A tensor-based algorithm for high-order graph matching

Duchenne, Olivier; Bach, Francis; Kweon, In-So; Ponce, Jean

doi:10.1109/cvpr.2009.5206619

Cited by 128 publications

(142 citation statements)

References 25 publications

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“…Hence, the problem of finding correspondences can be formulated as a graph matching problem that maximizes the sum of node affinity (capturing attribute similarity) and edge affinity (capturing distortion) over all the matched node pairs and edge pairs. Note that more complex forms of distortion can be formulated between triples or n-tuples of features, but optimization is significantly more complex [6,10].…”

Section: Related Workmentioning

confidence: 99%

Graph-based deformable matching of 3D line with application in protein fitting

Dou

Baker

2015

Vis Comput

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We present an algorithm for matching two sets of line segments in 3D that have undergone non-rigid deformations. This problem is motivated by a biology application that seeks a correspondence between the alpha-helices from two proteins, so that matching helices have similar lengths and these can be aligned by some low-distortion deformation. While matching between two feature sets have been extensively studied, particularly for point features, matching line segments has received little attention so far. As typical in point-matching methods, we formulate a graph matching problem and solve it using continuous relaxation. We make two technical contributions. First, we propose a graph construction for undirected line segments such that the optimal matching between two graphs represents an as-rigidas-possible deformation between the two sets of segments. Second, we propose a novel heuristic for discretizing the continuous solution in graph matching. Our heuristic can be applied to matching problems (such as ours) that are not amenable to certain heuristics, and it produces better solutions than those applicable heuristics. Our method is compared with a state-of-art method motivated by the same biological application and demonstrates improved accuracy.

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Section: Related Workmentioning

confidence: 99%

Graph-based deformable matching of 3D line with application in protein fitting

Dou

Baker

2015

Vis Comput

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“…In order to evaluate the proposed algorithm in a practical environment, we used the hotel and house sequences in CMU PIE database [26], which has been widely used in previous studies [6][7][8][9]19]. …”

Section: Performance Evaluation Under Viewpoint Variationsmentioning

confidence: 99%

“…The graph structure has a strong capacity for representing objects and is robust to various deformations and outliers. Thus, many correspondence problems in computer vision are formulated as graph matching problems such as object recognition [2], object tracking [3,4], and shape matching [5,6]. Theoretically, the problem can be solved by checking all of the possible combinations of candidate matches.…”

Section: Introductionmentioning

confidence: 99%

“…However, because of the NP-hard nature of this problem, the exhaustive method is unfeasible in practice. Therefore, previous works have attempted to solve the graph matching problem by using various approximation algorithms [5][6][7][8][9][10][11][12]. These methods have shown satisfactory results in the computational complexity while sacrificing some accuracy in return.…”

Section: Introductionmentioning

confidence: 99%

“…Because second-order consistency represents the consistency of the graph structure, it can achieve a greater reduction in the matching ambiguity than first-order consistency. In fact, high-order information is often employed to mitigate the matching ambiguity in pairwise graph matching algorithms [6,9,22,23]. The second contribution is that we design an iterative optimization framework.…”

Section: Introductionmentioning

confidence: 99%

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Encouraging second-order consistency for multiple graph matching

Park

Yoon

2016

Machine Vision and Applications

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The problems in computer vision of finding the global correspondences across a set of images can be formulated as a multiple graph matching problem consisting of pairwise matching problems. In the multiple graph matching problem, matching consistency is as important as matching accuracy for preventing the contrariety among matched results. Unfortunately, since the majority of conventional pairwise matching methods only approximate the original graph matching problem owing to its computational complexity, a framework that separately matches each graph pair could generate inconsistent results in practical environments. In this paper, we propose a novel multiple graph matching method based on the second-order consistency concept, which simultaneously considers the matching information of all possible graph pairs. We reformulate the multiple graph matching problem to encourage second-order consistency and design an iterative optimization framework. In our experiments, the proposed method outperforms the state-of-the-art methods in terms of both consistency and accuracy.

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The perturbation bound for the Perron vector of a transition probability tensor

Cui

2013

Numerical Linear Algebra App

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SUMMARYIn this paper, we study the perturbation bound for the Perron vector of an mth‐order n‐dimensional transition probability tensor scriptPMathClass-rel=(pi1MathClass-punc,i2MathClass-punc,MathClass-op…MathClass-punc,im) with pi1MathClass-punc,i2MathClass-punc,MathClass-op…MathClass-punc,im⩾0 and MathClass-op∑i1MathClass-rel=1npi1MathClass-punc,i2MathClass-punc,MathClass-op…MathClass-punc,imMathClass-rel=1. The Perron vector x associated to the largest Z‐eigenvalue 1 of scriptP, satisfies scriptPbold-italicxmMathClass-bin−1MathClass-rel=bold-italicx where the entries xi of x are non‐negative and MathClass-op∑iMathClass-rel=1nxiMathClass-rel=1. The main contribution of this paper is to show that when scriptP is perturbed to an another transition probability tensor truescriptP̃ by ΔscriptP, the 1‐norm error between x and truebold-italicx̃ is bounded by m, ΔscriptP, and the computable quantity related to the uniqueness condition for the Perron vector truebold-italicx̃ of truescriptP̃. Based on our analysis, we can derive a new perturbation bound for the Perron vector of a transition probability matrix which refers to the case of m = 2. Numerical examples are presented to illustrate the theoretical results of our perturbation analysis. Copyright © 2013 John Wiley & Sons, Ltd.

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A tensor-based algorithm for high-order graph matching

Cited by 128 publications

References 25 publications

Graph-based deformable matching of 3D line with application in protein fitting

Graph-based deformable matching of 3D line with application in protein fitting

Encouraging second-order consistency for multiple graph matching

The perturbation bound for the Perron vector of a transition probability tensor

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