively parallel implementation of the computation of (co)evolutionary signals from biomolecular sequence alignments based on mutual information (MI) and a normalization procedure to neutral evolution. The MI is computed for two-point and three-point correlations within any multiple sequence alignment. We meet the high computational demand in the normalization procedure efficiently with an implementation on Graphics Processing Units (GPUs) using NVIDIA's CUDA framework. In particular, the normalization of the MI for three-point 'cliques' of amino acids or nucleotides requires large sampling numbers in the normalization, which we achieve by using GPUs. GPU computation serves as an enabling technology here insofar as MI normalization is also possible using traditional computational methods [1] or cluster computation, but only GPU computation makes MI normalization for sequence analysis feasible in a statistically sufficient sample and in acceptable time given affordable commodity hardware. We illustrate (i) the computational efficiency and (ii) the biological usefulness of two-point and three-point MI by applications to the well-known protein calmodulin and the variable surface glycoprotein (VSG) of Trypanosoma brucei, which are subject to involved evolutionary pressure. Here, we find striking coevolutionary patterns and distinct information on the molecular evolution of these molecules that question previous work that relied on non-efficient MI computations.

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