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434
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...
Estimating and interpreting the instantaneous frequency of a signal—Part I
 Fundamentals—Part II: Algorithms,” Proc. IEEE
, 1992
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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 122 (5 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 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 119 (6 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)–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 CSF1–induced migration, since migration speed was reduced to background levels in
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 118 (3 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.
Primate motor cortex and free arm movements to visual targets in threedimensional space. II. Coding of the direction of movement by a neuronal population
 Journal of Neuroscience
, 1988
"... We describe a code by which a population of motor cortical neurons could determine uniquely the direction of reaching movements in threedimensional space. The population consisted of 475 directionally tuned cells whose functional properties are described in the preceding paper (Schwartz et al., 1 ..."
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Cited by 98 (6 self)
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We describe a code by which a population of motor cortical neurons could determine uniquely the direction of reaching movements in threedimensional space. The population consisted of 475 directionally tuned cells whose functional properties are described in the preceding paper (Schwartz et al., 1988). Each cell discharged at the highest rate with movements in its “preferred direction ” and at progressively lower rates with movements in directions away from the preferred one. The neuronal population code assumes that for a particular movement direction each cell makes a vectorial contribution (“votes”) with direction in the cell’s preferred direction and magnitude proportional to the change in the cell’s discharge rate associated with the particular direction of movement. The vector sum of these contributions is the outcome of the population code (the “neuronal population vec
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 83 (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.
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 82 (23 self)
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We study the problem of learning groups or categories that are local
A parametric model for the distribution of the angle of arrival and the associated correlation function and power spectrum at the mobile station
 IEEE Trans. Veh. Technol
, 2002
"... Abstract _ _ One of the main assumptions in the Clarke’s classic channel model is isotropic scattering, i.e. uniform distribution for the angle of arrival of multipath components at the mobile station. However, in many mobile radio channels we encounter nonisotropic scattering, which strongly affec ..."
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Cited by 79 (10 self)
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Abstract _ _ One of the main assumptions in the Clarke’s classic channel model is isotropic scattering, i.e. uniform distribution for the angle of arrival of multipath components at the mobile station. However, in many mobile radio channels we encounter nonisotropic scattering, which strongly affects the correlation function and power spectrum of the complex envelope at the mobile receiver. In this contribution, we propose the use of the versatile von Mises angular distribution, which includes and/or closely approximates important distributions like uniform, impulse, cardioid, Gaussian, and wrapped Gaussian, for modeling the nonuniform angle of arrivals at the mobile. Based on this distribution, associated correlation function and power spectrum of the complex envelope at the mobile receiver are derived. The utility of the new results is demonstrated by comparison with the correlation function estimates of measured data. Point of contact: Ali Abdi
Online MultiPerson TrackingbyDetection from a Single, Uncalibrated Camera
 PAMI
, 2010
"... In this paper, we address the problem of automatically detecting and tracking a variable number of persons in complex scenes using a monocular, potentially moving, uncalibrated camera. We propose a novel approach for multiperson trackingbydetection in a particle filtering framework. In addition ..."
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Cited by 78 (0 self)
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In this paper, we address the problem of automatically detecting and tracking a variable number of persons in complex scenes using a monocular, potentially moving, uncalibrated camera. We propose a novel approach for multiperson trackingbydetection in a particle filtering framework. In addition to final highconfidence detections, our algorithm uses the continuous confidence of pedestrian detectors and online trained, instancespecific classifiers as a graded observation model. Thus, generic object category knowledge is complemented by instancespecific information. The main contribution of this paper is to explore how these unreliable information sources can be used for robust multiperson tracking. The algorithm detects and tracks a large number of dynamically moving persons in complex scenes with occlusions, does not rely on background modeling, requires no camera or ground plane calibration, and only makes use of information from the past. Hence, it imposes very few restrictions and is suitable for online applications. Our experiments show that the method yields good tracking performance in a large variety of highly dynamic scenarios, such as typical surveillance videos, webcam footage, or sports sequences. We demonstrate that our algorithm outperforms other methods that rely on additional information. Furthermore, we analyze the influence of different algorithm components on the robustness.