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42
On aligning curves
 IEEE TPAMI
, 2003
"... We present a novel approach to finding a correspondence (alignment) between two curves. The correspondence is based on a notion of an alignment curve which treats both curves symmetrically. We then define a similarity metric based on the alignment curve using two intrinsic properties of the curve, ..."
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Cited by 133 (4 self)
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We present a novel approach to finding a correspondence (alignment) between two curves. The correspondence is based on a notion of an alignment curve which treats both curves symmetrically. We then define a similarity metric based on the alignment curve using two intrinsic properties of the curve, namely, length and curvature. The optimal correspondence is found by an efficient dynamicprogramming method both for aligning pairs of curve segments and pairs of closed curves, and is effective in the presence of a variety of transformations of the curve. Finally, the correspondence is shown in application to handwritten character recognition, prototype formation, and object recognition, and is potentially useful in other applications such as registration and tracking.
Flexible Syntactic Matching of Curves and its Application to Automatic Hierarchical Classification of Silhouettes
 IEEE Transactions on Pattern Analysis and Machine Intelligence
"... Curve matching is one instance of the fundamental correspondence problem. Our exible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations. A syntactic representation is constructed for both curves, and an edit transformation which ..."
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Cited by 131 (2 self)
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Curve matching is one instance of the fundamental correspondence problem. Our exible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations. A syntactic representation is constructed for both curves, and an edit transformation which maps one curve to the other is found using dynamic programming. We present extensive...
Shape Matching: Similarity Measures and Algorithms
, 2001
"... Shape matching is an important ingredient in shape retrieval, recognition and classification, alignment and registration, and approximation and simplification. This paper treats various aspects that are needed to solve shape matching problems: choosing the precise problem, selecting the properties o ..."
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Cited by 114 (1 self)
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Shape matching is an important ingredient in shape retrieval, recognition and classification, alignment and registration, and approximation and simplification. This paper treats various aspects that are needed to solve shape matching problems: choosing the precise problem, selecting the properties of the similarity measure that are needed for the problem, choosing the specific similarity measure, and constructing the algorithm to compute the similarity. The focus is on methods that lie close to the field of computational geometry.
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 104 (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...
Graph Matching With a DualStep EM Algorithm
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1998
"... Abstract—This paper describes a new approach to matching geometric structure in 2D pointsets. The novel feature is to unify the tasks of estimating transformation geometry and identifying pointcorrespondence matches. Unification is realized by constructing a mixture model over the bipartite graph ..."
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Cited by 104 (6 self)
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Abstract—This paper describes a new approach to matching geometric structure in 2D pointsets. The novel feature is to unify the tasks of estimating transformation geometry and identifying pointcorrespondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected loglikelihood function. In this way, the two processes bootstrap one another. This provides a means of rejecting structural outliers. We evaluate the technique on two realworld problems. The first involves the matching of different perspective views of 3.5inch floppy discs. The second example is furnished by the matching of a digital map against aerial images that are subject to severe barrel distortion due to a linescan sampling process. We complement these experiments with a sensitivity study based on synthetic data.
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 49 (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.
Integral invariants for shape matching
 PAMI
, 2006
"... Abstract—For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential ..."
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Cited by 42 (2 self)
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Abstract—For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database. Index Terms—Integral invariants, shape, shape matching, shape distance, shape retrieval. Ç 1
A statistical method for robust 3D surface reconstruction from sparse data
 In Int. Symp. on 3D Data Processing, Visualization and Transmission
, 2004
"... General information about a class of objects, such as human faces or teeth, can help to solve the otherwise illposed problem of reconstructing a complete surface from sparse 3D feature points or 2D projections of points. We present a technique that uses a vector space representation of shape (3D Mo ..."
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Cited by 38 (5 self)
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General information about a class of objects, such as human faces or teeth, can help to solve the otherwise illposed problem of reconstructing a complete surface from sparse 3D feature points or 2D projections of points. We present a technique that uses a vector space representation of shape (3D Morphable Model) to infer missing vertex coordinates. Regularization derived from a statistical approach makes the system stable and robust with respect to noise by computing the optimal tradeoff between fitting quality and plausibility. We present a direct, noniterative algorithm to calculate this optimum efficiently, and a method for simultaneously compensating unknown rigid transformations. The system is applied and evaluated in two different fields: (1) reconstruction of 3D faces at unknown orientations from 2D feature points at interactive rates, and (2) restoration of missing surface regions of teeth for CADCAM production of dental inlays and other medical applications. I.
Fast algorithm for point pattern matching: Invariant to translations rotations and scale changes
 Pattern Recognition
, 1997
"... AbstractBased on 2D cluster approach, a fast algorithm for point pattern matching is proposed to effectively solve the problems of optimal matches between two point pattern under geometrical transformation and correctly identify the missing or spurious points of patterns. Theorems and algorithms ..."
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Cited by 36 (0 self)
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AbstractBased on 2D cluster approach, a fast algorithm for point pattern matching is proposed to effectively solve the problems of optimal matches between two point pattern under geometrical transformation and correctly identify the missing or spurious points of patterns. Theorems and algorithms are developed to determine the matching pairs support of each point pair and its transformation parameters (scaling s and rotation 0) on a twoparameter space (s,O). Experiments are conducted both on real and synthetic data. The experimental results show that the proposed matching algorithm can handle translation, rotation, and scaling differences under noisy or distorted condition. The computational time is just about 0.5 s for 50 to 50 point matching on Sun4 workstation. Copyright © 1997 Pattern Recognition Society. Published by Elsevier Science Ltd. Point pattern matching Affine transformation Maximum matching pairs support Hough transform Inexact matching Registration 1.
Alignmentbased Recognition of Shape Outlines
 IWVF
, 2001
"... We present a 2D shape recognition and classication method based on matching shape outlines. The correspondence between outlines (curves) is based on a notion of an alignment curve and on a measure of similarity between the intrinsic properties of the curve, namely, length and curvature, and is found ..."
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Cited by 21 (5 self)
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We present a 2D shape recognition and classication method based on matching shape outlines. The correspondence between outlines (curves) is based on a notion of an alignment curve and on a measure of similarity between the intrinsic properties of the curve, namely, length and curvature, and is found by an ecient dynamicprogramming method. The correspondence is used to nd a similarity measure which is used in a recognition system. We explore the strengths and weaknesses of the outlinebased representation by examining the eectiveness of the recognition system on a variety of examples.