Scale and rotation invariant matching using linearly augmented trees

We propose a novel linearly augmented tree method for efficient scale and rotation invariant object matching. The proposed method enforces pairwise matching consistency defined on trees, and high-order constraints on all the sites of a template. The pairwise constraints admit arbitrary metrics while the high-order constraints use L1 norms and therefore can be linearized. Such a linearly augmented tree formulation introduces hyperedges and loops into the basic tree structure, but different from a general loopy graph, its special structure allows us to relax and decompose the optimization into a sequence of tree matching problems efficiently solvable by dynamic programming. The proposed method also works on continuous scale and rotation parameters; we can match with a scale up to any large number with the same efficiency. Our experiments on ground truth data and a variety of real images and videos show that the proposed method is efficient, accurate and reliable.