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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 247 (2 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.
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 169 (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 Bayesian Network Framework for Relational Shape Matching
 In 9th IEEE ICCV
, 2003
"... A Bayesian network formulation for relational shape matching is presented. The main advantage of the relational shape matching approach is the obviation of the nonrigid spatial mappings used by recent nonrigid matching approaches. The basic variables that need to be estimated in the relational sha ..."
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Cited by 9 (2 self)
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A Bayesian network formulation for relational shape matching is presented. The main advantage of the relational shape matching approach is the obviation of the nonrigid spatial mappings used by recent nonrigid matching approaches. The basic variables that need to be estimated in the relational shape matching objective function are the global rotation and scale and the local displacements and correspondences. The new Bethe free energy approach is used to estimate the pairwise correspondences between links of the template graphs and the data. The resulting framework is useful in both registration and recognition contexts. Results are shown on handdrawn templates and on 2D transverse T1weighted MR images. 1.
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 5 (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
A New Distance Measure for NonRigid Image Matching
, 1999
"... . We construct probabilistic generative models for the nonrigid matching of pointsets. Our formulation is explicitly Platonist. Beginning with a Platonist super pointset, we derive realworld pointsets through the application of four operations: i) splinebased warping, ii) addition of noise, iii ..."
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Cited by 4 (0 self)
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. We construct probabilistic generative models for the nonrigid matching of pointsets. Our formulation is explicitly Platonist. Beginning with a Platonist super pointset, we derive realworld pointsets through the application of four operations: i) splinebased warping, ii) addition of noise, iii) point removal and iii) amnesia regarding the pointto point correspondences between the realworld pointsets and the Platonist source. Given this generative model, we are able to derive new nonquadratic distance measures w.r.t. the "forgotten" correspondences by a) eliminating the spline parameters from the generative model and by b) integrating out the Platonist super pointset. The result is a new nonquadratic distance measure which has the interpretation of weighted graph matching. The graphs are related in a straightfoward manner to the spline kernel used for nonrigid warping. Experimentally, we show that the new distance measure outperforms the conventional quadratic assignment di...
A Relationship between Splinebased Deformable Models and Weighted Graphs in Nonrigid Matching
, 2001
"... Deformable models are central to nonrigid motion analysis, shape matching and nonrigid medical image registration. Splinebased deformations are a very popular class of parameterizations of deformable models and have been heavily used in multiple domains. In a somewhat separate subfield, weighted ..."
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Cited by 1 (0 self)
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Deformable models are central to nonrigid motion analysis, shape matching and nonrigid medical image registration. Splinebased deformations are a very popular class of parameterizations of deformable models and have been heavily used in multiple domains. In a somewhat separate subfield, weighted graphs are a frequently used object parameterization. Graph matching using weighted graph object parameterizations finds application in a spectrum ranging from rigid pose estimation to deformable object recognition. Here, we demonstrate a hitherto unsuspected relationship between splinebased deformable models and weighted graphs. It turns out that spline parameterizations in the kernel representation can be used to construct equivalent weighted graphs. With this connection established, we envision a crossfertilization between these two seemingly disparate subfields of computer vision.
1 A Bayesian Network Framework for Relational Shape Matching
"... A Bayesian network formulation for relational shape matching is presented. The main advantage of the relational shape matching approach is the obviation of the nonrigid spatial mappings used by recent nonrigid matching approaches. The basic variables that need to be estimated in the relational sha ..."
Abstract
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A Bayesian network formulation for relational shape matching is presented. The main advantage of the relational shape matching approach is the obviation of the nonrigid spatial mappings used by recent nonrigid matching approaches. The basic variables that need to be estimated in the relational shape matching objective function are the global rotation and scale and the local displacements and correspondences. The new Bethe free energy approach is used to estimate the pairwise correspondences between links of the template graphs and the data. The resulting framework is useful in both registration and recognition contexts. Results are shown on handdrawn templates and on 2D transverse T1weighted MR images. 1.