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A New Point Matching Algorithm for NonRigid Registration
, 2002
"... Featurebased methods for nonrigid registration frequently encounter the correspondence problem. Regardless of whether points, lines, curves or surface parameterizations are used, featurebased nonrigid matching requires us to automatically solve for correspondences between two sets of features. I ..."
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Cited by 326 (3 self)
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Featurebased methods for nonrigid registration frequently encounter the correspondence problem. Regardless of whether points, lines, curves or surface parameterizations are used, featurebased nonrigid matching requires us to automatically solve for correspondences between two sets of features. In addition, there could be many features in either set that have no counterparts in the other. This outlier rejection problem further complicates an already di#cult correspondence problem. We formulate featurebased nonrigid registration as a nonrigid point matching problem. After a careful review of the problem and an indepth examination of two types of methods previously designed for rigid robust point matching (RPM), we propose a new general framework for nonrigid point matching. We consider it a general framework because it does not depend on any particular form of spatial mapping. We have also developed an algorithmthe TPSRPM algorithmwith the thinplate spline (TPS) as the parameterization of the nonrigid spatial mapping and the softassign for the correspondence. The performance of the TPSRPM algorithm is demonstrated and validated in a series of carefully designed synthetic experiments. In each of these experiments, an empirical comparison with the popular iterated closest point (ICP) algorithm is also provided. Finally, we apply the algorithm to the problem of nonrigid registration of cortical anatomical structures which is required in brain mapping. While these results are somewhat preliminary, they clearly demonstrate the applicability of our approach to real world tasks involving featurebased nonrigid registration.
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 98 (20 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...
A Robust Point Matching Algorithm for Autoradiograph Alignment
, 1997
"... We present a novel method for the geometric alignment of autoradiographs of the brain. The method is based on finding the spatial mapping and the onetoone correspondences (or homologies) between point features extracted from the images and rejecting nonhomologies as outliers. In this way, we atte ..."
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Cited by 44 (12 self)
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We present a novel method for the geometric alignment of autoradiographs of the brain. The method is based on finding the spatial mapping and the onetoone correspondences (or homologies) between point features extracted from the images and rejecting nonhomologies as outliers. In this way, we attempt to account for the local natural and artifactual differences between the autoradiograph slices. We have executed the resulting automated algorithm on a set of left prefrontal cortex autoradiograph slices, specifically demonstrated its ability to perform point outlier rejection, validated it using synthetically generated spatial mappings and provided a visual comparison against the well known iterated closest point (ICP) algorithm. Visualization of a stack of aligned left prefrontal cortex autoradiograph slices is also provided.
Limitations of Geometric Hashing in the Presence of Gaussian Noise
 Laboratory, Massachusetts Institute of Technology
, 1992
"... This paper presents a detailed error analysis of geometric hashing in the domain of 2D object recogition. Earlier analysis has shown that these methods are likely to produce false positive hypotheses when one allows for uniform bounded sensor error and moderate amounts of extraneous clutter point ..."
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Cited by 7 (1 self)
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This paper presents a detailed error analysis of geometric hashing in the domain of 2D object recogition. Earlier analysis has shown that these methods are likely to produce false positive hypotheses when one allows for uniform bounded sensor error and moderate amounts of extraneous clutter points. These false positives must be removed by a subsequentverification step. Later work has incorporated an explicit 2D Gaussian instead of a bounded error model to improve performance of the hashing method.
NonRigid Point Matching: Algorithms, Extensions and Applications
, 2001
"... A new algorithm has been developed in this thesis for the nonrigid point matching problem. Designed as an integrated framework, the algorithm jointly estimates a onetoone correspondence and a nonrigid transformation between two sets of points. The resulting algorithm is called “robust point matc ..."
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Cited by 7 (0 self)
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A new algorithm has been developed in this thesis for the nonrigid point matching problem. Designed as an integrated framework, the algorithm jointly estimates a onetoone correspondence and a nonrigid transformation between two sets of points. The resulting algorithm is called “robust point matching (RPM) algorithm ” because of its capability to tolerate noise and to reject possible outliers existed within the data points. The algorithm is built upon the heuristic of “fuzzy correspondence”, which allows for multiple partial correspondences between points. With the help of the deterministic annealing technique, this new heuristic enables the algorithm to overcome many local minima that can be encountered in the matching process. Devised as a general point matching framework, the algorithm can be easily extended to accommodate different speci£c requirements in many registration applications. Firstly, the modular design of the transformation module enables convenient incorporation of different nonrigid splines. Secondly, the point matching algorithm can be easily extended into a symmetric joint clusteringmatching framework. It will be shown that by introducing a super pointset, the joint clustermatching extension can be applied to estimate an average shape pointset from multiple point shape sets. The algorithm is applied to the registration of 3D brain anatomical structures. We proposed in this work a joint feature registration framework, which is mainly based on the joint clusteringmatching extension of the robust
Object Recognition Using Optimal AffineInvariant Matching
"... The affineinvariant matching scheme proposed by Hummel and Wolfson (1988) can be very efficient in a modelbased matching system, not only in terms of the computational complexity involved, but also in terms of the simplicity of the method. This paper addresses the implementation of the affinei ..."
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Cited by 2 (0 self)
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The affineinvariant matching scheme proposed by Hummel and Wolfson (1988) can be very efficient in a modelbased matching system, not only in terms of the computational complexity involved, but also in terms of the simplicity of the method. This paper addresses the implementation of the affineinvariant point matching, applied to the problem of recognizing and determining the pose of sheet metal parts. We discuss errors that can occur with this method due to quantization, stability, symmetry, and noise problems. These errors make the original affineinvariant matching technique unsuitable for use on the factory floor. Beginning with an explicit noise model, which the Hummel and Wolfson technique lacks, we derive an optimal approach which overcomes these problems. We show that results obtained with the new algorithm are clearly better than the results from the original method. In terms of performance, the experiments indicate that with a model having 10 to 14 points, with 2 points ...