This paper discusses the unsupervised learning problem for a mixture of gamma distributions. An important pan of the unsupervised problem is determining the number of components which best describes some data. We apply the minimum message length (MML) criterion to the unsupervised learning problem in the case of a mixture of gamma distributions. We give a comparison of criteria in the literature for estimating the number of components in a data set. The comparison concerns synthetic and RADARSAT SAR images.