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Title: An efficient globally optimal algorithm for asymmetric point matching
Authors: Lian, W 
Zhang, L 
Yang, MH
Keywords: Branch and bound
Concave optimization
Linear assignment
Point correspondence
Robust point matching
Issue Date: 2017
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on pattern analysis and machine intelligence, 2017, v. 39, no. 7, p. 1281-1293 How to cite?
Journal: IEEE transactions on pattern analysis and machine intelligence 
Abstract: Although the robust point matching algorithm has been demonstrated to be effective for non-rigid registration, there are several issues with the adopted deterministic annealing optimization technique. First, it is not globally optimal and regularization on the spatial transformation is needed for good matching results. Second, it tends to align the mass centers of two point sets. To address these issues, we propose a globally optimal algorithm for the robust point matching problem in the case that each model point has a counterpart in scene set. By eliminating the transformation variables, we show that the original matching problem is reduced to a concave quadratic assignment problem where the objective function has a low rank Hessian matrix. This facilitates the use of large scale global optimization techniques. We propose a modified normal rectangular branch-and-bound algorithm to solve the resulting problem where multiple rectangles are simultaneously subdivided to increase the chance of shrinking the rectangle containing the global optimal solution. In addition, we present an efficient lower bounding scheme which has a linear assignment formulation and can be efficiently solved. Extensive experiments on synthetic and real datasets demonstrate the proposed algorithm performs favorably against the state-of-the-art methods in terms of robustness to outliers, matching accuracy, and run-time.
ISSN: 0162-8828
EISSN: 1939-3539
DOI: 10.1109/TPAMI.2016.2603988
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