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38
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 287 (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...
Matching Hierarchical Structures Using Association Graphs
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1998
"... this article, please send email to: tpami@computer.org, and reference IEEECS Log Number 108453 ..."
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Cited by 169 (26 self)
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this article, please send email to: tpami@computer.org, and reference IEEECS Log Number 108453
A New Algorithm for NonRigid Point Matching
 IN CVPR
, 2000
"... We present a new robust point matching algorithm (RPM) that can jointly estimate the correspondence and nonrigid transformations between two pointsets that may be of different sizes. The algorithm utilizes the softassign for the correspondence and the thinplate spline for the nonrigid mapping. E ..."
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Cited by 157 (7 self)
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We present a new robust point matching algorithm (RPM) that can jointly estimate the correspondence and nonrigid transformations between two pointsets that may be of different sizes. The algorithm utilizes the softassign for the correspondence and the thinplate spline for the nonrigid mapping. Embedded within a deterministic annealing framework, the algorithm can automatically reject a fraction of the points as outliers. Experiments on both 2D synthetic pointsets with varying degrees of deformation, noise and outliers, and on real 3D sulcal pointsets (extracted from brain MRI) demonstrate the robustness of the algorithm.
A DoubleLoop Algorithm to Minimize the Bethe and Kikuchi Free Energies
 NEURAL COMPUTATION
, 2001
"... Recent work (Yedidia, Freeman, Weiss [22]) has shown that stable points of belief propagation (BP) algorithms [12] for graphs with loops correspond to extrema of the Bethe free energy [3]. These BP algorithms have been used to obtain good solutions to problems for which alternative algorithms fail t ..."
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Cited by 109 (4 self)
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Recent work (Yedidia, Freeman, Weiss [22]) has shown that stable points of belief propagation (BP) algorithms [12] for graphs with loops correspond to extrema of the Bethe free energy [3]. These BP algorithms have been used to obtain good solutions to problems for which alternative algorithms fail to work [4], [5], [10] [11]. In this paper we rst obtain the dual energy of the Bethe free energy which throws light on the BP algorithm. Next we introduce a discrete iterative algorithm which we prove is guaranteed to converge to a minimum of the Bethe free energy. We call this the doubleloop algorithm because it contains an inner and an outer loop. It extends a class of mean eld theory algorithms developed by [7],[8] and, in particular, [13]. Moreover, the doubleloop algorithm is formally very similar to BP which may help understand when BP converges. Finally, we extend all our results to the Kikuchi approximation which includes the Bethe free energy as a special case [3]. (Yedidia et al [22] showed that a \generalized belief propagation" algorithm also has its xed points at extrema of the Kikuchi free energy). We are able both to obtain a dual formulation for Kikuchi but also obtain a doubleloop discrete iterative algorithm that is guaranteed to converge to a minimum of the Kikuchi free energy. It is anticipated that these doubleloop algorithms will be useful for solving optimization problems in computer vision and other applications.
New Algorithms for 2D and 3D Point Matching: Pose Estimation and Correspondence
"... A fundamental open problem in computer visiondetermining pose and correspondence between two sets of points in spaceis solved with a novel, fast [O(nm)], robust and easily implementable algorithm. The technique works on noisy 2D or 3D point sets that may be of unequal sizes and may differ by n ..."
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Cited by 85 (19 self)
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A fundamental open problem in computer visiondetermining pose and correspondence between two sets of points in spaceis solved with a novel, fast [O(nm)], robust and easily implementable algorithm. The technique works on noisy 2D or 3D point sets that may be of unequal sizes and may differ by nonrigid transformations. Using a combination of optimization techniques such as deterministic annealing and the softassign, which have recently emerged out of the recurrent neural network/statistical physics framework, analog objective functions describing the problems are minimized. Over thirty thousand experiments, on randomly generated points sets with varying amounts of noise and missing and spurious points, and on handwritten character sets demonstrate the robustness of the algorithm. Keywords: Pointmatching, pose estimation, correspondence, neural networks, optimization, softassign, deterministic annealing, affine. 1 Introduction Matching the representations of two images has long...
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 77 (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.
The Softassign Procrustes Matching Algorithm
 Information Processing in Medical Imaging
, 1997
"... . The problem of matching shapes parameterized as a set of points is frequently encountered in medical imaging tasks. When the pointsets are derived from landmarks, there is usually no problem of determining the correspondences or homologies between the two sets of landmarks. However, when the poin ..."
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Cited by 61 (4 self)
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. The problem of matching shapes parameterized as a set of points is frequently encountered in medical imaging tasks. When the pointsets are derived from landmarks, there is usually no problem of determining the correspondences or homologies between the two sets of landmarks. However, when the point sets are automatically derived from images, the difficult problem of establishing correspondence and rejecting nonhomologies as outliers remains. The Procrustes method is a wellknown method of shape comparison and can always be pressed into service when homologies between pointsets are known in advance. This paper presents a powerful extension of the Procrustes method to pointsets of differing point counts with correspondences unknown. The result is the softassign Procrustes matching algorithm which iteratively establishes correspondence, rejects nonhomologies as outliers, determines the Procrustes rescaling and the spatial mapping between the pointsets. 1 Introduction One of the mos...
The concaveconvex procedure (CCCP)
, 2003
"... The ConcaveConvex procedure (CCCP) is a way to construct discrete time iterative dynamical systems which are guaranteed to monotonically decrease global optimization/energy functions. This procedure can be applied to almost any optimization problem and many existing algorithms can be interpreted ..."
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Cited by 45 (5 self)
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The ConcaveConvex procedure (CCCP) is a way to construct discrete time iterative dynamical systems which are guaranteed to monotonically decrease global optimization/energy functions. This procedure can be applied to almost any optimization problem and many existing algorithms can be interpreted in terms of it. In particular, we prove that all EM algorithms and classes of Legendre minimization and variational bounding algorithms can be reexpressed in terms of CCCP. We show that many existing neural network and mean field theory algorithms are also examples of CCCP. The Generalized Iterative Scaling (GIS) algorithm and Sinkhornâ€™s algorithm can also be expressed as CCCP by changing variables. CCCP can be used both as a new way to understand, and prove convergence of, existing optimization algorithms and as a procedure for generating new algorithms.
Efficient learning in Boltzmann Machines using linear response theory
 Neural Computation
, 1997
"... The learning process in Boltzmann Machines is computationally very expensive. The computational complexity of the exact algorithm is exponential in the number of neurons. We present a new approximate learning algorithm for Boltzmann Machines, which is based on mean field theory and the linear respon ..."
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Cited by 44 (5 self)
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The learning process in Boltzmann Machines is computationally very expensive. The computational complexity of the exact algorithm is exponential in the number of neurons. We present a new approximate learning algorithm for Boltzmann Machines, which is based on mean field theory and the linear response theorem. The computational complexity of the algorithm is cubic in the number of neurons. In the absence of hidden units, we show how the weights can be directly computed from the fixed point equation of the learning rules. Thus, in this case we do not need to use a gradient descent procedure for the learning process. We show that the solutions of this method are close to the optimal solutions and give a significant improvement when correlations play a significant role. Finally, we apply the method to a pattern completion task and show good performance for networks up to 100 neurons. 1 Introduction Boltzmann Machines (BMs) (Ackley et al., 1985), are networks of binary neurons with a stoc...