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35
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 285 (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...
Creating connected representations of cortical gray matter for functional MRI visualization
 IEEE Transactions on Medical Imaging
, 1997
"... Abstract—We describe a system that is being used to segment gray matter from magnetic resonance imaging (MRI) and to create connected cortical representations for functional MRI visualization (fMRI). The method exploits knowledge of the anatomy of the cortex and incorporates structural constraints i ..."
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Cited by 88 (8 self)
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Abstract—We describe a system that is being used to segment gray matter from magnetic resonance imaging (MRI) and to create connected cortical representations for functional MRI visualization (fMRI). The method exploits knowledge of the anatomy of the cortex and incorporates structural constraints into the segmentation. First, the white matter and cerebral spinal fluid (CSF) regions in the MR volume are segmented using a novel techniques of posterior anisotropic diffusion. Then, the user selects the cortical white matter component of interest, and its structure is verified by checking for cavities and handles. After this, a connected representation of the gray matter is created by a constrained growingout from the white matter boundary. Because the connectivity is computed, the segmentation can be used as input to several methods of visualizing the spatial pattern of cortical activity within gray matter. In our case, the connected representation of gray matter is used to create a flattened representation of the cortex. Then, fMRI measurements are overlaid on the flattened representation, yielding a representation of the volumetric data within a single image. The software is freely available to the research community. Index Terms — Functional MRI, human cortex, segmentation, structural MRI, visualization.
Deformable shape detection and description via modelbased region grouping
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... AbstractÐA method for deformable shape detection and recognition is described. Deformable shape templates are used to partition the image into a globally consistent interpretation, determined in part by the minimum description length principle. Statistical shape models enforce the prior probabilitie ..."
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Cited by 42 (2 self)
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AbstractÐA method for deformable shape detection and recognition is described. Deformable shape templates are used to partition the image into a globally consistent interpretation, determined in part by the minimum description length principle. Statistical shape models enforce the prior probabilities on global, parametric deformations for each object class. Once trained, the system autonomously segments deformed shapes from the background, while not merging them with adjacent objects or shadows. The formulation can be used to group image regions obtained via any region segmentation algorithm, e.g., texture, color, or motion. The recovered shape models can be used directly in object recognition. Experiments with color imagery are reported. Index TermsÐImage segmentation, region merging, object detection and recognition, deformable templates, nonrigid shape models, statistical shape models. 1
Matching: Invariant to Translations, Rotations and Scale Changes
 Pattern Recognition
, 1992
"... We present an approach to invariant matching. In this approach, an object or a pattern is invariantly represented by an objectcentered description called an attributed relational structure (ARS) embedding invariant properties and relations between the primitives of the pattern such as line segments ..."
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Cited by 39 (5 self)
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We present an approach to invariant matching. In this approach, an object or a pattern is invariantly represented by an objectcentered description called an attributed relational structure (ARS) embedding invariant properties and relations between the primitives of the pattern such as line segments and points. Noise effect is taken into account such that a scene can consist of noisy subparts of a model. The matching is then to find the optimal mapping between the ARSs of the scene and the model. A gain functional is formulated to measure the goodness of fit and is to be maximized by using the relaxation labeling method. Experiments are shown to illustrate the matching algorithm and to demonstrate that the approach is truly invariant to arbitrary translations, rotations, and scale changes under noise. Index terms  Attributed relational structures, invariance, pattern recognition, relaxation labeling, subgraph matching. Pattern Recognition, 25(6):583594, June 1992 2 Contents 1...
Image classification using Markov Random Fields with two new relaxation methods: Deterministic pseudo . . .
, 1991
"... In this paper, we present two relaxation techniques: Deterministic PseudoAnnealing (DPA) and Modified Metropolis Dynamics (MMD) in order to do image classification using a Markov Random Field modelization. For the first algorithm (DPA), the a posteriori probability of a tentative labeling is genera ..."
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Cited by 34 (4 self)
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In this paper, we present two relaxation techniques: Deterministic PseudoAnnealing (DPA) and Modified Metropolis Dynamics (MMD) in order to do image classification using a Markov Random Field modelization. For the first algorithm (DPA), the a posteriori probability of a tentative labeling is generalized to continuous labeling. The merit function thus defined has the same maxima under constraints yielding probability vectors. Changing these constraints convexify the merit function. The algorithm solve this unambigous maximization problem and then tracks down the solution while the original constraints are restored yielding a good even if suboptimal solution to the original labeling assignment problem. As for the second method (MMD), it is a modified version of the Metropolis algorithm: at each iteration the new state is chosen randomly but the decision to accept it is purely deterministic. This is of course also a suboptimal technique which gives faster results than stochastic relaxation. These two methods have been implemented on a Connection Machine CM2 and simulation results are shown with a synthetic noisy image and a SPOT image. These results are compared to those obtained with the Metropolis algorithm, the Gibbs sampler and ICM (Iterated Conditional Mode).
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 31 (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
The Dynamics of Nonlinear Relaxation Labeling Processes
, 1997
"... We present some new results which definitively explain the behavior of the classical, heuristic nonlinear relaxation labeling algorithm of Rosenfeld, Hummel, and Zucker in terms of the HummelZucker consistency theory and dynamical systems theory. In particular, it is shown that, when a certain symm ..."
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Cited by 31 (10 self)
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We present some new results which definitively explain the behavior of the classical, heuristic nonlinear relaxation labeling algorithm of Rosenfeld, Hummel, and Zucker in terms of the HummelZucker consistency theory and dynamical systems theory. In particular, it is shown that, when a certain symmetry condition is met, the algorithm possesses a Liapunov function which turns out to be (the negative of) a wellknown consistency measure. This follows almost immediately from a powerful result of Baum and Eagon developed in the context of Markov chain theory. Moreover, it is seen that most of the essential dynamical properties of the algorithm are retained when the symmetry restriction is relaxed. These properties are also shown to naturally generalize to higherorder relaxation schemes. Some applications and implications of the presented results are finally outlined.
Token Tracking in a Cluttered Scene
 Image and Vision Computing
, 1993
"... The statistical data association technique is an important approach to analyze long sequences of images in Computer Vision. Although it has extensively been studied in other domains such as in radar imagery, it was introduced only recently in Computer Vision, and is already recognized as an efficien ..."
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Cited by 21 (0 self)
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The statistical data association technique is an important approach to analyze long sequences of images in Computer Vision. Although it has extensively been studied in other domains such as in radar imagery, it was introduced only recently in Computer Vision, and is already recognized as an efficient approach to solving correspondence and motion problems. This paper has two purposes. The first is to present a general formulation of token tracking. The parameterization of tokens is not addressed. This might be useful to those who are not familiar with statistical tracking techniques. The second is to introduce some strategies for tracking with emphasis on practical importance. They include beam search for resolving multiple matches, support of existence for discarding false matches, and locking on reliable tokens and maximizing local rigidity for handling combinatorial explosion. We have implemented those strategies in a 3D line segment tracking algorithm and found them very useful.
Toward 3D Vision from Range Images: An Optimization Framework and Parallel Networks
"... We propose a unified approach to solve low, intermediate and high level computer vision problems for 3D object recognition from range images. All three levels of computation are cast in an optimization framework and can be implemented on neural network style architecture. In the low level computatio ..."
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Cited by 15 (10 self)
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We propose a unified approach to solve low, intermediate and high level computer vision problems for 3D object recognition from range images. All three levels of computation are cast in an optimization framework and can be implemented on neural network style architecture. In the low level computation, the tasks are to estimate curvature images from the input range data. Subsequent processing at the intermediate level is concerned with segmenting these curvature images into coherent curvature sign maps. In the high level, image features are matched against model features based on an object description called attributed relational graph (ARG). We show that the above computational tasks at each of the three different levels can all be formulated as optimizing a twoterm energy function. The first term encodes unary constraints while the second term binary ones. These energy functions are minimized using parallel and distributed relaxationbased algorithms which are well suited for neural...
Relaxation Labeling of Markov Random Fields
 In Proceedings of International Conference Pattern Recognition
, 1994
"... Using Markov random field (MRF) theory, a variety of computer vision problems can be modeled in terms of optimization based on the maximum a posteriori (MAP) criterion. The MAP configuration minimizes the energy of a posterior (Gibbs) distribution. When the label set is discrete, the minimization is ..."
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Cited by 8 (1 self)
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Using Markov random field (MRF) theory, a variety of computer vision problems can be modeled in terms of optimization based on the maximum a posteriori (MAP) criterion. The MAP configuration minimizes the energy of a posterior (Gibbs) distribution. When the label set is discrete, the minimization is combinatorial. This paper proposes to use the continuous relaxation labeling (RL) method for the minimization. The RL converts the original NP complete problem into one of polynomial complexity. Annealing may be combined into the RL process to improve the quality (globalness) of RL solutions. Performance comparison among four different RL algorithms is given. 1 Introduction Since 1980's, there has been considerable interest in image and vision modeling using Markov random field (MRF) theory [3]. MRF theory provides us with a tool for modeling a vision problem within the established Bayes framework. In MRF based Bayes modeling, a problem is posed as one of labeling. When the interaction bet...