Smoothness in layers: Motion segmentation using nonparametric mixture estimation

Grouping based on common motion, or `common fate' provides a powerful cue for segmenting image sequences. Recently a number of algorithms have been developed that successfully perform motion segmentation by assuming that the motion of each group can be described by a low dimensional parametric model (e.g. affine). Typically the assumption is that motion segments correspond to planar patches in 3D undergoing rigid motion. Here we develop an alternative approach, where the motion of each group is described by a smooth dense flow field and the stability of the estimation is ensured by means of a prior distribution on the class of flow fields. We present a variant of the EM algorithm that can segment image sequences by fitting multiple smooth flow fields to the spatiotemporal data. Using the method of Green's functions, we show how the estimation of a single smooth flow field can be performed in closed form, thus making the multiple model estimation computationally feasible. Furthermore, the number of models is estimated automatically using similar methods to those used in the parametric approach. We illustrate the algorithm's performance on synthetic and real image sequences.