Multi-body factorization with uncertainty: Revisiting motion consistency

Dynamic analysis of video sequences often relies on the segmentation of the sequence into regions of consistent motions. Approaching this problem requires a definition of which motions are regarded as consistent. Common approaches to motion segmentation usually group together points or image regions that have the same motion between successive frames (where the same motion can be 2D, 3D, or non-rigid). In this paper we define a new type of motion consistency, which is based on temporal consistency of behaviors across multiple frames in the video sequence. Our definition of consistent "temporal behavior" is expressed in terms of multi-frame linear subspace constraints. This definition applies to 2D, 3D, and some non-rigid motions without requiring prior model selection. We further show that our definition of motion consistency extends to data with directional uncertainty, thus leading to a dense segmentation of the entire image. Such segmentation is obtained by applying the new motion consistency constraints directly to covariance-weighted image brightness measurements. This is done without requiring prior correspondence estimation nor feature tracking.