Before revision:  For instance, mixtures are common in unsupervised image segmentation, and typically rely on averaging the posterior mixing probabilities of spatially adjacent data points (i. e. smoothing). However, this approach has had limited success with natural images. Herewe make three contributions. First, we show that a Dirichlet prior with an appropriate choice of parameters allows -- using the  Expectation-Maximization approach -- to define any linear update rule for the mixing probabilities, including many smoothing regularizations as special cases.
After revision:  For instance, in order to classify spatially adjacent data points similarly, it is common to introduce a Laplacian constraint on the Expectation-Maximization approach -- to define any linear update rule for the mixing probabilities, including many smoothing regularizations as special cases.