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66
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 235 (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 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.
Nonrigid point set registration: Coherent Point Drift (CPD)
 IN ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 19
, 2006
"... We introduce Coherent Point Drift (CPD), a novel probabilistic method for nonrigid registration of point sets. The registration is treated as a Maximum Likelihood (ML) estimation problem with motion coherence constraint over the velocity field such that one point set moves coherently to align with ..."
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Cited by 48 (0 self)
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We introduce Coherent Point Drift (CPD), a novel probabilistic method for nonrigid registration of point sets. The registration is treated as a Maximum Likelihood (ML) estimation problem with motion coherence constraint over the velocity field such that one point set moves coherently to align with the second set. We formulate the motion coherence constraint and derive a solution of regularized ML estimation through the variational approach, which leads to an elegant kernel form. We also derive the EM algorithm for the penalized ML optimization with deterministic annealing. The CPD method simultaneously finds both the nonrigid transformation and the correspondence between two point sets without making any prior assumption of the transformation model except that of motion coherence. This method can estimate complex nonlinear nonrigid transformations, and is shown to be accurate on 2D and 3D examples and robust in the presence of outliers and missing points.
Distance sets for shape filters and shape recognition
 IEEE TRANS. IMAGE PROCESSING
, 2003
"... We introduce a novel rich local descriptor of an image point, we call the (labeled) distance set, which is determined by the spatial arrangement of image features around that point. We describe a twodimensional (2D) visual object by the set of (labeled) distance sets associated with the feature p ..."
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Cited by 46 (7 self)
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We introduce a novel rich local descriptor of an image point, we call the (labeled) distance set, which is determined by the spatial arrangement of image features around that point. We describe a twodimensional (2D) visual object by the set of (labeled) distance sets associated with the feature points of that object. Based on a dissimilarity measure between (labeled) distance sets and a dissimilarity measure between sets of (labeled) distance sets, we address two problems that are often encountered in object recognition: object segmentation, for which we formulate a distance sets shape filter, and shape matching. The use of the shape filter is illustrated on printed and handwritten character recognition and detection of traffic signs in complex scenes. The shape comparison procedure is illustrated on handwritten character classification, COIL20 database object recognition and MPEG7 silhouette database retrieval.
Indexing Hierarchical Structures Using Graph Spectra
, 2005
"... Hierarchical image structures are abundant in computer vision and have been used to encode part structure, scale spaces, and a variety of multiresolution features. In this paper, we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic g ..."
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Cited by 44 (10 self)
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Hierarchical image structures are abundant in computer vision and have been used to encode part structure, scale spaces, and a variety of multiresolution features. In this paper, we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic graph (DAG) into a lowdimensional vector space. Based on a novel spectral characterization of a DAG, this topological signature allows us to efficiently retrieve a promising set of candidates from a database of models using a simple nearestneighbor search. We establish the insensitivity of the signature to minor perturbation of graph structure due to noise, occlusion, or node split/merge. To accommodate largescale occlusion, the DAG rooted at each nonleaf node of the query "votes" for model objects that share that "part," effectively accumulating local evidence in a model DAG's topological subspaces. We demonstrate the approach with a series of indexing experiments in the domain of viewbased 3D object recognition using shock graphs.
Spectral correspondence for point pattern matching
, 2002
"... This paper investigates the correspondence matching of pointsets using spectral graph analysis. In particular, we are interested in the problem of how the modal analysis of pointsets can be rendered robust to contamination and dropout. We make three contributions. First, we show how the modal str ..."
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Cited by 35 (2 self)
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This paper investigates the correspondence matching of pointsets using spectral graph analysis. In particular, we are interested in the problem of how the modal analysis of pointsets can be rendered robust to contamination and dropout. We make three contributions. First, we show how the modal structure of pointsets can be embedded within the framework ofthe EM algorithm. Second, we present several methods for computing the probabilities of point correspondences from the modes ofthe point proximity matrix. Third, we consider alternatives to the Gaussian proximity matrix. We evaluate the new method on both synthetic and realworld data. Here we show that the method can be used to compute useful correspondences even when the level ofpoint contamination is as large as 50%. We also provide some examples on deformed pointset tracking.
A Feature Registration Framework using Mixture Models
 In Proc. IEEE Workshop on Mathematical Methods in Biomedical Image Analysis
"... We formulate feature registration problems as maximum likelihood or Bayesian maximum a posteriori estimation problems using mixture models. An EMlike algorithm is proposed to jointly solve for the feature correspondences as well as the geometric transformations. A novel aspect of our approach is th ..."
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Cited by 26 (1 self)
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We formulate feature registration problems as maximum likelihood or Bayesian maximum a posteriori estimation problems using mixture models. An EMlike algorithm is proposed to jointly solve for the feature correspondences as well as the geometric transformations. A novel aspect of our approach is the embedding of the EM algorithm within a deterministic annealing scheme in order to directly control the fuzziness of the correspondences. The resulting algorithm  termed mixture point matching (MPM)  can solve for both rigid and high dimensional (thinplate splinebased) nonrigid transformations between point sets in the presence of noise and outliers. We demonstrate the algorithm's performance on 2D and 3D data.
A comparative study of transformation functions for nonrigid image registration
 IEEE Transactions on Image Processing
, 2006
"... Abstract–Transformation functions play a major role in nonrigid image registration. In this paper, the characteristics of thinplate spline (TPS), multiquadric (MQ), piecewise linear (PL), and weighted mean (WM) transformations are explored and their performances in nonrigid image registration are ..."
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Cited by 20 (2 self)
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Abstract–Transformation functions play a major role in nonrigid image registration. In this paper, the characteristics of thinplate spline (TPS), multiquadric (MQ), piecewise linear (PL), and weighted mean (WM) transformations are explored and their performances in nonrigid image registration are compared. TPS and MQ are found to be most suitable when the set of controlpoint correspondences is not large (fewer than a thousand) and variation in spacing between the control points is not large. When spacing between the control points varies greatly, PL is found to produce a more accurate registration than TPS and MQ. When a very large set of control points is given and the control points contain positional inaccuracies, WM is preferred over TPS, MQ, and PL because it uses an averaging process that smoothes the noise and does not require the solution of a very large system of equations. Use of transformation functions in the detection of incorrect correspondences is also discussed. Index Terms–Image registration, transformation function, thinplate spline, multiquadric, radial basis functions, piecewise linear, weightedmean
Probabilistic subgraph matching based on convex relaxation
 In Energy Minimization Methods in Computer Vision and Pattern Recognition
, 2005
"... Abstract. We present a novel approach to the matching of subgraphs for object recognition in computer vision. Feature similarities between object model and scene graph are complemented with a regularization term that measures differences of the relational structure. For the resulting quadratic integ ..."
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Cited by 18 (0 self)
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Abstract. We present a novel approach to the matching of subgraphs for object recognition in computer vision. Feature similarities between object model and scene graph are complemented with a regularization term that measures differences of the relational structure. For the resulting quadratic integer program, a mathematically tight relaxation is derived by exploiting the degrees of freedom of the embedding space of positive semidefinite matrices. We show that the global minimum of the relaxed convex problem can be interpreted as probability distribution over the original space of matching matrices, providing a basis for efficiently sampling all closetooptimal combinatorial matchings within the original solution space. As a result, the approach can even handle completely ambiguous situations, despite uniqueness of the relaxed convex problem. Exhaustive numerical experiments demonstrate the promising performance of the approach which – up to a single inevitable regularization parameter that weights feature similarity against structural similarity – is free of any further tuning parameters. 1
Correspondence matching with modal clusters
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... The modal correspondence method of Shapiro and Brady aims to match pointsets by comparing the eigenvectors of a pairwise point proximity matrix. Although elegant by means of its matrix representation, the method is notoriously susceptible to differences in the relational structure of the pointset ..."
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Cited by 17 (2 self)
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The modal correspondence method of Shapiro and Brady aims to match pointsets by comparing the eigenvectors of a pairwise point proximity matrix. Although elegant by means of its matrix representation, the method is notoriously susceptible to differences in the relational structure of the pointsets under consideration. In this paper, we demonstrate how the method can be rendered robust to structural differences by adopting a hierarchical approach. To do this, we place the modal matching problem in a probabilistic setting in which the correspondences between pairwise clusters can be used to constrain the individual point correspondences. We demonstrate the utility of the method on a number of synthetic and realworld pointpattern matching problems.