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We introduced a graph matching framework based on random walks and proposed a novel graph matching algorithm inspired by the personalized random walks and the Sinkhorn method
Reweighted random walks for graph matching
ECCV (5), (2010): 492-505
Graph matching is an essential problem in computer vision and machine learning. In this paper, we introduce a random walk view on the problem and propose a robust graph matching algorithm against outliers and deformation. Matching between two graphs is formulated as node selection on an association graph whose nodes represent candidate co...More
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- Graph matching is an essential problem in theoretical computer science; it is related to various research areas in computer vision, pattern recognition, and machine learning .
- The problem of graph matching is to determine a mapping between the nodes of the two graphs that preserves the relationships between the nodes as much as possible.
- Many graph matching algorithms proposed in the 1980s and 1990s focused on exploiting relatively weak unary and pair-wise attributes and did not aim at optimizing a well-defined objective function .
- IQP explicitly takes into consideration both unary and pair-wise terms reflecting the compatibilities in local appearance as well as the pair-wise geometric relationships between the matching features.
- Since IQP is known to be NP-hard, approximate solutions
- Graph matching is an essential problem in theoretical computer science; it is related to various research areas in computer vision, pattern recognition, and machine learning 
- Recent resurgence of combinatorial optimization approaches to feature matching [2,3,4,5,6,7,8] has changed the situation and firmly settled graph matching formulations based on Integer Quadratic Programming (IQP), which is a generalization of the classical graph matching problems
- Our work provides a novel interpretation of graph matching in a random walk view and relates it to the Integer Quadratic Programming formulation
- Introducing an association graph constructed with nodes as candidate correspondences and edges as pair-wise compatibilities between candidate correspondences, we show that the search for correspondences between the given two graphs can be cast as a node ranking [9,10] and selection problem in the association graph
- We introduced a graph matching framework based on random walks and proposed a novel graph matching algorithm inspired by the personalized random walks [10,11] and the Sinkhorn method 
- The comparison reveals that the matching accuracy in the challenging situations largely depends on the effective exploitation of the matching constraints
- The authors introduced a graph matching framework based on random walks and proposed a novel graph matching algorithm inspired by the personalized random walks [10,11] and the Sinkhorn method .
- The experiments demonstrated that it outperforms the state-of-the-art methods [3,4,6,8,13,14] in the presence of outliers and deformation.
- The authors will improve the framework and method for this direction
- Table1: Matching performance on the real image dataset (30 pairs)
- This work was supported by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD) (KRF-2008-314-D00377). 8 http://research.microsoft.com/en-us/projects/objectclassrecognition/
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