Mixed-State Markov Models in Image Motion Analysis

When analyzing motion observations extracted from image sequences, one notes that the histogram of the velocity magnitude at each pixel shows a large probability mass at zero velocity, while the rest of the motion values may be appropriately modeled with a continuous distribution. This suggests the introduction of mixed-state random variables that have probability mass concentrated in discrete states, while they have a probability density over a continuous range of values. In the first part of the chapter, we give a comprehensive description of the theory behind mixed-state statistical models, in particular the development of mixed-state Markov models that permits to take into account spatial and temporal interaction. The presentation generalizes the case of simultaneous modeling of continuous values and any type of discrete symbolic states. For the second part, we present the application of mixed-state models to motion texture analysis. Motion textures correspond to the instantaneous apparent motion maps extracted from dynamic textures. They depict mixed-state motion values with a discrete state at zero and a Gaussian distribution for the rest. Mixed-state Markov random fields and mixed-state Markov chains are defined and applied to motion texture recognition and tracking.