Identification of spatial-temporal switched ARX systems

We consider the problem of identifying a model for data generated by a mixture of dynamical models, both in space and in time. We assume that the measurements at a particular time instant depend on a spatial variable, and that the dynamics of the data in different spatial regions can be modeled with different hybrid systems. We also assume that both the spatial regions as well as the discrete states of the hybrid systems are unknown. Furthermore, we allow the number of models to vary as a function of time. We call such a dynamical model a spatial-temporal hybrid system, and develop a recursive identification algorithm for the class of spatial-temporal switched ARX models. We demonstrate the applicability of our method to the segmentation of videos of dynamic textures, such as segmenting a bird floating on water.