Bayesian Inference for Color Image Quantization via Model-Based Clustering Trees

\Ve consider the problem of color image quantization, or clustering of the color space. vVe propose a new methodology for doing this, called model-based clustering trees. This is grounded in model-based clustering, which bases inference on finite mixture models estimated by maximum likelihood using the EM algorithm, and automatically chooses the number of clusters by Bayesian model selection, approximated using BIC, the Bayesian Information Criterion. We build a clustering tree by first clustering the first color band, then using the second color band to cluster each of the clusters found at the first stage, and the resulting clusters are then further subdivided in the same way using the third color band. The tree is pruned automatically as part of the algorithm by using Bayesian model selection to choose the number of clusters at each stage. An efficient algorithm for implementing the methodology is proposed. The method is applied to several real data sets and compared, with good results, to an alternative method that clusters simultaneously on all bands.