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A concave optimization algorithm for matching partially overlapping point sets
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DOI：10.1016/j.patcog.2020.107322.png)
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Abstract
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Matching partially overlapping point sets is a challenging problem in computer vision. To achieve this goal, we model point matching as a mixed linear assignment - least square problem. By eliminating the transformation variable, we reduce the minimization problem to a concave optimization problem with the property that the objective function can be converted into a form with few nonlinear terms. We then use a heuristic variant of the branch-and-bound algorithm for optimization where convergence of the upper bound is used as the stopping criterion. We also propose a new lower bounding scheme which involves solving a k-cardinality linear assignment problem. Two cases of transformations, transformation output being linear with respect to parameters and 2D/3D similarity transformations, are discussed, resulting in ability to handle unknown arbitrary translation and similarity, respectively. Experimental results demonstrate better robustness of the algorithm over state-of-the-art methods. (C) 2020 Elsevier Ltd. All rights reserved.
Keywords:
Concave optimization
Point matching
Branch-and-bound
Linear assignment
Global optimization
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