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2,325
Tracking People with Twists and Exponential Maps
, 1998
"... This paper demonstrates a new visual motion estimation technique that is able to recover high degreeoffreedom articulated human body configurations in complex video sequences. We introduce the use of a novel mathematical technique, the product of exponential maps and twist motions, and its integra ..."
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Cited by 450 (5 self)
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This paper demonstrates a new visual motion estimation technique that is able to recover high degreeoffreedom articulated human body configurations in complex video sequences. We introduce the use of a novel mathematical technique, the product of exponential maps and twist motions, and its
The Convergence Approach to Exponentiable Maps
 352 MARIA MANUEL CLEMENTINO, DIRK HOFMANN AND WALTER
, 2000
"... Exponentiable maps in the category Top of topological spaces are characterized by an easy ultrafilterinterpolation property, in generalization of a recent result by Pisani for spaces. From this characterization we deduce that perfect (= proper and separated) maps are exponentiable, generalizing the ..."
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Cited by 11 (7 self)
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Exponentiable maps in the category Top of topological spaces are characterized by an easy ultrafilterinterpolation property, in generalization of a recent result by Pisani for spaces. From this characterization we deduce that perfect (= proper and separated) maps are exponentiable, generalizing
THE SQUARE DISCRETE EXPONENTIATION MAP
, 2011
"... We will examine the square discrete exponentiation map x → g x2 (mod p) and its properties. The square discrete exponentiation map is a variation on a commonly seen problem in crytographic algorithms. This paper focuses on understanding the underlying structure of the functional graphs generated by ..."
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We will examine the square discrete exponentiation map x → g x2 (mod p) and its properties. The square discrete exponentiation map is a variation on a commonly seen problem in crytographic algorithms. This paper focuses on understanding the underlying structure of the functional graphs generated
The exponential map of GL(N)
, 1996
"... A finite expansion of the exponential map for a N × N matrix is presented. The method uses the CayleyHamilton theorem for writing the higher matrix powers in terms of the first N1 ones. The resulting sums over the corresponding coefficients are rational functions of the eigenvalues of the matrix. ..."
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A finite expansion of the exponential map for a N × N matrix is presented. The method uses the CayleyHamilton theorem for writing the higher matrix powers in terms of the first N1 ones. The resulting sums over the corresponding coefficients are rational functions of the eigenvalues of the matrix.
THE EXPONENTIAL MAP AND THE EUCLIDEAN ISOMETRIES
"... Abstract. In the first section the basic properties of the exponential map of a Lie group are reviewed. The second section contains the Tarence Tao proof to the property that every compact connected Lie group is exponential. A direct specific proof to this property in the case of the special orthogo ..."
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Cited by 1 (1 self)
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Abstract. In the first section the basic properties of the exponential map of a Lie group are reviewed. The second section contains the Tarence Tao proof to the property that every compact connected Lie group is exponential. A direct specific proof to this property in the case of the special
THE EXPONENTIAL MAP FOR THE UNITARY GROUP
, 1994
"... Abstract: In this article we extend our previous results for the orthogonal group, SO(2, 4), to its homomorphic group SU(2, 2). Here we present a closed, finite formula for the exponential of a 4 × 4 traceless matrix, which can be viewed as the generator (Lie algebra elements) of the SL(4, C) group. ..."
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. We apply this result to the SU(2, 2) group, which Lie algebra can be represented by the Dirac matrices, and discuss how the exponential map for SU(2, 2) can be written by means of the Dirac matrices.
On geodesic exponential maps of the Virasoro group
, 2004
"... We study the geodesic exponential maps corresponding to Sobolev type rightinvariant (weak) Riemannian metrics µ (k) (k ≥ 0) on the Virasoro group Vir and show that for k ≥ 2, but not for k = 0, 1, each of them defines a smooth Fréchet chart of the unital element e ∈ Vir. In particular, the geodesic ..."
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Cited by 37 (4 self)
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We study the geodesic exponential maps corresponding to Sobolev type rightinvariant (weak) Riemannian metrics µ (k) (k ≥ 0) on the Virasoro group Vir and show that for k ≥ 2, but not for k = 0, 1, each of them defines a smooth Fréchet chart of the unital element e ∈ Vir. In particular
Practical parameterization of rotations using the exponential map
 Journal of Graphics Tools
, 1998
"... Parameterizing three degreeoffreedom (DOF) rotations is difficult to do well. Many graphics applications demand that we be able to compute and differentiate positions and orientations of articulated figures with respect to their rotational (and other) parameters, as well as integrate differential ..."
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Cited by 135 (2 self)
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equations, optimize functions of DOFs, and interpolate orientations. Widely used parameterizations such as Euler angles and quaternions are well suited to only a few of these operations. The exponential map maps a vector in R 3 describing the axis and magnitude of a three DOF rotation to the corresponding
Bifurcations in the space of exponential maps
 Preprint 3 (2004), Institute for Mathematical Sciences, SUNY StonyBrook. ArXiv:math.DS/0311480
"... Abstract. This article investigates the parameter space of the exponential family z ↦→ exp(z)+κ. We prove that the boundary (in C) of every hyperbolic component is a Jordan arc, as conjectured by Eremenko and Lyubich as well as Baker and Rippon, and that ∞ is not accessible through any nonhyperbolic ..."
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Cited by 10 (6 self)
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Abstract. This article investigates the parameter space of the exponential family z ↦→ exp(z)+κ. We prove that the boundary (in C) of every hyperbolic component is a Jordan arc, as conjectured by Eremenko and Lyubich as well as Baker and Rippon, and that ∞ is not accessible through any
Classification of escaping exponential maps
"... Abstract. We give a complete classification of the set of parameters κ for which the singular value of Eκ: z ↦ → exp(z) + κ escapes to ∞ under iteration. In particular, we show that every pathconnected component of this set is a curve to infinity. 1. ..."
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Cited by 10 (7 self)
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Abstract. We give a complete classification of the set of parameters κ for which the singular value of Eκ: z ↦ → exp(z) + κ escapes to ∞ under iteration. In particular, we show that every pathconnected component of this set is a curve to infinity. 1.
Results 1  10
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2,325