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160,365
Fronts propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations
, 1988
"... We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front also can be passively advected by an underlying flow. These algorithms approximate the equations of motion, w ..."
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Cited by 1167 (60 self)
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, which resemble HamiltonJacobi equations with parabolic righthand sides, by using techniques from hyperbolic conservation laws. Nonoscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps
Nonlinear total variation based noise removal algorithms
, 1992
"... A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the g ..."
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Cited by 2238 (50 self)
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to be stateoftheart for very noisy images. The method is noninvasive, yielding sharp edges in the image. The technique could be interpreted as a first step of moving each level set of the image normal to itself with velocity equal to the curvature of the level set divided by the magnitude of the gradient
A scaled conjugate gradient algorithm for fast supervised learning
 NEURAL NETWORKS
, 1993
"... A supervised learning algorithm (Scaled Conjugate Gradient, SCG) with superlinear convergence rate is introduced. The algorithm is based upon a class of optimization techniques well known in numerical analysis as the Conjugate Gradient Methods. SCG uses second order information from the neural netwo ..."
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Cited by 438 (0 self)
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A supervised learning algorithm (Scaled Conjugate Gradient, SCG) with superlinear convergence rate is introduced. The algorithm is based upon a class of optimization techniques well known in numerical analysis as the Conjugate Gradient Methods. SCG uses second order information from the neural
A HYBRID FINITE VOLUME/PDF MONTE CARLO METHOD TO CAPTURE SHARP GRADIENTS IN UNSTRUCTURED GRIDS
, 2000
"... The hybrid finite volume/PDF Monte Carlo method has both the advantages of the finite volume method’s efficiency in solving flow fields and the PDF method’s exactness in dealing with chemical reactions. It is, therefore, increasingly used in turbulent reactive flow calculations. In order to resolve ..."
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the sharp gradients of flow velocities and/or scalars, fine grids or unstructured solutionadaptive grids have to be used in the finite volume code. As a result, the calculation domain is covered by a grid system with very large variations in cell size. Such grids present a challenge for a combined PDF
SHARP GRADIENT ESTIMATE AND YAU’S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
, 2005
"... Abstract. We derive a sharp, localized version of elliptic type gradient estimates for positive solutions (bounded or not) to the heat equation. These estimates are akin to the ChengYau estimate for the Laplace equation and Hamilton’s estimate for bounded solutions to the heat equation on compact m ..."
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Cited by 5 (1 self)
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Abstract. We derive a sharp, localized version of elliptic type gradient estimates for positive solutions (bounded or not) to the heat equation. These estimates are akin to the ChengYau estimate for the Laplace equation and Hamilton’s estimate for bounded solutions to the heat equation on compact
Edge Detection and Ridge Detection with Automatic Scale Selection
 CVPR'96
, 1996
"... When extracting features from image data, the type of information that can be extracted may be strongly dependent on the scales at which the feature detectors are applied. This article presents a systematic methodology for addressing this problem. A mechanism is presented for automatic selection of ..."
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Cited by 341 (24 self)
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of scale levels when detecting onedimensional features, such as edges and ridges. Anovel concept of a scalespace edge is introduced, defined as a connected set of points in scalespace at which: (i) the gradient magnitude assumes a local maximum in the gradient direction, and (ii) a normalized measure
Sharp
"... bounds for the heat kernel on certain symmetric spaces of noncompact type ..."
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bounds for the heat kernel on certain symmetric spaces of noncompact type
Sharp
"... decay estimates of the solutions to a class of nonlinear second order ODE ..."
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decay estimates of the solutions to a class of nonlinear second order ODE
Results 1  10
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160,365