Phase Transitions and the Perceptual Organization of Video Sequences

Estimating motion in scenes containing multiple moving objects remains a difficult problem in computer vision. A promising ap(cid:173) proach to this problem involves using mixture models, where the motion of each object is a component in the mixture. However, ex(cid:173) isting methods typically require specifying in advance the number of components in the mixture, i.e. the number of objects in the scene. Here we show that the number of objects can be estimated auto(cid:173) matically in a maximum likelihood framework, given an assumption about the level of noise in the video sequence. We derive analytical results showing the number of models which maximize the likeli(cid:173) hood for a given noise level in a given sequence.