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Sven Dickinson - One of the best experts on this subject based on the ideXlab platform.
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a framework for Symmetric Part detection in cluttered scenes
Symmetry, 2015Co-Authors: Sanja Fidler, Alex Levinshtein, Cristian Sminchisescu, Sven DickinsonAbstract:The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favour as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the Parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial Parts. However, today’s recognition systems are faced with cluttered scenes and the assumption that a closed contour exists, i.e., that figure-ground segmentation has been solved, rendering much of the medial axis community’s work inapplicable. In this article, we review a computational framework, previously reported in [1–3], that bridges the representation power of the medial axis and the need to recover and group an object’s Parts in a cluttered scene. Our framework is rooted in the idea that a maximally-inscribed disc, the building block of a medial axis, can be modelled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes.
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a framework for Symmetric Part detection in cluttered scenes
arXiv: Computer Vision and Pattern Recognition, 2015Co-Authors: Sanja Fidler, Alex Levinshtein, Cristian Sminchisescu, Sven DickinsonAbstract:The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favor as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the Parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial Parts. However, today's recognition systems are faced with cluttered scenes, and the assumption that a closed contour exists, i.e. that figure-ground segmentation has been solved, renders much of the medial axis community's work inapplicable. In this article, we review a computational framework, previously reported in Lee et al. (2013), Levinshtein et al. (2009, 2013), that bridges the representation power of the medial axis and the need to recover and group an object's Parts in a cluttered scene. Our framework is rooted in the idea that a maximally inscribed disc, the building block of a medial axis, can be modeled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes.
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detecting curved Symmetric Parts using a deformable disc model
International Conference on Computer Vision, 2013Co-Authors: Tom Sie Ho Lee, Sanja Fidler, Sven DickinsonAbstract:Symmetry is a powerful shape regularity that's been exploited by perceptual grouping researchers in both human and computer vision to recover Part structure from an image without a priori knowledge of scene content. Drawing on the concept of a medial axis, defined as the locus of centers of maximal inscribed discs that sweep out a Symmetric Part, we model Part recovery as the search for a sequence of deformable maximal inscribed disc hypotheses generated from a multiscale super pixel segmentation, a framework proposed by LEV09. However, we learn affinities between adjacent super pixels in a space that's invariant to bending and tapering along the symmetry axis, enabling us to capture a wider class of Symmetric Parts. Moreover, we introduce a global cost that perceptually integrates the hypothesis space by combining a pair wise and a higher-level smoothing term, which we minimize globally using dynamic programming. The new framework is demonstrated on two datasets, and is shown to significantly outperform the baseline LEV09.
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Multiscale Symmetric Part Detection and Grouping
International Journal of Computer Vision, 2013Co-Authors: Alex Levinshtein, Cristian Sminchisescu, Sven DickinsonAbstract:Skeletonization algorithms typically decompose an object’s silhouette into a set of Symmetric Parts, offering a powerful representation for shape categorization. However, having access to an object’s silhouette assumes correct figure-ground segmentation, leading to a disconnect with the mainstream categorization community, which attempts to recognize objects from cluttered images. In this paper, we present a novel approach to recovering and grouping the Symmetric Parts of an object from a cluttered scene. We begin by using a multiresolution superpixel segmentation to generate medial point hypotheses, and use a learned affinity function to perceptually group nearby medial points likely to belong to the same medial branch. In the next stage, we learn higher granularity affinity functions to group the resulting medial branches likely to belong to the same object. The resulting framework yields a skeletal approximation that is free of many of the instabilities that occur with traditional skeletons. More importantly, it does not require a closed contour, enabling the application of skeleton-based categorization systems to more realistic imagery.
Christiane Quesne - One of the best experts on this subject based on the ideXlab platform.
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quasi hermitian superSymmetric extensions of a non hermitian oscillator hamiltonian and of its generalizations
Journal of Physics A, 2008Co-Authors: Christiane QuesneAbstract:A harmonic oscillator Hamiltonian augmented by a non-Hermitian -Symmetric Part and its su(1,1) generalizations, for which a family of positive-definite metric operators was recently constructed, are re-examined in a superSymmetric context. Some quasi-Hermitian superSymmetric extensions of such Hamiltonians are proposed by enlarging su(1,1) to a superalgebra. This allows the construction of new non-Hermitian Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.
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quasi hermitian superSymmetric extensions of a non hermitian oscillator hamiltonian and of its generalizations
arXiv: Mathematical Physics, 2007Co-Authors: Christiane QuesneAbstract:A harmonic oscillator Hamiltonian augmented by a non-Hermitian \pt-Symmetric Part and its su(1,1) generalizations, for which a family of positive-definite metric operators was recently constructed, are re-examined in a superSymmetric context. Quasi-Hermitian superSymmetric extensions of such Hamiltonians are proposed by enlarging su(1,1) to a ${\rm su}(1,1/1) \sim {\rm osp}(2/2, \R)$ superalgebra. This allows the construction of new non-Hermitian Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.
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non hermitian oscillator hamiltonian and su 1 1 a way towards generalizations
arXiv: Mathematical Physics, 2007Co-Authors: Christiane QuesneAbstract:The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian $\cal PT$-Symmetric Part, is re-examined in the light of an su(1,1) approach. An alternative derivation, only relying on properties of su(1,1) generators, is proposed. Being independent of the realization considered for the latter, it opens the way towards the construction of generalized non-Hermitian (not necessarily $\cal PT$-Symmetric) oscillator Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.
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swanson s non hermitian hamiltonian and su 1 1 a way towards generalizations
2007Co-Authors: Christiane QuesneAbstract:The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian $\cal PT$-Symmetric Part, is re-examined in the light of an su(1,1) approach. An alternative derivation, only relying on properties of su(1,1) generators, is proposed. Being independent of the realization considered for the latter, it opens the way towards the construction of generalized non-Hermitian (not necessarily $\cal PT$-Symmetric) oscillator Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.
Geoffrey Bodenhausen - One of the best experts on this subject based on the ideXlab platform.
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determination of the antiSymmetric Part of the chemical shift anisotropy tensor via spin relaxation in nuclear magnetic resonance
Journal of Chemical Physics, 2010Co-Authors: Raphael Paquin, Luminita Duma, Philippe Pelupessy, Christel Gervais, Geoffrey BodenhausenAbstract:Relaxation processes induced by the antiSymmetric Part of the chemical shift anisotropy tensor (henceforth called anti-CSA) are usually neglected in NMR relaxation studies. It is shown here that anti-CSA components contribute to longitudinal relaxation rates of the indole N15 nucleus in tryptophan in solution at different magnetic fields and temperatures. To determine the parameters of several models for rotational diffusion and internal dynamics, we measured the longitudinal relaxation rates R1=1/T1 of N15, the N15–H1 dipole-dipole (DD) cross-relaxation rates (Overhauser effects), and the cross-correlated CSA/DD relaxation rates involving the second-rank Symmetric Part of the CSA tensor of N15 at four magnetic fields B0=9.4, 14.1, 18.8, and 22.3 T (400, 600, 800, and 950 MHz for protons) over a temperature range of 270
Joscha Gedicke - One of the best experts on this subject based on the ideXlab platform.
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residual based a posteriori error analysis for Symmetric mixed arnold winther fem
Numerische Mathematik, 2019Co-Authors: Carsten Carstensen, Dietmar Gallistl, Joscha GedickeAbstract:This paper introduces an explicit residual-based a posteriori error analysis for the Symmetric mixed finite element method in linear elasticity after Arnold–Winther with pointwise Symmetric and \(H({\text {div}})\)-conforming stress approximation. The residual-based a posteriori error estimator of this paper is reliable and efficient and truly explicit in that it solely depends on the Symmetric stress and does neither need any additional information of some skew Symmetric Part of the gradient nor any efficient approximation thereof. Hence, it is straightforward to implement an adaptive mesh-refining algorithm. Numerical experiments verify the proven reliability and efficiency of the new a posteriori error estimator and illustrate the improved convergence rate in comparison to uniform mesh-refining. A higher convergence rate for piecewise affine data is observed in the \(L^2\) stress error and reproduced in non-smooth situations by the adaptive mesh-refining strategy.
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residual based a posteriori error analysis for Symmetric mixed arnold winther fem
arXiv: Numerical Analysis, 2017Co-Authors: Carsten Carstensen, Dietmar Gallistl, Joscha GedickeAbstract:This paper introduces an explicit residual-based a posteriori error analysis for the Symmetric mixed finite element method in linear elasticity after Arnold-Winther with pointwise Symmetric and H(div)-conforming stress approximation. Opposed to a previous publication, the residual-based a posteriori error estimator of this paper is reliable and efficient and truly explicit in that it solely depends on the Symmetric stress and does neither need any additional information of some skew Symmetric Part of the gradient nor any efficient approximation thereof. Hence it is straightforward to implement an adaptive mesh-refining algorithm obligatory in practical computations. Numerical experiments verify the proven reliability and efficiency of the new a posteriori error estimator and illustrate the improved convergence rate in comparison to uniform mesh-refining. A higher convergence rates for piecewise affine data is observed in the L2 stress error and reproduced in non-smooth situations by the adaptive mesh-refining strategy.
Jill Pipher - One of the best experts on this subject based on the ideXlab platform.
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the dirichlet problem for elliptic operators having a bmo anti Symmetric Part
Mathematische Annalen, 2021Co-Authors: Steve Hofmann, Svitlana Mayboroda, Jill PipherAbstract:The present paper establishes the first result on the absolute continuity of elliptic measure with respect to the Lebesgue measure for a divergence form elliptic operator with non-smooth coefficients that have a $${{\,\mathrm{BMO}\,}}$$ anti-Symmetric Part. In Particular, the coefficients are not necessarily bounded. We prove that the Dirichlet problem for elliptic equation $$\mathrm{div}(A\nabla u)=0$$ in the upper half-space $$(x,t)\in {\mathbb {R}}^{n+1}_+$$ is uniquely solvable when $$n\ge 2$$ and the boundary data is in $$L^p({\mathbb {R}}^n,dx)$$ for some $$p\in (1,\infty )$$ . This result is equivalent to saying that the elliptic measure associated to L belongs to the $$A_\infty $$ class with respect to the Lebesgue measure dx, a quantitative version of absolute continuity.
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Boundary behavior of solutions of elliptic operators in divergence form with a BMO anti-Symmetric Part
Communications in Partial Differential Equations, 2019Co-Authors: Jill PipherAbstract:In this article, we investigate the boundary behavior of solutions of divergence-form operators with an elliptic Symmetric Part and a BMO antiSymmetric Part. Our results will hold in non-tangential...
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boundary behavior of solutions of elliptic operators in divergence form with a bmo anti Symmetric Part
arXiv: Analysis of PDEs, 2017Co-Authors: Jill PipherAbstract:In this paper, we investigate the boundary behavior of solutions of divergence-form operators with an elliptic Symmetric Part and a $BMO$ anti-Symmetric Part. Our results will hold in non-tangentially accessible (NTA) domains; these general domains were introduced by Jerison and Kenig and include the class of Lipschitz domains. We establish the H\"older continuity of the solutions at the boundary, existence of elliptic measures $\omega_L$ associated to such operators, and the well-posedness of the continuous Dirichlet problem as well as the $L^p(d\omega)$ Dirichlet problem in NTA domains. The equivalence in the $L^p$ norm of the square function and the non-tangential maximal function under certain conditions remains valid. When specialized to Lipschitz domains, it is then possible to extend, to these operators, various criteria for determining mutual absolute continuity of elliptic measure with surface measure.
