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16
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 351 (16 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...
Image Processing With Neural Networks  a Review
, 2002
"... We review more than two hundred applications of neural networks in image processing and discuss the present and possible future role of neural networks, especially feedforward neural networks, Kohonen feature maps and Hopfield neural networks. The various applications are categorised into a novel t ..."
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Cited by 45 (0 self)
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We review more than two hundred applications of neural networks in image processing and discuss the present and possible future role of neural networks, especially feedforward neural networks, Kohonen feature maps and Hopfield neural networks. The various applications are categorised into a novel twodimensional taxonomy for image processing algorithms. One dimension specifies the type of task performed by the algorithm: preprocessing, data reduction/feature extraction, segmentation, object recognition, image understanding and optimisation. The other dimension captures the abstraction level of the input data processed by the algorithm: pixellevel, local featurelevel, structurelevel, objectlevel, objectset level and scene characterisation. Each of the six types of tasks poses specific constraints to a neuralbased approach. These specific conditions are discussed in detail. A synthesis is made of unresolved problems related to application of pattern recognition techniques in image processing and specifically to the application of neural networks. Finally, we present an outlook into the future application of neural networks and relate them to novel developments. Keywords: neural networks; digital image processing; invariant pattern recognition; preprocessing; feature extraction; image compression; segmentation; object recognition; image understanding; optimization. * Corresponding author. M. EgmontPetersen, Institute of Information and Computing Sciences, Utrecht University, P.O.B. 80.089, 3508 TB Utrecht, The Netherlands. Email: michael@cs.uu.nl. WWW: Http://www.cs.uu.nl/people/michael/nnreview.html.
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 29 (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...
Graph matching by relaxation of fuzzy assignments
 IEEE Trans. Fuzzy Systems
, 2001
"... Abstract—Graphs are very powerful and widely used representational tools in computer applications. In this paper, we present a relaxation approach to (sub)graph matching based on a fuzzy assignment matrix. The algorithm has a computational complexity of ( 2 2) where and are the number of nodes in th ..."
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Cited by 12 (1 self)
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Abstract—Graphs are very powerful and widely used representational tools in computer applications. In this paper, we present a relaxation approach to (sub)graph matching based on a fuzzy assignment matrix. The algorithm has a computational complexity of ( 2 2) where and are the number of nodes in the two graphs being matched, and can perform both exact and inexact matching. To illustrate the performance of the algorithm, we summarize the results obtained for more than 12 000 pairs of graphs of varying types (weighted graphs, attributed graphs, and noisy graphs). We also compare our results with those obtained using the Graduated Assignment algorithm. Index Terms—Graph isomorphism, graph matching, inexact graph matching, subgraph matching. I.
A Graph Isomorphism Algorithm for Object Recognition
, 1998
"... We present an algorithm to solve the graph isomorphism problem for the purpose of object recognition. Objects, such as those that exist in a robot workspace, may be represented by labeled graphs (graphs with attributes on their nodes and/or edges). Object recognition, thereafter, is achieved by matc ..."
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Cited by 6 (0 self)
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We present an algorithm to solve the graph isomorphism problem for the purpose of object recognition. Objects, such as those that exist in a robot workspace, may be represented by labeled graphs (graphs with attributes on their nodes and/or edges). Object recognition, thereafter, is achieved by matching pairs of these graphs. Assuming that all objects are sufficiently different that their corresponding representative graphs are distinct, then given a new graph, the algorithm efficiently finds the isomorphic stored graph (if it exists). The algorithm consists of three phases: preprocessing, link construction, and ambiguity resolution. Results from experiments on a wide variety and sizes of graphs are reported. Results are also reported for experiments on recognizing graphs that represent protein molecules. The algorithm works for all types of graphs except for a class of highly ambiguous graphs that includes strongly regular graphs. However, members of this class are detected in polynom...
Curvature computation on freeform 3d meshes at multiple scales. Computer Vision and Image Understanding 83(2
, 2001
"... A novel technique for multiscale curvature computation on a smoothed 3D surface is presented. This is achieved by iteratively convolving local parameterizations of the surface with 2D Gaussian filters. In our technique, semigeodesic coordinates are constructed at each vertex of the mesh which beco ..."
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A novel technique for multiscale curvature computation on a smoothed 3D surface is presented. This is achieved by iteratively convolving local parameterizations of the surface with 2D Gaussian filters. In our technique, semigeodesic coordinates are constructed at each vertex of the mesh which becomes the local origin. A geodesic from the origin is first constructed in an arbitrary direction such as the direction of one of the incident edges. The smoothing eliminates surface noise and small surface detail gradually and results in gradual simplification of the object shape. The surface Gaussian and mean curvature values are estimated accurately at multiple scales together with curvature zerocrossing contours. The curvature values are then mapped to colors and displayed directly on the surface. Furthermore, maxima of Gaussian and mean curvatures are also located and displayed on the surface. These features have been utilized by later processes for robust surface matching and object recognition. Our technique is independent of the underlying triangulation and is also more efficient than volumetric diffusion techniques since 2D rather than 3D convolutions are employed. Another advantage is that it is applicable to incomplete surfaces which arise during occlusion or to surfaces with holes. c ° 2001 Academic Press 1.
Estimation of error in curvature computation on multiscale freeform surfaces
 Int. J. Comput. Vision
"... Abstract. A novel technique for multiscale curvature computation on a freeform 3D surface is presented. This is achieved by convolving local parametrisations of the surface with 2D Gaussian filters iteratively. In our technique, semigeodesic coordinates are constructed at each vertex of the mesh ..."
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Abstract. A novel technique for multiscale curvature computation on a freeform 3D surface is presented. This is achieved by convolving local parametrisations of the surface with 2D Gaussian filters iteratively. In our technique, semigeodesic coordinates are constructed at each vertex of the mesh. Smoothing results are shown for 3D surfaces with different shapes indicating that surface noise is eliminated and surface details are removed gradually. A number of evolution properties of 3D surfaces are described. Next, the surface Gaussian and mean curvature values are estimated accurately at multiple scales which are then mapped to colours and displayed directly on the surface. The performance of the technique when selecting different directions as an arbitrary direction for the geodesic at each vertex are also presented. The results indicate that the error observed for the estimation of Gaussian and mean curvatures is quite low after only one iteration. Furthermore, as the surface is smoothed iteratively, the error is further reduced. The results also show that the estimation error of Gaussian curvature is less than that of mean curvature. Our experiments demonstrate that estimation of smoothed surface curvatures are very accurate and not affected by the arbitrary direction of the first geodesic line when constructing semigeodesic coordinates. Our technique is independent of the underlying triangulation and is also more efficient than volumetric diffusion techniques since 2D rather than 3D convolutions are employed. Finally, the method presented here is a generalisation of the Curvature Scale Space method for 2D contours. The CSS method has outperformed comparable techniques
Freeform 3d object recognition at multiple scales
 in Proc. British Machine Vision Conference
, 2000
"... The recognition of freeform 3D objects using multiscale features recovered from 3D models, and based on the geometric hashing algorithm and global verication is presented. The feature points on the object are detected by smoothing its surface after construction of semigeodesic coordinates at ea ..."
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Cited by 2 (2 self)
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The recognition of freeform 3D objects using multiscale features recovered from 3D models, and based on the geometric hashing algorithm and global verication is presented. The feature points on the object are detected by smoothing its surface after construction of semigeodesic coordinates at each point (mesh vertex). This technique is the generalisation of the CSS method which is a powerful shape descriptor expected to be in the MPEG7 standard. Smoothing is used to remove noise and to select multiscale feature points to add to the eÆciency and robustness of the system. The local maxima of Gaussian and mean curvatures are selected as feature points. Furthermore the torsion maxima of the zerocrossing contours of Gaussian and mean curvatures are also selected as feature points. Recognition results are demonstrated for rotated and scaled as well as partially occluded objects. In order to conrm the match, 3D translation, rotation and scaling parameters are used for verication and results indicate that our technique is invariant to those transformations. 1
www.elsevier.com/locate/patcog Image processing with neural networks—a review
, 2001
"... We review more than 200 applications of neural networks in image processing and discuss the present and possible future role of neural networks, especially feedforward neural networks, Kohonen feature maps and Hop1eld neural networks. The various applications are categorised into a novel twodimens ..."
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Cited by 1 (0 self)
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We review more than 200 applications of neural networks in image processing and discuss the present and possible future role of neural networks, especially feedforward neural networks, Kohonen feature maps and Hop1eld neural networks. The various applications are categorised into a novel twodimensional taxonomy for image processing algorithms. One dimension speci1es the type of task performed by the algorithm: preprocessing, data reduction=feature extraction, segmentation, object recognition, image understanding and optimisation. The other dimension captures the abstraction level of the input data processed by the algorithm: pixellevel, local featurelevel, structurelevel, objectlevel, objectsetlevel and scene characterisation. Each of the six types of tasks poses speci1c constraints to a neuralbased approach. These speci1c conditions are discussed in detail. A synthesis is made of unresolved problems related to the application of pattern recognition techniques in image processing and speci1cally to the application of neural networks. Finally, we present an outlook into the future application of neural networks and relate them to novel developments.
CONTOUR RECOGNITION USING NEURAL NETWORK APPLICATION
"... The most important step for contour recognition systems is the feature extraction, because the reliability of the recognition system depends only on the quality of the feature. In this paper a new approach for feature extraction based on the calculation of eigenvalues from a contour is proposed. In ..."
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The most important step for contour recognition systems is the feature extraction, because the reliability of the recognition system depends only on the quality of the feature. In this paper a new approach for feature extraction based on the calculation of eigenvalues from a contour is proposed. In the first part, we will introduce the different steps of feature extraction. Then we describe the applied neural network for the recognition of noisy contours. Finally the recognition results for different SNR (Signal to noise ratio) are shown and discussed. 1