Matching by linear programming and successive convexification

We present a novel convex programming scheme to solve matching problems, focusing on the challenging problem of matching in a large search range and with cluttered background. Matching is formulated as metric labeling with L-1 regularization terms, for which we propose a novel linear programming relaxation method and an efficient successive convexification implementation. The unique feature of the proposed relaxation scheme is that a much smaller set of basis labels is used to represent the original label space. This greatly reduces the size of the searching space. A successive convexification scheme solves the labeling problem in a coarse to fine manner. Importantly, the original cost function is reconvexified at each stage, in the new focus region only, and the focus region is updated so as to refine the searching result. This makes the method well-suited for large label set matching. Experiments demonstrate successful applications of the proposed matching scheme in object detection, motion estimation, and tracking.