Random walk approach to image enhancement

In the presented paper a new probabilistic approach to the problem of image enhancement has been presented. The algorithms introduced here 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 or median distribution, defined on a specified neighbourhood system. In this work two new algorithms of contrast enhancement has been presented. The first algorithm is based on a concept of a jumping particle and the second makes use of the information contained in the statistical sum of the Gibbs distribution of transition probabilities. The probabilistic algorithms of noise reduction presented in this paper constitute new efficient techniques of noise suppression, capable of preserving edges and other image features. They can can be seen as a generalization and refinement of the commonly used smoothing operations applied in the spatial domain.