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261
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 468 (15 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...
Estimating and Interpreting the Instantaneous Frequency of a Signal
 Proceedings of the IEEE
, 1992
"... The frequency of a sinusoidal signal is a well defined quantity. However, often in practice, signals are not truly sinusoidal, or even aggregates of sinusoidal components. Nonstationary signals in particular do not lend themselves well to decomposition into sinusoidal components. For such signals, t ..."
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Cited by 132 (3 self)
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The frequency of a sinusoidal signal is a well defined quantity. However, often in practice, signals are not truly sinusoidal, or even aggregates of sinusoidal components. Nonstationary signals in particular do not lend themselves well to decomposition into sinusoidal components. For such signals, the notion of frequency loses its effectiveness, and one needs to use a parameter which accounts for the timevarying nature of the process. This need has given rise to the idea of instantaneous frequency. The instantaneous frequency (IF) of a signal is a parameter which is often of significant practical importance. In many situations such as seismic, radar, sonar, communications, and biomedical applications, the IF is a good descriptor of some physical phenomenon. This paper discusses the concept of instantaneous frequency, its definitions, and the correspondence between the various mathematical models formulated for representation of IF. The paper also considers the extent to which the IF corresponds to our intuitive expectation of reality. A historical review of the successive attempts to define the IF is presented. Then the relationships between the IF and the groupdelay, analytic signal, and bandwidthtime (BT) product are explored, as well as the relationship with timefrequency distributions. Finally, the notions of monocomponent and multicomponent signals, and instantaneous bandwidth are discussed. It is shown that all these notions are well described in the context of the theory presented. I.
Clustering Based on Conditional Distributions in an Auxiliary Space
 Neural Computation
, 2001
"... We study the problem of learning groups or categories that are local ..."
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Cited by 80 (22 self)
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We study the problem of learning groups or categories that are local
Vanishing point calculation as a statistical inference on the unit sphere
 In Proc. ICCV
, 1990
"... \Lambda In this paper vanishing point computation is characterized as a statistical estimation problem on the unit sphere; in particular as the estimation of the polar axis of an equatorial distribution. This framework facilitates the construction of confidence regions for 3D line orientation. ..."
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Cited by 68 (7 self)
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\Lambda In this paper vanishing point computation is characterized as a statistical estimation problem on the unit sphere; in particular as the estimation of the polar axis of an equatorial distribution. This framework facilitates the construction of confidence regions for 3D line orientation.
Means and Averaging in the Group of Rotations
, 2002
"... In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to ..."
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Cited by 65 (1 self)
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In this paper we give precise definitions of different, properly invariant notions of mean or average rotation. Each mean is associated with a metric in SO(3). The metric induced from the Frobenius inner product gives rise to a mean rotation that is given by the closest special orthogonal matrix to the usual arithmetic mean of the given rotation matrices. The mean rotation associated with the intrinsic metric on SO(3) is the Riemannian center of mass of the given rotation matrices. We show that the Riemannian mean rotation shares many common features with the geometric mean of positive numbers and the geometric mean of positive Hermitian operators. We give some examples with closedform solutions of both notions of mean.
Chromatic mechanisms in striate cortex of macaque
 LeonGarcia A. Probability and Random Processes for Electrical Engineering
, 1990
"... We measured the responses of 305 neurons in striate cortex to moving sinusoidal gratings modulated in chromaticity and luminance about a fixed white point. Stimuli were represented in a 3dimensional color space defined by 2 chromatic axes and a third along which luminance varied. With rare exceptio ..."
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Cited by 58 (1 self)
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We measured the responses of 305 neurons in striate cortex to moving sinusoidal gratings modulated in chromaticity and luminance about a fixed white point. Stimuli were represented in a 3dimensional color space defined by 2 chromatic axes and a third along which luminance varied. With rare exceptions the chromatic properties of cortical neurons were well described by a linear model in which the response of a cell is proportional to the sum (for complex cells, the rectified sum) of the signals from the 3 classes of cones. For each cell there is a vector passing through the white point along which modulation gives rise to a maximal response. The elevation (0,) and azimuth (4,) of this vector fully describe the chromatic properties of the cell. The linear model also describes neurons in 1.g.n. (Derrington et al., 1984), so most neurons in striate cortex have the same chromatic
A Unified Framework for Modelbased Clustering
 Journal of Machine Learning Research
, 2003
"... Modelbased clustering techniques have been widely used and have shown promising results in many applications involving complex data. This paper presents a unified framework for probabilistic modelbased clustering based on a bipartite graph view of data and models that highlights the commonaliti ..."
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Cited by 57 (6 self)
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Modelbased clustering techniques have been widely used and have shown promising results in many applications involving complex data. This paper presents a unified framework for probabilistic modelbased clustering based on a bipartite graph view of data and models that highlights the commonalities and differences among existing modelbased clustering algorithms. In this view, clusters are represented as probabilistic models in a model space that is conceptually separate from the data space. For partitional clustering, the view is conceptually similar to the ExpectationMaximization (EM) algorithm. For hierarchical clustering, the graphbased view helps to visualize critical/important distinctions between similaritybased approaches and modelbased approaches.
A role for Cdc42 in macrophage chemotaxis
 J. Cell
, 1998
"... Abstract. Three members of the Rho family, Cdc42, Rac, and Rho are known to regulate the organization of actinbased cytoskeletal structures. In Bac1.2F5 macrophages, we have shown that Rho regulates cell contraction, whereas Rac and Cdc42 regulate the formation of lamellipodia and filopodia, respec ..."
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Cited by 53 (3 self)
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Abstract. Three members of the Rho family, Cdc42, Rac, and Rho are known to regulate the organization of actinbased cytoskeletal structures. In Bac1.2F5 macrophages, we have shown that Rho regulates cell contraction, whereas Rac and Cdc42 regulate the formation of lamellipodia and filopodia, respectively. We have now tested the roles of Cdc42, Rac, and Rho in colony stimulating factor1 (CSF1)â€“induced macrophage migration and chemotaxis using the Dunn chemotaxis chamber. Microinjection of constitutively activated RhoA, Rac1, or Cdc42 inhibited cell migration, presumably because the cells were unable to polarize significantly in response to CSF1. Both Rho and Rac were required for CSF1â€“induced migration, since migration speed was reduced to background levels in
From Laplace To Supernova Sn 1987a: Bayesian Inference In Astrophysics
, 1990
"... . The Bayesian approach to probability theory is presented as an alternative to the currently used longrun relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions ..."
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Cited by 52 (2 self)
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. The Bayesian approach to probability theory is presented as an alternative to the currently used longrun relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions to wellposed statistical problems, and is historically the original approach to statistics. The reasons for earlier rejection of Bayesian methods are discussed, and it is noted that the work of Cox, Jaynes, and others answers earlier objections, giving Bayesian inference a firm logical and mathematical foundation as the correct mathematical language for quantifying uncertainty. The Bayesian approaches to parameter estimation and model comparison are outlined and illustrated by application to a simple problem based on the gaussian distribution. As further illustrations of the Bayesian paradigm, Bayesian solutions to two interesting astrophysical problems are outlined: the measurement of wea...