Feature-based object matching is a fundamental problem for many applications in computer vision, such as object recognition, 3D reconstruction, tracking, and motion segmentation. In this work, we consider simultaneously matching object instances in a set of images, where both inlier and outlier features are extracted. The task is to identify the inlier features and establish their consistent correspondences across the image set. This is a challenging combinatorial problem, and the problem complexity grows exponentially with the image number. To this end, we propose a novel framework, termed ROML, to address this problem. ROML optimizes simultaneously a partial permutation matrix (PPM) for each image, and feature correspondences are established by the obtained PPMs. Two of our key contributions are summarized as follows. (1) We formulate the problem as rank and sparsity minimization for PPM optimization, and treat simultaneous optimization of multiple PPMs as a regularized consensus problem in the context of distributed optimization. (2) We use the ADMM method to solve the thus formulated ROML problem, in which a subproblem associated with a single PPM optimization appears to be a difficult integer quadratic program (IQP). We prove that under wildly applicable conditions, this IQP is equivalent to a linear sum assignment problem (LSAP), which can be efficiently solved to an exact solution. Extensive experiments on rigid non-rigid object matching, matching instances of a common object category, and common object localization show the efficacy of our proposed method.
Recently, a low-dimensional embedding method was proposed in @cite_15 for feature matching. Given feature points extracted from each of a set of images, it can learn an embedded feature space, which encodes information of both region descriptors and the geometric structure of points in each image. @cite_15 used k-means clustering in the embedded space for feature matching. As we will show in Section , k-means based on Euclidean distances of embedded features is not a good way to establish correspondences. There is no explicit outlier rejection mechanism in @cite_15 either. Compared to @cite_15 , our method uses the low-rank and sparse constraints to optimize PPMs, which integrates correspondence and outlier rejection in a single step.
@cite_15
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Object recognition can be formulated as matching image features to model features. When recognition is exemplar-based, feature correspondence is one-to-one. However, segmentation errors, articulation, scale difference, and within-class deformation can yield image and model features which don't match one-to-one but rather many-to-many. Adopting a graph-based representation of a set of features, we present a matching algorithm that establishes many-to-many correspondences between the nodes of two noisy, vertex-labeled weighted graphs. Our approach reduces the problem of many-to-many matching of weighted graphs to that of many-to-many matching of weighted point sets in a normed vector space. This is accomplished by embedding the initial weighted graphs into a normed vector space with low distortion using a novel embedding technique based on a spherical encoding of graph structure. Many-to-many vector correspondences established by the Earth Mover's Distance framework are mapped back into many-to-many correspondences between graph nodes. Empirical evaluation of the algorithm on an extensive set of recognition trials, including a comparison with two competing graph matching approaches, demonstrates both the robustness and efficacy of the overall approach.