Feature-based object matching is a fundamental problem for many applicationsin computer vision, such as object recognition, 3D reconstruction, tracking,and motion segmentation. In this work, we consider simultaneously matchingobject instances in a set of images, where both inlier and outlier features areextracted. The task is to identify the inlier features and establish theirconsistent correspondences across the image set. This is a challengingcombinatorial problem, and the problem complexity grows exponentially with theimage number. To this end, we propose a novel framework, termed ROML, toaddress this problem. ROML optimizes simultaneously a partial permutationmatrix (PPM) for each image, and feature correspondences are established by theobtained PPMs. Two of our key contributions are summarized as follows. (1) Weformulate the problem as rank and sparsity minimization for PPM optimization,and treat simultaneous optimization of multiple PPMs as a regularized consensusproblem in the context of distributed optimization. (2) We use the ADMM methodto solve the thus formulated ROML problem, in which a subproblem associatedwith a single PPM optimization appears to be a difficult integer quadraticprogram (IQP). We prove that under wildly applicable conditions, this IQP isequivalent to a linear sum assignment problem (LSAP), which can be efficientlysolved to an exact solution. Extensive experiments on rigid/non-rigid objectmatching, matching instances of a common object category, and common objectlocalization show the efficacy of our proposed method.
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