In this paper we have proposed a spatial mixture model which automatically determines the amount of spatial regularisation. This is achieved by using a Gaussian MRF prior on a vector of continuous weights, instead of using the standard approach of a discrete MRF prior on discrete labels, whilst approximating the same posterior. With the continuous Gaussian MRF prior we know the normalising constant. Subsequently, are able to automatically determine the continuous Gaussian MRF control parameter, allowing us to adaptively determine the amount of spatial regularisation. All parameters in the model are adaptively determined from the data and heuristic tuning of control parameters is no longer required.
We applied the mixture models to artificial data and demonstrated the usefulness and effectiveness of the adaptive determination of the amount of spatial regularisation. We also applied the mixture model to statistical parametric maps in FMRI.