The Experts below are selected from a list of 201 Experts worldwide ranked by ideXlab platform
Christoph Schnorr - One of the best experts on this subject based on the ideXlab platform.
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variational recursive joint estimation of dense scene structure and camera motion from monocular high speed traffic sequences
International Conference on Computer Vision, 2011Co-Authors: Florian Becker, Frank Lenzen, Jorg Hendrik Kappes, Christoph SchnorrAbstract:We present an approach to jointly estimating camera motion and dense scene structure in terms of depth maps from monocular image sequences in driver-assistance scenarios. For two consecutive frames of a sequence taken with a single fast moving camera, the approach combines numerical estimation of egomotion on the Euclidean Manifold of motion parameters with variational regularization of dense depth map estimation. Embedding this online joint estimator into a recursive framework achieves a pronounced spatio-temporal filtering effect and robustness. We report the evaluation of thousands of images taken from a car moving at speed up to 100 km/h. The results compare favorably with two alternative settings that require more input data: stereo based scene reconstruction and camera motion estimation in batch mode using multiple frames. The employed benchmark dataset is publicly available.
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Model-Based Multiple Rigid Object Detection and Registration in Unstructured Range Data
International Journal of Computer Vision, 2011Co-Authors: Dirk Breitenreicher, Christoph SchnorrAbstract:We present a two-stage approach to the simultaneous detection and registration of multiple instances of industrial 3D objects in unstructured noisy range data. The first non-local processing stage takes all data into account and computes in parallel multiple localizations of the object along with rough pose estimates. The second stage computes accurate registrations for all detected object instances individually by using local optimization. Both stages are designed using advanced numerical techniques, large-scale sparse convex programming, and second-order geometric optimization on the Euclidean Manifold, respectively. They complement each other in that conflicting interpretations are resolved through non-local convex processing, followed by accurate non-convex local optimization based on sufficiently good initializations. As input data a sparse point sample of the object’s surface is required exclusively. Our experiments focus on industrial applications where multiple 3D object instances are randomly assembled in a bin, occlude each other, and unstructured noisy range data is acquired by a laser scanning device.
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ICCV - Variational recursive joint estimation of dense scene structure and camera motion from monocular high speed traffic sequences
2011 International Conference on Computer Vision, 2011Co-Authors: Florian Becker, Frank Lenzen, Jorg Hendrik Kappes, Christoph SchnorrAbstract:We present an approach to jointly estimating camera motion and dense scene structure in terms of depth maps from monocular image sequences in driver-assistance scenarios. For two consecutive frames of a sequence taken with a single fast moving camera, the approach combines numerical estimation of egomotion on the Euclidean Manifold of motion parameters with variational regularization of dense depth map estimation. Embedding this online joint estimator into a recursive framework achieves a pronounced spatio-temporal filtering effect and robustness. We report the evaluation of thousands of images taken from a car moving at speed up to 100 km/h. The results compare favorably with two alternative settings that require more input data: stereo based scene reconstruction and camera motion estimation in batch mode using multiple frames. The employed benchmark dataset is publicly available.
David J. Gross - One of the best experts on this subject based on the ideXlab platform.
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Two-dimensional QCD is a string theory☆
Nuclear Physics, 1993Co-Authors: David J. GrossAbstract:I explore the possibility of finding an equivalent string representation of two-dimensional QCD. I develop the large N expansion of the QCD2 partition function on an arbitrary two-dimensional Euclidean Manifold. If this is related to a two-dimensional string theory then many of the coefficients of the 1N expansion must vanish. This is shown to be true to all orders, giving strong evidence for the existence of a string representation.
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Two-dimensional QCD as a string theory
Nuclear Physics B, 1993Co-Authors: David J. GrossAbstract:I explore the possibility of finding an equivalent string representation of two dimensional QCD. I develop the large N expansion of the ${\rm QCD_2}$ partition function on an arbitrary two dimensional Euclidean Manifold. If this is related to a two-dimensional string theory then many of the coefficients of the ${1\over N}$ expansion must vanish. This is shown to be true to all orders, giving strong evidence for the existence of a string representation.Comment: 24 page
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Two Dimensional QCD as a String Theory
Nuclear Physics B, 1993Co-Authors: David J. GrossAbstract:I explore the possibility of finding an equivalent string representation of two dimensional QCD. I develop the large N expansion of the ${\rm QCD_2}$ partition function on an arbitrary two dimensional Euclidean Manifold. If this is related to a two-dimensional string theory then many of the coefficients of the ${1\over N}$ expansion must vanish. This is shown to be true to all orders, giving strong evidence for the existence of a string representation.
Michel Verleysen - One of the best experts on this subject based on the ideXlab platform.
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nonlinear data projection on non Euclidean Manifolds with controlled trade off between trustworthiness and continuity
Neurocomputing, 2009Co-Authors: Victor Onclinx, Vincent Wertz, Michel VerleysenAbstract:This paper presents a framework for nonlinear dimensionality reduction methods aimed at projecting data on a non-Euclidean Manifold, when their structure is too complex to be embedded in an Euclidean space. The methodology proposes an optimization procedure on Manifolds to minimize a pairwise distance criterion that implements a control of the trade-off between trustworthiness and continuity, two criteria that, respectively, represent the risks of flattening and tearing the projection. The methodology is presented as general as possible and is illustrated in the specific case of the sphere.
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Nonlinear data projection on non-Euclidean Manifolds with controlled trade-off between trustworthiness and continuity
Neurocomputing, 2009Co-Authors: Victor Onclinx, Vincent Wertz, Michel VerleysenAbstract:This paper presents a framework for nonlinear dimensionality reduction methods aimed at projecting data on a non-Euclidean Manifold, when their structure is too complex to be embedded in an Euclidean space. The methodology proposes an optimization procedure on Manifolds to minimize a pairwise distance criterion that implements a control of the trade-off between trustworthiness and continuity, two criteria that, respectively, represent the risks of flattening and tearing the projection. The methodology is presented as general as possible and is illustrated in the specific case of the sphere. (C) 2009 Elsevier B.V. All rights reserved
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nonlinear data projection on a sphere with a controlled trade off between trustworthiness and continuity
The European Symposium on Artificial Neural Networks, 2008Co-Authors: Victor Onclinx, Vincent Wertz, Michel VerleysenAbstract:This paper presents a nonlinear method aimed to project data on a non-Euclidean Manifold, when their structure is too complex to be embedded in an Euclidean space. The method optimizes a pairwise distance criterion that implements a control between trustworthiness and continuity that respectively represent the risks of attening and tearing the projection. The method is illustrated to project data on a sphere, but can be extended to other Manifolds such as the torus and the cylinder.
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ESANN - Nonlinear data projection on a sphere with a controlled trade-off between trustworthiness and continuity
2008Co-Authors: Victor Onclinx, Vincent Wertz, Michel VerleysenAbstract:This paper presents a nonlinear method aimed to project data on a non-Euclidean Manifold, when their structure is too complex to be embedded in an Euclidean space. The method optimizes a pairwise distance criterion that implements a control between trustworthiness and continuity that respectively represent the risks of attening and tearing the projection. The method is illustrated to project data on a sphere, but can be extended to other Manifolds such as the torus and the cylinder.
Florian Becker - One of the best experts on this subject based on the ideXlab platform.
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variational recursive joint estimation of dense scene structure and camera motion from monocular high speed traffic sequences
International Conference on Computer Vision, 2011Co-Authors: Florian Becker, Frank Lenzen, Jorg Hendrik Kappes, Christoph SchnorrAbstract:We present an approach to jointly estimating camera motion and dense scene structure in terms of depth maps from monocular image sequences in driver-assistance scenarios. For two consecutive frames of a sequence taken with a single fast moving camera, the approach combines numerical estimation of egomotion on the Euclidean Manifold of motion parameters with variational regularization of dense depth map estimation. Embedding this online joint estimator into a recursive framework achieves a pronounced spatio-temporal filtering effect and robustness. We report the evaluation of thousands of images taken from a car moving at speed up to 100 km/h. The results compare favorably with two alternative settings that require more input data: stereo based scene reconstruction and camera motion estimation in batch mode using multiple frames. The employed benchmark dataset is publicly available.
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ICCV - Variational recursive joint estimation of dense scene structure and camera motion from monocular high speed traffic sequences
2011 International Conference on Computer Vision, 2011Co-Authors: Florian Becker, Frank Lenzen, Jorg Hendrik Kappes, Christoph SchnorrAbstract:We present an approach to jointly estimating camera motion and dense scene structure in terms of depth maps from monocular image sequences in driver-assistance scenarios. For two consecutive frames of a sequence taken with a single fast moving camera, the approach combines numerical estimation of egomotion on the Euclidean Manifold of motion parameters with variational regularization of dense depth map estimation. Embedding this online joint estimator into a recursive framework achieves a pronounced spatio-temporal filtering effect and robustness. We report the evaluation of thousands of images taken from a car moving at speed up to 100 km/h. The results compare favorably with two alternative settings that require more input data: stereo based scene reconstruction and camera motion estimation in batch mode using multiple frames. The employed benchmark dataset is publicly available.
Eberhard Zeidler - One of the best experts on this subject based on the ideXlab platform.
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Velocity Vector Fields on the Euclidean Manifold $\mathbb{E}^{3}$
Quantum Field Theory III: Gauge Theory, 2011Co-Authors: Eberhard ZeidlerAbstract:We want to study vector fields $$\mathbf{w}=\mathbf{w}(P), \quad P \in \mathbb{E}^3$$ on the 3-dimensional Euclidean Manifold \(\mathbb{E}^{3}\). For example, this concerns velocity vector fields or force fields like Newton’s gravitational field w=F grav, Maxwell’s electric field w=E, or Maxwell’s magnetic field w=B. We will frequently use the intuitive picture of the velocity vector field of a fluid. For such vector fields w on \(\mathbb{E}^{3}\), one has to distinguish between the covariant directional derivative D v w, and the Lie derivative \(\mathcal{L}_{\mathbf{v}}\mathbf{w}=D_{\mathbf{v}}\mathbf{w}-D_{\mathbf{w}}\mathbf{v}\). Here, v is the velocity field of the flow of fluid particles on \(\mathbb{E}^{3}\).
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velocity vector fields on the Euclidean Manifold mathbb e 3
2011Co-Authors: Eberhard ZeidlerAbstract:We want to study vector fields $$\mathbf{w}=\mathbf{w}(P), \quad P \in \mathbb{E}^3$$ on the 3-dimensional Euclidean Manifold \(\mathbb{E}^{3}\). For example, this concerns velocity vector fields or force fields like Newton’s gravitational field w=F grav, Maxwell’s electric field w=E, or Maxwell’s magnetic field w=B. We will frequently use the intuitive picture of the velocity vector field of a fluid. For such vector fields w on \(\mathbb{E}^{3}\), one has to distinguish between the covariant directional derivative D v w, and the Lie derivative \(\mathcal{L}_{\mathbf{v}}\mathbf{w}=D_{\mathbf{v}}\mathbf{w}-D_{\mathbf{w}}\mathbf{v}\). Here, v is the velocity field of the flow of fluid particles on \(\mathbb{E}^{3}\).
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Temperature Fields on the Euclidean Manifold \mathbb{E}^{3}
Quantum Field Theory III: Gauge Theory, 2011Co-Authors: Eberhard ZeidlerAbstract:In mathematics and physics, differentiation describes the linearization of analytic objects like physical fields. In this chapter, let us study the directional derivative of a temperature field Θ on the Euclidean Manifold \(\mathbb{E}^{3}\). To this end, let $$\varTheta: \mathbb{E}^3\to \mathbb{R}$$ be a smooth function. In terms of physics, we regard Θ(P) as the temperature at the point P on \(\mathbb{E}^{3}\). We are given the smooth curve $$C: P=P(t), \qquad t\in \mathbb{R}$$ on \(\mathbb{E}^{3}\) with P 0:=P(0). In terms of position vectors at the origin, we describe the curve C by the smooth vector function x=x(t),t∈ℝ. The derivative $$\fbox{$d_{\mathbf{h}}\varTheta (P_{0}):= \frac{d\varTheta (\mathbf{x}(t))}{dt}_{|t=0}$}$$ is called the directional derivative of the temperature field Θ along the trajectory C at the point P 0.
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temperature fields on the Euclidean Manifold mathbb e 3
2011Co-Authors: Eberhard ZeidlerAbstract:In mathematics and physics, differentiation describes the linearization of analytic objects like physical fields. In this chapter, let us study the directional derivative of a temperature field Θ on the Euclidean Manifold \(\mathbb{E}^{3}\). To this end, let $$\varTheta: \mathbb{E}^3\to \mathbb{R}$$ be a smooth function. In terms of physics, we regard Θ(P) as the temperature at the point P on \(\mathbb{E}^{3}\). We are given the smooth curve $$C: P=P(t), \qquad t\in \mathbb{R}$$ on \(\mathbb{E}^{3}\) with P 0:=P(0). In terms of position vectors at the origin, we describe the curve C by the smooth vector function x=x(t),t∈ℝ. The derivative $$\fbox{$d_{\mathbf{h}}\varTheta (P_{0}):= \frac{d\varTheta (\mathbf{x}(t))}{dt}_{|t=0}$}$$ is called the directional derivative of the temperature field Θ along the trajectory C at the point P 0.
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The Euclidean Manifold \mathbb{E}^{3}
Quantum Field Theory III: Gauge Theory, 2011Co-Authors: Eberhard ZeidlerAbstract:Let us use the notation introduced at the beginning of Sect. 1.2 on page 71. Consider the motion $$P=P(t), \qquad t \in \mathbb{R}$$ of a particle (Fig. 4.1). Equivalently, we write $$\mathbf{x}= \mathbf{x}(t), \qquad t\in \mathbb{R}.$$ Here, x(t) denotes the position vector starting at the origin O at time t with the terminal point P(t)=O+x(t). Let E 3(P) denote the space of all the position vectors starting at the point P. This is a real 3-dimensional Hilbert space equipped with the inner product 〈u|w〉 P :=uw and the norm \(|\mathbf{u}|_{P}:= \sqrt {\langle \mathbf{u}|\mathbf{u}\rangle_{P}}\) for all u,w∈E 3(P).