Extending the Bayesian mixture model to incorporate spatial information in analysing sheep CAT scan images

The purpose of CAT scanning in some animal science experiments is to provide estimates of the proportion of the tissues, fat, muscle, and bone present in an individual body, and compare some of the density characteristics. In this paper we present an extension to the hierarchical Bayesian Normal mixture model, which incorporates some of the information provided by the neighbouring pixels in a CAT scan image. This neighbour information is included in the model through the use of a Markov random field for the component allocation variable. This extended mixture model provides a more responsive fit to the local likelihood of the data than that of the independent mixture model. The effectiveness of this modelling technique is illustrated by comparing its performance with that of a Normal mixture model and a fixed boundary method in 3 examples. In these examples it is shown that the extended mixture model we propose is most useful in situations that involve only slight separation of components. The advantages of the model decline as the separation of components increases.