Coarsening rules for regularization parameters in multiresolution approaches

We present results concerning the coarsening of model parameters which are independent of the position in the image. We argue that these parameters can be seen in one of two ways: either as the regularisation parameters which effectively control the amount of smoothing imposed to the data, or as the Markov random field parameters which, for example, describe the model of the underlying texture that is being restored by the optimization process. We review results derived by Szeliski (1989) which are concerned with the regularization case and describe experiments which check these results. We examine the case when the model parameters are not only regularization parameters, but also attempt to model a (possibly) intricate texture pattern