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New theoretical results are presented here on the recently introduced modelcalled mixed states MRF. Such models were introduced in the context of imagemotion analysis and are useful to represent information which can take bothdiscrete values accounting for symbolic states, and real values correspondingto continuous measurements. In particular, results are given when the globalenergy for the Gibbs formulation expressing the mixed states model, can bedecomposed into one term accounting for the discrete part of the model, and asecond term related to the continuous part. This decomposition theorem permitsto define conditional mixed states models in a very simple way.

Mixed States Markov Random Fields with Symbolic Labels and Multidimensional Real Values