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56
A Graduated Assignment Algorithm for Graph Matching
, 1996
"... A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational comp ..."
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Cited by 291 (15 self)
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A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational complexity [O(lm), where l and m are the number of links in the two graphs] and robustness in the presence of noise offer advantages over traditional combinatorial approaches. The algorithm, not restricted to any special class of graph, is applied to subgraph isomorphism, weighted graph matching, and attributed relational graph matching. To illustrate the performance of the algorithm, attributed relational graphs derived from objects are matched. Then, results from twentyfive thousand experiments conducted on 100 node random graphs of varying types (graphs with only zeroone links, weighted graphs, and graphs with node attributes and multiple link types) are reported. No comparable results have...
Symmetrybased Indexing of Image Databases
 J. VISUAL COMMUNICATION AND IMAGE REPRESENTATION
, 1998
"... The use of shape as a cue for indexing into pictorial databases has been traditionally based on global invariant statistics and deformable templates, on the one hand, and local edge correlation on the other. This paper proposes an intermediate approach based on a characterization of the symmetry in ..."
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Cited by 79 (5 self)
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The use of shape as a cue for indexing into pictorial databases has been traditionally based on global invariant statistics and deformable templates, on the one hand, and local edge correlation on the other. This paper proposes an intermediate approach based on a characterization of the symmetry in edge maps. The use of symmetry matching as a joint correlation measure between pairs of edge elements further constrains the comparison of edge maps. In addition, a natural organization of groups of symmetry into a hierarchy leads to a graphbased representation of relational structure of components of shape that allows for deformations by changing attributes of this relational graph. A graduate assignment graph matching algorithm is used to match symmetry structure in images to stored prototypes or sketches. The results of matching sketches and greyscale images against a small database consisting of a variety of fish, planes, tools, etc., are depicted.
Structural graph matching using the em algorithm and singular value decomposition
 IEEE Trans. PAMI
, 2001
"... AbstractÐThis paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is to say, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions. Commencing from a probability distri ..."
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Cited by 69 (8 self)
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AbstractÐThis paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is to say, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions. Commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximumlikelihood estimation using the apparatus of the EM algorithm. Our second contribution is to cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows us to efficiently recover correspondence matches using singular value decomposition. We experiment with the method on both realworld and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding methods. Index TermsÐInexact graph matching, EM algorithm, matrix factorization, mixture models, Delaunay triangulations. 1
INFORMys: A Flexible InvoiceLike FormReader System
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 1998
"... Abstract—In this paper, we describe a flexible formreader system capable of extracting textual information from accounting documents, like invoices and bills of service companies. In this kind of document, the extraction of some information fields cannot take place without having detected the corre ..."
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Cited by 32 (6 self)
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Abstract—In this paper, we describe a flexible formreader system capable of extracting textual information from accounting documents, like invoices and bills of service companies. In this kind of document, the extraction of some information fields cannot take place without having detected the corresponding instruction fields, which are only constrained to range in given domains. We propose modeling the document’s layout by means of attributed relational graphs, which turn out to be very effective for form registration, as well as for performing a focussed search for instruction fields. This search is carried out by means of a hybrid model, where proper algorithms, based on morphological operations and connected components, are integrated with connectionist models. Experimental results are given in order to assess the actual performance of the system. Index Terms—Attributed relational graphs, document analysis and recognition, document registration, invoice processing, location of information fields. ————————— — F ——————————
PolynomialTime Metrics for Attributed Trees
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... We address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree. The proposed measures are general and defined on trees endowed with either symbolic or continuousvalued attributes, and can be equally app ..."
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Cited by 28 (1 self)
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We address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree. The proposed measures are general and defined on trees endowed with either symbolic or continuousvalued attributes, and can be equally applied to ordered and unordered, rooted and unrooted trees. We prove that our measures satisfy the metric constraints and provide a polynomialtime algorithm to compute them. This is a remarkable and attractive property, since the computation of traditional editdistancebased metrics is NPcomplete, except for ordered structures. We experimentally validate the usefulness of our metrics on shape matching tasks, and compare them with editdistance measures. ∗ Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence 1
A Lagrangian Relaxation Network for Graph Matching
 IEEE Trans. Neural Networks
, 1996
"... A Lagrangian relaxation network for graph matching is presented. The problem is formulated as follows: given graphs G and g, find a permutation matrix M that brings the two sets of vertices into correspondence. Permutation matrix constraints are formulated in the framework of deterministic annealing ..."
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Cited by 27 (7 self)
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A Lagrangian relaxation network for graph matching is presented. The problem is formulated as follows: given graphs G and g, find a permutation matrix M that brings the two sets of vertices into correspondence. Permutation matrix constraints are formulated in the framework of deterministic annealing. Our approach is in the same spirit as a Lagrangian decomposition approach in that the row and column constraints are satisfied separately with a Lagrange multiplier used to equate the two "solutions." Due to the unavoidable symmetries in graph isomorphism (resulting in multiple global minima), we add a symmetrybreaking selfamplification term in order to obtain a permutation matrix. With the application of a fixpoint preserving algebraic transformation to both the distance measure and selfamplification terms, we obtain a Lagrangian relaxation network. The network performs minimization with respect to the Lagrange parameters and maximization with respect to the permutation matrix variable...
Spectral embedding of graphs
 PATTERN RECOGNITION
, 2003
"... In this paper we explore how to embed symbolic relational graphs with unweighted edges in a patternspace. We adopt a graphspectral approach. We use the leading eigenvectors of the graph adjacency matrix to define eigenmodes of the adjacency matrix. For each eigenmode, we compute vectors of spectra ..."
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Cited by 23 (4 self)
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In this paper we explore how to embed symbolic relational graphs with unweighted edges in a patternspace. We adopt a graphspectral approach. We use the leading eigenvectors of the graph adjacency matrix to define eigenmodes of the adjacency matrix. For each eigenmode, we compute vectors of spectral properties. These include the eigenmode perimeter, eigenmode volume, Cheeger number, intermode adjacency matrices and intermode edgedistance. We embed these vectors in a patternspace using two contrasting approaches. The first of these involves performing principal or independent components analysis on the covariance matrix for the spectral pattern vectors. The second approach involves performing multidimensional scaling on the L2 norm for pairs of pattern vectors. We illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2D images of 3D polyhedral objects. Two problems are investigated. The first of these is the clustering of graphs representing distinct objects viewed from different directions. The second is the identification of characteristic views of single objects. These two studies reveal that both embedding methods result in wellstructured view spaces for graphdata extracted from 2D views of 3D objects.
A TreeEditDistance Algorithm for Comparing Simple, Closed Shapes
 In Proceedings of the 11th ACMSIAM Symposium on Discrete Algorithms (SODA
, 2000
"... We discuss a graphalgorithmic approach to comparing shapes. We focus in this paper on comparing simple closed curves in the plane. Our approach is to (1) represent such a shape by its skeleton, which is a tree embedded in the plane, and (2) compare two shapes by comparing their skeletons via tree e ..."
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Cited by 23 (0 self)
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We discuss a graphalgorithmic approach to comparing shapes. We focus in this paper on comparing simple closed curves in the plane. Our approach is to (1) represent such a shape by its skeleton, which is a tree embedded in the plane, and (2) compare two shapes by comparing their skeletons via tree editdistance. In this paper, we dene our version of tree editdistance (it diers from that previously described in the literature), and give a polynomialtime algorithm to compute the distance between two trees. 1 Introduction This paper arose out of a collaboration between a computervision researcher and an algorithms researcher. Kimia et al. [4] had previously compared shapes by comparing their graphs using a heuristic for general graphcomparison. The heuristic, due to Gold and Rangarajan [3], is based on nding a local minimum to a quadratic program. This approach had several disadvantages, however, and Kimia was searching for another approach. Klein suggested that the notion of ed...
Unsupervised Category Modeling, Recognition, and Segmentation in Images
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2008
"... paper is aimed at simultaneously solving the following related problems: 1) unsupervised identification of photometric, geometric, and topological properties of multiscale regions comprising instances of the 2D category, 2) learning a regionbased structural model of the ..."
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Cited by 22 (7 self)
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paper is aimed at simultaneously solving the following related problems: 1) unsupervised identification of photometric, geometric, and topological properties of multiscale regions comprising instances of the 2D category, 2) learning a regionbased structural model of the