Successive Convexification for Consistent Labeling

In this thesis, a novel successive convexification scheme is proposed for solving consistent labeling problems with convex regularization terms. Many computer vision problems can be modeled as such consistent labeling problems. The main optimization term, the labeling cost, however, is typically non-convex, which makes the problem difficult. As well, the large search space, i.e., formally the large label set, makes such applications thorny and inefficient to solve using traditional schemes. The proposed scheme successively convexifies the labeling cost surfaces by replacing them with their lower convex hulls, each time starting from the original cost surfaces but within shrinking trust regions, with a careful scheme for choosing new search regions. This enables the new scheme to solve a sequence of much easier convex programming problems and almost always find the correct labeling. The proposed scheme can be applied to labeling problems with any convex regularization terms. In particular, problems with L1-norm regularization terms can be solved with sequential linear programming; and problems with L2-norm regularization terms with sequential quadratic programming. To zero in on the targets in the search space, the method uses a set of basis labels to approximate the cost surface for each site, and this essentially decouples the size of the relaxed convex problem from the number of labels. The proposed scheme also has other useful properties making it well-suited to very large label-set problems, e.g. searching within an entire image. The proposed successive convexification scheme has been applied to many challenging computer vision problems: the task of robustly locating objects in cluttered environments, dense motion estimation with occlusion inference, appearance-adaptive object tracking with boundary refinement, and finally the challenging problem of human posture and action detection both in still images and in video. Compared with traditional methods, the proposed scheme is shown to have a clear advantage in these applications.