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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...
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2004
"... For analyzing shapes of planar, closed curves, we propose di#erential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinitedimensional spaces and their pairwise di#erences are quantified using the lengths of ge ..."
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Cited by 170 (37 self)
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For analyzing shapes of planar, closed curves, we propose di#erential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinitedimensional spaces and their pairwise di#erences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier basis to represent tangents to the shape spaces and then use a gradientbased shooting method to solve for the tangent that connects any two shapes via a geodesic.
Biometric Gait Recognition
 Biometrics School 2003, LNCS 3161
, 2005
"... Abstract. Psychological studies indicate that people have a small but statistically significant ability to recognize the gaits of individuals that they know. Recently, there has been much interest in machine vision systems that can duplicate and improve upon this human ability for application to bio ..."
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Cited by 14 (0 self)
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Abstract. Psychological studies indicate that people have a small but statistically significant ability to recognize the gaits of individuals that they know. Recently, there has been much interest in machine vision systems that can duplicate and improve upon this human ability for application to biometric identification. While gait has several attractive properties as a biometric (it is unobtrusive and can be done with simple instrumentation), there are several confounding factors such as variations due to footwear, terrain, fatigue, injury, and passage of time. This paper gives an overview of the factors that affect both human and machine recognition of gaits, data used in gait and motion analysis, evaluation methods, existing gait and quasi gait recognition systems, and uses of gait analysis beyond biometric identification. We compare the reported recognition rates as a function of sample size for several published gait recognition systems. 1
General Shape and Registration Analysis
 In
, 1997
"... The paper reviews various topics in shape analysis. In particular, matching configurations using regression is emphasized. Connections with general shape spaces and shape distances are discussed. Kendall's shape space and the affine shape space are considered in particular detail. Matching two ..."
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Cited by 12 (1 self)
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The paper reviews various topics in shape analysis. In particular, matching configurations using regression is emphasized. Connections with general shape spaces and shape distances are discussed. Kendall's shape space and the affine shape space are considered in particular detail. Matching two configurations and the extension to generalized matching are illustrated with applications in electrophoresis and biology. Shape distributions are briefly discussed and inference in tangent spaces is considered. Finally, some robustness and smoothing issues are highlighted. 1 Introduction The geometrical description of an object can be decomposed into registration and shape information. For example, an object's location, rotation and size could be the registration information and the geometrical information that remains is the object's shape. An object's shape is invariant under registration transformations and two objects have the same shape if they can be registered to match exactly. Depending...
2008a), ‘A multidimensional scaling approach to shape analysis’, Submitted for publication
, 1993
"... We propose an alternative to Kendall’s shape space for reflection shapes of configurations in Rm with k labelled vertices, where reflection shape consists of all the geometric information that is invariant under compositions of similarity and reflection transformations. The proposed approach embeds ..."
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Cited by 7 (0 self)
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We propose an alternative to Kendall’s shape space for reflection shapes of configurations in Rm with k labelled vertices, where reflection shape consists of all the geometric information that is invariant under compositions of similarity and reflection transformations. The proposed approach embeds the space of such shapes into the space P(k − 1) of (k − 1) × (k − 1) real symmetric positive semidefinite matrices, which is the closure of an open subset of a Euclidean space, and defines mean shape as the natural projection of Euclidean means in P(k − 1) on to the embedded copy of the shape space. This approach has strong connections with multidimensional scaling, and the mean shape so defined gives good approximations to other commonly used definitions of mean shape. We also use standard perturbation arguments for eigenvalues and eigenvectors to obtain a central limit theorem which then enables the application of standard statistical techniques to shape analysis in m> 2 dimensions.
Analysis of Planar Shapes Using Geodesic Lengths on a Shape Manifold
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2002
"... For analyzing shapes of planar, closed curves, we propose a mathematical representation of closed curves using "direction" functions (integrals of the signed curvature functions). Shapes are ..."
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Cited by 3 (0 self)
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For analyzing shapes of planar, closed curves, we propose a mathematical representation of closed curves using "direction" functions (integrals of the signed curvature functions). Shapes are
Gait Curves for Human Recognition, Backpack Detection and Silhouette Correction in a Nighttime Environment
"... The need for an automated surveillance system is pronounced at night when the capability of the human eye to detect anomalies is reduced. While there have been significant efforts in the classification of individuals using human metrology and gait, the majority of research assumes a daytime environ ..."
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Cited by 2 (1 self)
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The need for an automated surveillance system is pronounced at night when the capability of the human eye to detect anomalies is reduced. While there have been significant efforts in the classification of individuals using human metrology and gait, the majority of research assumes a daytime environment. The aim of this study is to move beyond traditional image acquisition modalities and explore the issues of object detection and human identification at night. To address these issues, a spatiotemporal gait curve that captures the shape dynamics of a moving human silhouette is employed. Initially proposed by Wang et al., 1 this representation of the gait is expanded to incorporate modules for individual classification, backpack detection, and silhouette restoration. Evaluation of these algorithms is conducted on the CASIA Night Gait Database, which includes 10 video sequences for each of 153 unique subjects. The video sequences were captured using a low resolution thermal camera. Matching performance of the proposed algorithms is evaluated using a nearest neighbor classifier. The outcome of this work is an efficient algorithm for backpack detection and human identification, and a basis for further study in silhouette enhancement.
Printed in Great Britain A multidimensional scaling approach to shape analysis
"... We propose an alternative to Kendall’s shape space for reflection shapes of configurations inRm with k labelled vertices, where reflection shape consists of all the geometric information that is invariant under compositions of similarity and reflection transformations. The proposed approach embeds t ..."
Abstract
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We propose an alternative to Kendall’s shape space for reflection shapes of configurations inRm with k labelled vertices, where reflection shape consists of all the geometric information that is invariant under compositions of similarity and reflection transformations. The proposed approach embeds the space of such shapes into the space P(k − 1) of (k − 1) × (k − 1) real symmetric positive semidefinite matrices, which is the closure of an open subset of a Euclidean space, and defines mean shape as the natural projection of Euclidean means in P(k − 1) on to the embedded copy of the shape space. This approach has strong connections with multidimensional scaling, and the mean shape so defined gives good approximations to other commonly used definitions of mean shape. We also use standard perturbation arguments for eigenvalues and eigenvectors to obtain a central limit theorem which then enables the application of standard statistical techniques to shape analysis in two or more dimensions.
Recognizing Complex Faces and Gaits Via Novel Probabilistic Models
, 2010
"... In the field of computer vision, developing automated systems to recognize people under unconstrained scenarios is a partially solved problem. In unconstrained scenarios a number of common variations and complexities such as occlusion, illumination, cluttered background and so on impose vast uncer ..."
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In the field of computer vision, developing automated systems to recognize people under unconstrained scenarios is a partially solved problem. In unconstrained scenarios a number of common variations and complexities such as occlusion, illumination, cluttered background and so on impose vast uncertainty to the recognition process. Among the various biometrics that have been emerging recently, this dissertation focus on two of them namely face and gait recognition. Firstly we address the problem of recognizing faces with major occlusions amidst other variations such as pose, scale, expression and illumination using a novel PRObabilistic Component based Interpretation Model (PROCIM) inspired by key psychophysical principles that are closely related to reasoning under uncertainty. The model basically employs Bayesian Networks to establish, learn, interpret and exploit intrinsic similarity mappings from the face domain. Then, by incorporating efficient inference strategies, robust decisions are made for successfully recognizing faces under uncertainty. PROCIM reports improved recognition rates over recent