A rank minimization approach to trajectory (in)validation

This paper addresses the problem of establishing whether two vector time sequences could have been generated by the same (unknown) linear time invariant system, possibly affected by bounded model uncertainty and measurement noise. This problem arises in multiple contexts, including, among others, behavioral systems model (in)validation, determining the minimum number of models needed to cover the set of operating points of a piecewise-linear plant and in several computer vision and image processing problems. The main result of the paper shows that this problem can be reduced to a rank-minimization form and efficiently solved by using recently proposed convex relaxations. These results are illustrated with both a theoretical example and two non-trivial computer vision problems: activity recognition in video sequences and textured image classification.