Entropy of markovian processes: Application to image entropy in computer vision

The main purpose of this paper is to consider once more the problem of defining the entropy of image in image processing, and to this end we shall proceed by combining some results related to the entropy of Markovian processes on the one hand and others related to the so-called monkey model of image entropy on the other hand. So, in a first stage, we derive the explicit expression for the entropy of stochastic processes. Then we construct a model of image spatial entropy which, in contrast to the monkey model, takes explicit account of the mutual dependence of neighbouring pixels. Next, we randomize this model to deal with images which evolve in time. As a conclusion, we shall show that the functionals which are used in integrated models of computer vision can be ascribed a meaning in terms of information theory, and moreover we shall be able to suggest new functionals which recall the maximum entropy principle.