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238
Feature Correspondence via Graph Matching: Models and Global Optimization
"... Abstract. In this paper we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion, such as points extracted from a pair of images containing a human figure in distinct poses. We formulate th ..."
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Cited by 120 (1 self)
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Abstract. In this paper we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion, such as points extracted from a pair of images containing a human figure in distinct poses. We formulate this matching task as an energy minimization problem by defining a complex objective function of the appearance and the spatial arrangement of the features. Optimization of this energy is an instance of graph matching, which is in general a NPhard problem. We describe a novel graph matching optimization technique, which we refer to as dual decomposition (DD), and demonstrate on a variety of examples that this method outperforms existing graph matching algorithms. In the majority of our examples DD is able to find the global minimum within a minute. The ability to globally optimize the objective allows us to accurately learn the parameters of our matching model from training examples. We show on several matching tasks that our learned model yields results superior to those of stateoftheart methods. 1
Efficient algorithms for detecting signaling pathways in protein interaction networks
 Journal of Computational Biology
, 2005
"... Abstract. The interpretation of largescale protein network data depends on our ability to identify significant substructures in the data, a computationally intensive task. Here we adapt and extend efficient techniques for finding paths in graphs to the problem of identifying pathways in protein in ..."
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Cited by 107 (3 self)
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Abstract. The interpretation of largescale protein network data depends on our ability to identify significant substructures in the data, a computationally intensive task. Here we adapt and extend efficient techniques for finding paths in graphs to the problem of identifying pathways in protein interaction networks. We present lineartime algorithms for finding paths in networks under several biologicallymotivated constraints. We apply our methodology to search for protein pathways in the yeast proteinprotein interaction network. We demonstrate that our algorithm is capable of reconstructing known signaling pathways and identifying functionally enriched paths in an unsupervised manner. The algorithm is very efficient, computing optimal paths of length 8 within minutes and paths of length 10 in less than two hours. 1
Probabilistic Graph and Hypergraph Matching
"... We consider the problem of finding a matching between two sets of features, given complex relations among them, going beyond pairwise. Each feature set is modeled by a hypergraph where the complex relations are represented by hyperedges. A match between the feature sets is then modeled as a hypergr ..."
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Cited by 67 (0 self)
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We consider the problem of finding a matching between two sets of features, given complex relations among them, going beyond pairwise. Each feature set is modeled by a hypergraph where the complex relations are represented by hyperedges. A match between the feature sets is then modeled as a hypergraph matching problem. We derive the hypergraph matching problem in a probabilistic setting represented by a convex optimization. First, we formalize a soft matching criterion that emerges from a probabilistic interpretation of the problem input and output, as opposed to previous methods that treat soft matching as a mere relaxation of the hard matching problem. Second, the model induces an algebraic relation between the hyperedge weight matrix and the desired vertextovertex probabilistic matching. Third, the model explains some of the graph matching normalization proposed in the past on a heuristic basis such as doubly stochastic normalizations of the edge weights. A key benefit of the model is that the global optimum of the matching criteria can be found via an iterative successive projection algorithm. The algorithm reduces to the well known Sinkhorn [15] row/column matrix normalization procedure in the special case when the two graphs have the same number of vertices and a complete matching is desired. Another benefit of our model is the straightforward scalability from graphs to hypergraphs.
A path following algorithm for the graph matching problem
, 2009
"... We propose a convexconcave programming approach for the labeled weighted graph matching problem. The convexconcave programming formulation is obtained by rewriting the weighted graph matching problem as a leastsquare problem on the set of permutation matrices and relaxing it to two different opti ..."
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Cited by 43 (4 self)
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We propose a convexconcave programming approach for the labeled weighted graph matching problem. The convexconcave programming formulation is obtained by rewriting the weighted graph matching problem as a leastsquare problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convexconcave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.
Global alignment of protein–protein interaction networks by graph matching methods
 BIOINFORMATICS
, 2009
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Reweighted random walks for graph matching
 In ECCV
, 2010
"... Abstract. 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 as ..."
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Cited by 40 (4 self)
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Abstract. 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 correspondences between the two graphs. The solution is obtained by simulating random walks with reweighting jumps enforcing the matching constraints on the association graph. Our algorithm achieves noiserobust graph matching by iteratively updating and exploiting the confidences of candidate correspondences. In a practical sense, our work is of particular importance since the realworld matching problem is made difficult by the presence of noise and outliers. Extensive and comparative experiments demonstrate that it outperforms the stateoftheart graph matching algorithms especially in the presence of outliers and deformation.
Graphical models and point pattern matching
 IEEE Trans. PAMI
, 2006
"... Abstract—This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless c ..."
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Cited by 39 (6 self)
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Abstract—This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes. Index Terms—Point pattern matching, graph matching, graphical models, Markov random fields, junction tree algorithm. 1
Differencing and Merging Architectural Views
 Automated Software Engineering Journal
"... As architecturebased techniques become more widely adopted, software architects face the problem of reconciling different versions of architectural models. However, existing approaches to differencing and merging architectural views are based on restrictive assumptions, such as requiring view eleme ..."
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Cited by 38 (15 self)
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As architecturebased techniques become more widely adopted, software architects face the problem of reconciling different versions of architectural models. However, existing approaches to differencing and merging architectural views are based on restrictive assumptions, such as requiring view elements to have unique identifiers or explicitly log changes between versions. To overcome some of the above limitations, we propose differencing and merging architectural views based on structural information. To that effect, we generalize a published polynomialtime treetotree correction algorithm (that detects inserts, renames and deletes) into a novel algorithm to additionally detect restricted moves and support forcing and preventing matches between view elements. We implement a set of tools to compare and merge componentandconnector (C&C) architectural views, incorporating the algorithm. Finally, we provide an empirical evaluation of the algorithm and the tools on case studies with real software, illustrating the practicality of the approach to find and reconcile interesting divergences between architectural views.
Static Extraction and Conformance Analysis of Hierarchical Runtime Architectural Structure
"... An object diagram makes explicit the object structures that are only implicit in a class diagram. An object diagram may be missing and must extracted from the code. Alternatively, an existing diagram may be inconsistent with the code, and must be analyzed for conformance with the implementation. One ..."
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Cited by 33 (26 self)
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An object diagram makes explicit the object structures that are only implicit in a class diagram. An object diagram may be missing and must extracted from the code. Alternatively, an existing diagram may be inconsistent with the code, and must be analyzed for conformance with the implementation. One can generalize the global object diagram of a system into a runtime architecture which abstracts objects into components, represents how those components interact, and can decompose a component into a nested subarchitecture. A static object diagram represents all objects and interobject relations possibly created, and is recovered by static analysis of a program. Existing analyses extract static object diagrams that are nonhierarchical, do not scale, and do not provide meaningful architectural abstraction. Indeed, architectural