Results 1  10
of
54
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 ..."
Abstract

Cited by 382 (16 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 122 (7 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 50 (2 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 47 (5 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 47 (6 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 42 (6 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 41 (12 self)
 Add to MetaCart
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.
EdgeLabeling Using DictionaryBased Relaxation
, 1990
"... We present an improved application of probabilistic relaxation to edgelabeling. The improvement derives from the use of a representation of the edgeprocess that is internally consistent and which utilizes a more complex description of edgestructure. The particular novelty of the application lies ..."
Abstract

Cited by 29 (3 self)
 Add to MetaCart
We present an improved application of probabilistic relaxation to edgelabeling. The improvement derives from the use of a representation of the edgeprocess that is internally consistent and which utilizes a more complex description of edgestructure. The particular novelty of the application lies in the use of a dictionary to represent permitted labelings of the entire contextconveying neighborhood of each pixel. This approach is to he contrasted with the use of approximate factorizations which have been employed in previous applications to decompose the neighborhood into objectpairs. We give details of the dictionary approach and the related representation of the edgeprocess. A comparison with other edgepostprocessing strategies is provided. This leads us to conclude that the dictionarybased approach is a powerful edgepostprocessing tool. It relaxes the demands on the level of filtering that has to be applied to cope with image noise with the benefit of reduced blurring of fine image features.
A GameTheoretic Approach to Hypergraph Clustering
, 2009
"... Hypergraph clustering refers to the process of extracting maximally coherent groups from a set of objects using highorder (rather than pairwise) similarities. Traditional approaches to this problem are based on the idea of partitioning the input data into a userdefined number of classes, thereby o ..."
Abstract

Cited by 27 (2 self)
 Add to MetaCart
(Show Context)
Hypergraph clustering refers to the process of extracting maximally coherent groups from a set of objects using highorder (rather than pairwise) similarities. Traditional approaches to this problem are based on the idea of partitioning the input data into a userdefined number of classes, thereby obtaining the clusters as a byproduct of the partitioning process. In this paper, we provide a radically different perspective to the problem. In contrast to the classical approach, we attempt to provide a meaningful formalization of the very notion of a cluster and we show that game theory offers an attractive and unexplored perspective that serves well our purpose. Specifically, we show that the hypergraph clustering problem can be naturally cast into a noncooperative multiplayer “clustering game”, whereby the notion of a cluster is equivalent to a classical gametheoretic equilibrium concept. From the computational viewpoint, we show that the problem of finding the equilibria of our clustering game is equivalent to locally optimizing a polynomial function over the standard simplex, and we provide a discretetime dynamics to perform this optimization. Experiments are presented which show the superiority of our approach over stateoftheart hypergraph clustering techniques.
Hyperbolic planforms in relation to visual edges and textures perception. Plos Computational Biology, 2009. Accepted for publication 11/04/2009
"... We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g., optical imaging, an ..."
Abstract

Cited by 25 (13 self)
 Add to MetaCart
(Show Context)
We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g., optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific secondorder tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the nonEuclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or Hplanforms that are reminiscent of Euclidean planar waves and of the planforms that were used in previous work to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the builtin or acquired invariance of the neural organization to the action of the corresponding subgroups.