Mixed-State Markov Models in Image Motion Analysis

Abstract

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 ap- propriately 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 be- hind 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 val- ues and any type of discrete symbolic states. For the second part, we present the application ofmixed-statemodels tomotion texture analysis.Motion textures corre- spond to the instantaneous apparent motion maps extracted from dynamic textures. They depict mixed-state motion values with a discrete state at zero and a Gaus- sian distribution for the rest. Mixed-state Markov random fields and mixed-state Markov chains are defined and applied to motion texture recognition and track- ing.