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28
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...
Wishart and PseudoWishart Distributions and Some Applications to Shape Theory
, 1997
"... Suppose that XtNN_m(+, 7, 3). An expression for the density function is given when 7 0 and or 3 0. An extension of Uhlig's result (Uhlig [17]) is expanded for the singular value decomposition of a matrix Z of order N_m when the rank (Z)=q min(N, m). This paper fills an important gap in unifying ..."
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Cited by 21 (5 self)
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Suppose that XtNN_m(+, 7, 3). An expression for the density function is given when 7 0 and or 3 0. An extension of Uhlig's result (Uhlig [17]) is expanded for the singular value decomposition of a matrix Z of order N_m when the rank (Z)=q min(N, m). This paper fills an important gap in unifying, for the first time, all Wishart and pseudoWishart distributions, whether central or noncentral, whether singular or nonsingular, and applying them in shape analysis. In particular, the shape density and the sizeandshape cone density are obtained for the singular general case.
SINGULAR RANDOM MATRIX DECOMPOSITIONS: JACOBIANS
, 2002
"... For a singular random matrix Y, we find the Jacobians associated with the following decompositions; QR, Polar, Singular Value (SVD), L´U, L´DM and modified QR (QDR). Similarly, we find the Jacobinas of the following decompositions: Spectral, Cholesky´s, L´DL and symmetric nonnegative definite squar ..."
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Cited by 18 (6 self)
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For a singular random matrix Y, we find the Jacobians associated with the following decompositions; QR, Polar, Singular Value (SVD), L´U, L´DM and modified QR (QDR). Similarly, we find the Jacobinas of the following decompositions: Spectral, Cholesky´s, L´DL and symmetric nonnegative definite square root, of the crossproduct matrix S = Y´Y.
Recognition of Visual Object Classes
"... Object recognition is both about recognizing specific objects, e.g., "That is my dog Spot." and about recognizing classes of objects, e.g., "That is a dog." Our focus is on the latter problem, even though we do not offer a precise definition for what constitutes a class. In some ..."
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Cited by 8 (1 self)
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Object recognition is both about recognizing specific objects, e.g., "That is my dog Spot." and about recognizing classes of objects, e.g., "That is a dog." Our focus is on the latter problem, even though we do not offer a precise definition for what constitutes a class. In some cases, for example with human faces, the objects in a class are visually similar and form a visual object class. In other cases, say chairs, objects in the class may not look at all alikethe only similarities are in function. Recognition of functional object classes requires higherlevel cognitive reasoning, we restrict here our attention to visual object classes. The main difficulty in object recognition is the problem of invariance. The pixel representation provided by the camera is dependent upon the lighting conditions, object pose, camera position, etc. Further, there is inherent variability between different instances from the same object class. Our approach to this problem is to model an object class ...
Wishart and PseudoWishart distributions under elliptical laws and related distributions in the shape theory context
 JOURNAL OF STATISTICAL PLANNING AND INFERENCE
, 2006
"... ..."
Sizeandshape Cone, Shape Disk and Configuration Densities for the Elliptical Models
, 2000
"... The sizeandshape cone, shape disk and configuration densities are studied under elliptically contoured distributions in the central case. We prove that the shape disk and confiuration densities are invariant on the family of elliptical laws. ..."
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Cited by 6 (2 self)
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The sizeandshape cone, shape disk and configuration densities are studied under elliptically contoured distributions in the central case. We prove that the shape disk and confiuration densities are invariant on the family of elliptical laws.
Bayesian flexible shape matching with applications to structural bioinformatics. (submitted to
 Journal of the American Statistical Association
, 2006
"... We introduce a method for flexible shape registration using Bayesian changepoint analysis. Our approach is particularly suitable for shapes containing “hinge”like flexibility, and is motivated by problems in structural proteomics and bioinformatics. We define a class of flexible shape spaces and an ..."
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Cited by 4 (3 self)
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We introduce a method for flexible shape registration using Bayesian changepoint analysis. Our approach is particularly suitable for shapes containing “hinge”like flexibility, and is motivated by problems in structural proteomics and bioinformatics. We define a class of flexible shape spaces and an associated Procrustestype metric, along with a highly efficient algorithm for computing flexible shape distance. We use this distance to define distributions over flexible shapes, and develop Bayesian models for several variants including both affine and rigidbody component transformations. We demonstrate the approach on several examples arising from protein structure analysis, including structure alignment and function discovery.
Noncentral, nonsingular matrix variate beta distribution
 BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS (2007), 21, PP. 175–186
, 2007
"... In this paper, we determine the density of a nonsingular noncentral matrix variate beta type I and II distributions under different definitions. ..."
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Cited by 3 (3 self)
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In this paper, we determine the density of a nonsingular noncentral matrix variate beta type I and II distributions under different definitions.