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.
Greedy approaches build a matching that has the lowest cost at each iteration, which has the obvious weakness that decisions once made, are fixed and may later be shown to be suboptimal. GRASP improves over greedy approaches by progressively constructing a list of best candidate matches and randomly selecting one from them. The process is repeated until all matches are exhausted. A final local search over the neighborhood of obtained matches may be used to further optimize the solution. In @cite_23 , Poore and Robertson presented a Lagrangian relaxation method that progressively relaxes the original and intermediate recovery MiAPs to linear assignment problems, by incorporating constraints of each MiAP into its objective function via the Lagrangian. However, this method involves implicitly enumerative procedure, and is difficult to implement and analyze.
@cite_23
2008285373
We propose a method for global multi-target tracking that can incorporate higher-order track smoothness constraints such as constant velocity. Our problem formulation readily lends itself to path estimation in a trellis graph, but unlike previous methods, each node in our network represents a candidate pair of matching observations between consecutive frames. Extra constraints on binary flow variables in the graph result in a problem that can no longer be solved by min-cost network flow. We therefore propose an iterative solution method that relaxes these extra constraints using Lagrangian relaxation, resulting in a series of problems that ARE solvable by min-cost flow, and that progressively improve towards a high-quality solution to our original optimization problem. We present experimental results showing that our method outperforms the standard network-flow formulation as well as other recent algorithms that attempt to incorporate higher-order smoothness constraints.