Random walk approach to image enhancement

In the paper a new probabilistic approach to the problem of image enhancement is presented. The introduced algorithms are based on a model of a virtual particle, which performs a random walk on the image lattice. It is assumed, that the probability of a transition of the walking particle from a lattice point to a point belonging to its neighbourhood is determined by the Gibbs statistical distribution. In this work four algorithms of contrast enhancement are presented. The first algorithm traces the visits of the walking particle and determines their relative frequencies. The second transformation assigns to each lattice point the probability of a stationary Markov chain, generated by the trajectory of the randomly walking particle. The third algorithm is based on a concept of a jumping particle and the last one is based on the maximization of the statistical sum of the Gibbs distribution. The probabilistic algorithms of noise reduction presented in the second part of this paper are able to eliminate strong noise, while preserving edges and image texture. They can be seen as a generalization and refinement of the commonly used smoothing operations applied in the spatial domain. They are fast, easy to implement and can be tuned to cope with different kinds of image deterioration.