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 approach to this problem involves using mixture models, where the motion of each object is a component in the mixture. However, existing 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 automatically 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 likelihood for a given noise level in a given sequence. We illustrate these results on a real video sequence, showing how the phase transitions correspond to different perceptual organizations of the scene.