Results 1  10
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808
Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2002
"... This paper presents a novel variational framework to deal with frame partition problems in Computer Vision. This framework exploits boundary and regionbased segmentation modules under a curvebased optimization objective function. The task of supervised texture segmentation is considered to demonst ..."
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Cited by 312 (9 self)
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by unifying region and boundarybased information as an improved Geodesic Active Contour Model. The defined objective function is minimized using a gradientdescent method where a level set approach is used to implement the obtained PDE. According to this PDE, the curve propagation towards the final solution
INTEGRABLE TRILINEAR PDE’s
, 1994
"... In a recent publication we proposed an extension of Hirota’s bilinear formalism to arbitrary multilinearities. The trilinear (and higher) operators were constructed from the requirement of gauge invariance for the nonlinear equation. Here we concentrate on the trilinear case, and use singularity ana ..."
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Cited by 1 (0 self)
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analysis in order to single out equations that are likely to be integrable. New PDE’s are thus obtained, along with others already wellknown for their integrability and for which we obtain here the trilinear expression. 1.
Robust Numerical Methods for PDE Models of Asian Options
 Journal of Computational Finance
, 1998
"... We explore the pricing of Asian options by numerically solving the the associated partial differential equations. We demonstrate that numerical PDE techniques commonly used in finance for standard options are inaccurate in the case of Asian options and illustrate modifications which alleviate this p ..."
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Cited by 58 (15 self)
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We explore the pricing of Asian options by numerically solving the the associated partial differential equations. We demonstrate that numerical PDE techniques commonly used in finance for standard options are inaccurate in the case of Asian options and illustrate modifications which alleviate
Implicit Solutions of PDE’s
, 2008
"... Further investigations of implicit solutions to nonlinear partial differential equations are pursued. Of particular interest are the equations which are Lorentz invariant. The question of which differential equations of second order for a single unknown φ are solved by the imposition of an inhomoge ..."
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of an inhomogeneous quadratic relationship among the independent variables, whose coefficients are functions of φ is discussed, and it is shown that if the discriminant of the quadratic vanishes, then an implicit solution of the socalled Universal Field Equation is obtained. The relation to the general solution
1 History of Tzitzeica PDE
"... Abstract. This paper applies the von Neumann analysis to a discrete Tzitzeica PDE. Section 1 recalls some data from the fascinating history of Tzitzeica PDE, emphasizing on its geometrical and physical roots. Section 2 gives the Tzitzeica Lagrangian and its associated Tzitzeica Hamiltonian. Section ..."
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3 shows that the Tzitzeica PDE can be obtained via geometric dynamics. Section 4 refreshes the theory of integrators for twoparameter Lagrangian dynamics. Section 5 finds the discrete Tzitzeica equation. Section 6 motivates the von Neumann stability analysis. Section 7 presents the von Neumann
Consider the following elliptic PDE
"... In this paper, a class of elliptic partial differential equations (PDEs) is considered. A sufficient condition for the existence and uniqueness of a solution to the problem is obtained. Discretizing the equation by the finite difference method yields a linear system whose matrix is nonsymmetric and ..."
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In this paper, a class of elliptic partial differential equations (PDEs) is considered. A sufficient condition for the existence and uniqueness of a solution to the problem is obtained. Discretizing the equation by the finite difference method yields a linear system whose matrix is nonsymmetric
NONLOCAL CONSTRUCTIONS IN GEOMETRY OF PDE
"... This is an overview of recent results obtained by S. Igonin, P. Kersten, and A. Verbovetsky in collaboration with the author and related to using of nonlocal constructions in geometry of partial di®erential equations. For general references concerning geometry of PDE see [1, 7]. Let E J1() 1¡¡! M b ..."
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This is an overview of recent results obtained by S. Igonin, P. Kersten, and A. Verbovetsky in collaboration with the author and related to using of nonlocal constructions in geometry of partial di®erential equations. For general references concerning geometry of PDE see [1, 7]. Let E J1() 1¡¡! M
Meanfield backward stochastic differential equations and related patial differential equations
, 2007
"... In [5] the authors obtained MeanField backward stochastic differential equations (BSDE) associated with a Meanfield stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward SDEs, corresponding to a large number of “particles” (or “a ..."
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Cited by 181 (14 self)
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for MeanField BSDEs we prove that this MeanField BSDE describes the viscosity solution of a nonlocal PDE. The uniqueness of this viscosity solution is obtained for the space of continuous functions with polynomial growth. With the help of an example it is shown that for the nonlocal PDEs associated
Dynamic Load Balancing for PDE Solvers on Adaptive Unstructured Meshes
, 1992
"... Modern PDE solvers written for timedependent problems increasingly employ adaptive unstructured meshes (see Flaherty et al. [4]) in order to both increase efficiency and control the numerical error. If a distributed memory parallel computer is to be used, there arises the significant problem of div ..."
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Cited by 65 (15 self)
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suitable for timedependent problems in which the mesh may be changed frequently. 1 Introduction Modern PDE solvers for timedependent applications are currently being written so as to obtain accurate solutions to reallife problems with the solution process as automatic as possible. The use
Towards PDEBased Image Compression
, 2005
"... While methods based on partial differential equations (PDEs) and variational techniques are powerful tools for denoising and inpainting digital images, their use for image compression was mainly focussing on pre or postprocessing so far. In our paper we investigate their potential within the decod ..."
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Cited by 13 (11 self)
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the decoding step. We start with the observation that edgeenhancing diffusion (EED), an anisotropic nonlinear diffusion filter with a diffusion tensor, is wellsuited for scattered data interpolation: Even when the interpolation data are very sparse, good results are obtained that respect discontinuities
Results 1  10
of
808