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301
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 794 (33 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...
A Minimum Description Length Approach to Statistical Shape Modelling
 IEEE Transactions on Medical Imaging
, 2001
"... We describe a method for automatically building statistical shape models from a training set of exam ple boundaries / surfaces. These models show considerable promise as a basis for segmenting and interpreting images. One of the drawbacks of the approach is, however, the need to establish a set of ..."
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Cited by 202 (12 self)
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We describe a method for automatically building statistical shape models from a training set of exam ple boundaries / surfaces. These models show considerable promise as a basis for segmenting and interpreting images. One of the drawbacks of the approach is, however, the need to establish a set of dense correspondences between all members of a set of training shapes. Often this is achieved by locating a set of qandmarks manually on each training image, which is timeconsuming and subjective in 2D, and almost impossible in 3D. We describe how shape models can be built automatically by posing the correspondence problem as one of finding the parameterization for each shape in the training set. We select the set of parameterizations that build the best model. We define best as that which min imizes the description length of the training set, arguing that this leads to models with good compactness, specificity and generalization ability. We show how a set of shape parameterizations can be represented and manipulated in order to build a minimum description length model. Results are given for several different training sets of 2D boundaries, showing that the proposed method constructs better models than other approaches including manual landmarking  the current gold standard. We also show that the method can be extended straightforwardly to 3D.
Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape
 TO APPEAR IEEE TRANSACTIONS ON MEDICAL IMAGING
, 2004
"... A primary goal of statistical shape analysis is to describe the variability of a population of geometric objects. A standard technique for computing such descriptions is principal component analysis. However, principal component analysis is limited in that it only works for data lying in a Euclidean ..."
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Cited by 181 (33 self)
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A primary goal of statistical shape analysis is to describe the variability of a population of geometric objects. A standard technique for computing such descriptions is principal component analysis. However, principal component analysis is limited in that it only works for data lying in a Euclidean vector space. While this is certainly sufficient for geometric models that are parameterized by a set of landmarks or a dense collection of boundary points, it does not handle more complex representations of shape. We have been developing representations of geometry based on the medial axis description or mrep. While the medial representation provides a rich language for variability in terms of bending, twisting, and widening, the medial parameters are not elements of a Euclidean vector space. They are in fact elements of a nonlinear Riemannian symmetric space. In this paper we develop the method of principal geodesic analysis, a generalization of principal component analysis to the manifold setting. We demonstrate its use in describing the variability of mediallydefined anatomical objects. Results of applying this framework on a population of hippocampi in a schizophrenia study are presented.
A Mixture Model for Representing Shape Variation
 Image and Vision Computing
, 1997
"... The shape variation displayed by a class of objects can be represented as a probability density function, allowing us to determine plausible and implausible examples of the class. Given a training set of example shapes we can align them into a common coordinate frame and use kernel based density es ..."
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Cited by 121 (7 self)
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The shape variation displayed by a class of objects can be represented as a probability density function, allowing us to determine plausible and implausible examples of the class. Given a training set of example shapes we can align them into a common coordinate frame and use kernel based density estimation techniques to represent this distribution. Such an estimate is complex and expensive, so we generate a simpler approximation using a mixture of gaussians. We show how to calculate the distribution, and how it can be used in image search to locate examples of the modelled object in new images.
Statistical Models of Appearance for Medical Image Analysis and Computer Vision
 In Proc. SPIE Medical Imaging
, 2001
"... Statistical models of shape and appearance are powerful tools for interpreting medical images. We assume a training set of images in which corresponding `landmark' points have been marked on every image. From this data we can compute a statistical model of the shape variation, a model of the te ..."
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Cited by 114 (1 self)
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Statistical models of shape and appearance are powerful tools for interpreting medical images. We assume a training set of images in which corresponding `landmark' points have been marked on every image. From this data we can compute a statistical model of the shape variation, a model of the texture variation and a model of the correlations between shape and texture. With enough training examples such models should be able to synthesize any image of normal anatomy. By finding the parameters which optimize the match between a synthesized model image and a target image we can locate all the structures represented by the model. Two approaches to the matching will be described. The Active Shape Model essentially matches a model to boundaries in an image. The Active Appearance Model finds model parameters which synthesize a complete image which is as similar as possible to the target image. By using a `difference decomposition' approach the current difference between target image and synthesi...
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 104 (5 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.
Representation and Detection of Deformable Shapes
 PAMI
, 2004
"... We describe some techniques that can be used to represent and detect deformable shapes in images. The main di#culty with deformable template models is the very large or infinite number of possible nonrigid transformations of the templates. This makes the problem of finding an optimal match of a ..."
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Cited by 95 (3 self)
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We describe some techniques that can be used to represent and detect deformable shapes in images. The main di#culty with deformable template models is the very large or infinite number of possible nonrigid transformations of the templates. This makes the problem of finding an optimal match of a deformable template to an image incredibly hard. Using a new representation for deformable shapes we show how to e#ciently find a global optimal solution to the nonrigid matching problem. The representation is based on the description of objects using triangulated polygons. Our matching algorithm can minimize a large class of energy functions, making it applicable to a wide range of problems. We present experimental results of detecting shapes in medical images and images of natural scenes. Our method does not depend on initialization and is very robust, yielding good matches even in images with high clutter.
Segmentation and Interpretation of MR Brain Images: An Improved Active Shape Model
, 1997
"... This paper reports a novel method for fully automated segmentation that is based on description of shape and its variation using Point Distribution Models (PDM). An improvement of the Active Shape procedure introduced by Cootes and Taylor to find new examples of previously learned shapes using PDMs ..."
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Cited by 76 (7 self)
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This paper reports a novel method for fully automated segmentation that is based on description of shape and its variation using Point Distribution Models (PDM). An improvement of the Active Shape procedure introduced by Cootes and Taylor to find new examples of previously learned shapes using PDMs is presented. The new method for segmentation and interpretation of deep neuroanatomic structures such as thalamus, putamen, ventricular system, etc. incorporates a priori knowledge about shapes of the neuroanatomic structures to provide their robust segmentation and labeling in MR brain images. The method was trained in 8 MR brain images and tested in 19 brain images by comparison to observerdefined independent standards. Neuroanatomic structures in all testing images were successfully identified. Computeridentified and observerdefined neuroanatomic structures agreed well. The average labeling error was 7 \Sigma 3%. Border positioning errors were quite small, with the average border posi...