A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated non-convexity, 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 twenty-five thousand experiments conducted on 100 node random graphs of varying types (graphs with only zero-one links, weighted graphs, and graphs with node attributes and multiple link types) are reported. No comparable results have...

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 graph-based 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 grey-scale images against a small database consisting of a variety of fish, planes, tools, etc., are depicted.

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 maximum-likelihood 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 real-world 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

Abstract—In this paper, we describe a flexible form-reader 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 ——————————

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 continuous-valued 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 polynomial-time algorithm to compute them. This is a remarkable and attractive property, since the computation of tra-ditional edit-distance-based metrics is NP-complete, except for ordered structures. We experimentally validate the usefulness of our metrics on shape matching tasks, and compare them with edit-distance measures. ∗ Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence 1

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 symmetry-breaking self-amplification term in order to obtain a permutation matrix. With the application of a fixpoint preserving algebraic transformation to both the distance measure and self-amplification 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...

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In Pattern Recognition, the Graph Matching problem involves the matching of a sample data graph with the subgraph of a larger model graph where vertices and edges correspond to pattern parts and their relations. In this paper, we present Rulegraphs, a new method that combines the Graph Matching approach with Rule-Based approaches from Machine Learning. This new method reduces the cardinality of the (NP-Complete) Graph Matching problem by replacing model part, and their relational, attribute states by rules which depict attribute bounds and evidence for di erent classes. We show how rulegraphs, when combined with techniques for checking feature label-compatibilities, not only reduce the search space but also improve the uniqueness of the matching process.

We discuss a graph-algorithmic 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 edit-distance. In this paper, we dene our version of tree edit-distance (it diers from that previously described in the literature), and give a polynomial-time algorithm to compute the distance between two trees. 1 Introduction This paper arose out of a collaboration between a computer-vision researcher and an algorithms researcher. Kimia et al. [4] had previously compared shapes by comparing their graphs using a heuristic for general graph-comparison. 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...

Abstract—This paper poses the problem of tree-clustering as that of fitting a mixture of tree unions to a set of sample trees. The treeunions are structures from which the individual data samples belonging to a cluster can be obtained by edit operations. The distribution of observed tree nodes in each cluster sample is assumed to be governed by a Bernoulli distribution. The clustering method is designed to operate when the correspondences between nodes are unknown and must be inferred as part of the learning process. We adopt a minimum description length approach to the problem of fitting the mixture model to data. We make maximum-likelihood estimates of the Bernoulli parameters. The tree-unions and the mixing proportions are sought so as to minimize the description length criterion. This is the sum of the negative logarithm of the Bernoulli distribution, and a message-length criterion that encodes both the complexity of the uniontrees and the number of mixture components. We locate node correspondences by minimizing the edit distance with the current tree unions, and show that the edit distance is linked to the description length criterion. The method can be applied to both unweighted and weighted trees. We illustrate the utility of the resulting algorithm on the problem of classifying 2D shapes using a shock graph representation. Index Terms—Structural learning, tree clustering, mixture modelinq, minimum description length, model codes, shock graphs. 1