A Tensor-Based Algorithm for High-Order Graph Matching
A Tensor-Based Algorithm for High-Order Graph Matching
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DOI：
10.1109/tpami.2011.110
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发表时间：
2011-12-01
影响因子：
23.6
通讯作者：
Ponce, Jean
中科院分区：
文献类型：
--
作者：
Duchenne, Olivier;Bach, Francis;Ponce, Jean
本文解决了使用高阶约束而不是经典方法中使用的一元或成对约束来建立两组视觉特征之间的对应关系的问题。具体地说，相应的超图匹配问题被表述为在特征的所有排列上的一个多线性目标函数的最大化。这个函数由一个张量定义，表示特征元组之间的亲和力。它使用谱技术的推广来最大化，其中首先用多维幂方法求解松弛问题，然后将解投影到最近的赋值矩阵上。所提出的方法已经实现，并在合成数据和实际数据上与最先进的算法进行了比较。
This paper addresses the problem of establishing correspondences between two sets of visual features using higher order constraints instead of the unary or pairwise ones used in classical methods. Concretely, the corresponding hypergraph matching problem is formulated as the maximization of a multilinear objective function over all permutations of the features. This function is defined by a tensor representing the affinity between feature tuples. It is maximized using a generalization of spectral techniques where a relaxed problem is first solved by a multidimensional power method and the solution is then projected onto the closest assignment matrix. The proposed approach has been implemented, and it is compared to state-of-the-art algorithms on both synthetic and real data.