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394
Shape Matching and Object Recognition Using Shape Contexts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2001
"... We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solv ing for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform ..."
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Cited by 1787 (21 self)
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We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solv ing for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape con texts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; reg ularized thin plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning trans form. We treat recognition in a nearestneighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits and the COIL dataset.
Directional Statistics and Shape Analysis
, 1995
"... There have been various developments in shape analysis in the last decade. We describe here some relationships of shape analysis with directional statistics. For shape, rotations are to be integrated out or to be optimized over whilst they are the basis for directional statistics. However, various c ..."
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Cited by 775 (31 self)
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There have been various developments in shape analysis in the last decade. We describe here some relationships of shape analysis with directional statistics. For shape, rotations are to be integrated out or to be optimized over whilst they are the basis for directional statistics. However, various concepts are connected. In particular, certain distributions of directional statistics have emerged in shape analysis, such a distribution is Complex Bingham Distribution. This paper first gives some background to shape analysis and then it goes on to directional distributions and their applications to shape analysis. Note that the idea of using tangent space for analysis is common to both manifold as well. 1 Introduction Consider shapes of configurations of points in Euclidean space. There are various contexts in which k labelled points (or "landmarks") x 1 ; :::; x k in IR m are given and interest is in the shape of (x 1 ; :::; x k ). Example 1 The microscopic fossil Globorotalia truncat...
Matching Shapes
, 2001
"... We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solving for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform. ..."
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Cited by 170 (12 self)
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We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by (1) solving for correspondences between points on the two shapes, (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; regularized thinplate splines provide a flexible class of transformation maps for this purpose. Dissimilarity between two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearestneighbor classification framework. Results are presented for silhouettes, trademarks, handwritten digits and the COIL dataset.
Spatial Pattern Analysis of Functional Brain Images Using Partial Least Squares
 Neuroimage
, 1996
"... This paper introduces a new tool for functional neuroimage analysis: partial least squares (PLS). It is unique as a multivariate method in its choice of emphasis for analysis, that being the covariance between brain images and exogenous blocks representing either the experiment design or some behavi ..."
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Cited by 152 (15 self)
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This paper introduces a new tool for functional neuroimage analysis: partial least squares (PLS). It is unique as a multivariate method in its choice of emphasis for analysis, that being the covariance between brain images and exogenous blocks representing either the experiment design or some behavioral measure. Whatemerges are spatial patterns of brain activity that represent the optimal association between the images and either of the blocks. This process differs substantially from other multivariate methods in that rather than attempting to predict the individual values of the image pixels, PLS attempts to explain the relation between image pixels and task or behavior. Data from a face encoding and recognition PET rCBF study are used to illustrate two types of PLS analysis: an activation analysis of task with images and a brain behavior analysis. The commonalities across the two analyses are suggestive of a general face memory network differentially engaged during encoding and recognition. PLS thus serves as an important extension by extracting new information from imaging data that is not accessible through other currently used univariate and multivariate image analysis tools. r 1996 Academic Press, Inc
Segmentation, registration, and measurement of shape variation via image object shape
 IEEE Transactions on Medical Imaging
, 1999
"... A model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives. Metrics are described that compute an object representation's pri ..."
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Cited by 147 (23 self)
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A model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives. Metrics are described that compute an object representation's prior probability of local geometry by reflecting variabilities in the net's node and link parameter values and that compute a likelihood function measuring the degree of match of an image to that object representation. A paradigm for image analysis of deforming such a model to optimize a posterior probability is described, and this paradigm is shown to be usable as a uniform approach for object definition, objectbased registration between images of the same or different imaging modalities, and measurement of shape variation of an abnormal anatomical object compared with a normal. Examples of applications of these methods in radiotherapy, surgery, and psychiatry are given.
Representation is Representation of Similarities
 Behavioral and Brain Sciences
, 1996
"... Advanced perceptual systems are faced with the problem of securing a principled relationship between the world and its internal representation. I propose a unified approach to visual representation, based on Shepard's (1968) notion of secondorder isomorphism. According to the proposed theory, ..."
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Cited by 108 (21 self)
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Advanced perceptual systems are faced with the problem of securing a principled relationship between the world and its internal representation. I propose a unified approach to visual representation, based on Shepard's (1968) notion of secondorder isomorphism. According to the proposed theory, a shape is represented internally by the responses of a few tuned modules, each of which is broadly selective for some reference shape, whose similarity to the stimulus it measures. The result is a philosophically appealing, computationally feasible, biologically credible, and formally veridical representation of a distal shape space. This approach supports representation of and discrimination among shapes radically different from the reference ones, while bypassing the need for the computationally problematic decomposition into parts; it also addresses the needs of shape categorization, and can be used to derive a range of models of perceived similarity. Representation is Representation of Sim...
Surface matching via currents
 IPMI 2005. LNCS
, 2005
"... Abstract. We present a new method for computing an optimal deformation between two arbitrary surfaces embedded in Euclidean 3dimensional space. Our main contribution is in building a norm on the space of surfaces via representation by currents of geometric measure theory. Currents are an appropriat ..."
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Cited by 105 (2 self)
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Abstract. We present a new method for computing an optimal deformation between two arbitrary surfaces embedded in Euclidean 3dimensional space. Our main contribution is in building a norm on the space of surfaces via representation by currents of geometric measure theory. Currents are an appropriate choice for representations because they inherit natural transformation properties from differential forms. We impose a Hilbert space structure on currents, whose norm gives a convenient and practical way to define a matching functional. Using this Hilbert space norm, we also derive and implement a surface matching algorithm under the large deformation framework, guaranteeing that the optimal solution is a onetoone regular map of the entire ambient space. We detail an implementation of this algorithm for triangular meshes and present results on 3D face and medical image data. 1
Fast parametric elastic image registration
 IEEE Transactions on Image Processing
, 2003
"... Abstract—We present an algorithm for fast elastic multidimensional intensitybased image registration with a parametric model of the deformation. It is fully automatic in its default mode of operation. In the case of hard realworld problems, it is capable of accepting expert hints in the form of so ..."
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Cited by 102 (8 self)
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Abstract—We present an algorithm for fast elastic multidimensional intensitybased image registration with a parametric model of the deformation. It is fully automatic in its default mode of operation. In the case of hard realworld problems, it is capable of accepting expert hints in the form of soft landmark constraints. Much fewer landmarks are needed and the results are far superior compared to pure landmark registration. Particular attention has been paid to the factors influencing the speed of this algorithm. The Bspline deformation model is shown to be computationally more efficient than other alternatives. The algorithm has been successfully used for several twodimensional (2D) and threedimensional (3D) registration tasks in the medical domain, involving MRI, SPECT, CT, and ultrasound image modalities. We also present experiments in a controlled environment, permitting an exact evaluation of the registration accuracy. Test deformations are generated automatically using a random hierarchical fractional waveletbased generator. Index Terms—Elastic registration, image registration, landmarks, splines. I.
Geometric morphometrics: ten years of progress following the ‘revolution
 Italian Journal of Zoology
, 2004
"... The analysis of shape is a fundamental part of much biological research. As the field of statistics developed, so have the sophistication of the analysis of these types of data. This lead to multivariate morphometrics in which suites of measurements were analyzed together using canonical variates an ..."
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Cited by 92 (4 self)
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The analysis of shape is a fundamental part of much biological research. As the field of statistics developed, so have the sophistication of the analysis of these types of data. This lead to multivariate morphometrics in which suites of measurements were analyzed together using canonical variates analysis, principal components analysis, and related methods. In the 1980s, a fundamental change began in the nature of the data gathered and analyzed. This change focused on the coordinates of landmarks and the geometric information about their relative positions. As a byproduct of such an approach, results of multivariate analyses could be visualized as configurations of landmarks back in the original space of the organism rather than only as statistical scatter plots. This new approach, called “geometric morphometrics”, had benefits that lead Rohlf and Marcus (1993) to proclaim a “revolution” in morphometrics. In this paper, we briefly update the discussion in that paper and summarize the advances in the ten years since the paper by Rohlf and Marcus. We also speculate on future directions in morphometric analysis.