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EDUCATIONAL ARTICLE PolyTop: a Matlab implementation of a general topology
"... optimization framework using unstructured polygonal finite element meshes ..."
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optimization framework using unstructured polygonal finite element meshes
TwoPhase Kernel Estimation for Robust Motion Deblurring
"... Abstract. We discuss a few new motion deblurring problems that are significant to kernel estimation and nonblind deconvolution. We found that strong edges do not always profit kernel estimation, but instead under certain circumstance degrade it. This finding leads to a new metric to measure the use ..."
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Cited by 93 (4 self)
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Abstract. We discuss a few new motion deblurring problems that are significant to kernel estimation and nonblind deconvolution. We found that strong edges do not always profit kernel estimation, but instead under certain circumstance degrade it. This finding leads to a new metric to measure the usefulness of image edges in motion deblurring and a gradient selection process to mitigate their possible adverse effect. We also propose an efficient and highquality kernel estimation method based on using the spatial prior and the iterative support detection (ISD) kernel refinement, which avoids hard threshold of the kernel elements to enforce sparsity. We employ the TVℓ1 deconvolution model, solved with a new variable substitution scheme to robustly suppress noise. 1
Dimensional Analysis and Numerical Solution of the Rigid Ice Model of Frost Heave with Hints on How to Implement the Solution in Matlab
, 1997
"... Each year, frost action in the ground causes very costly problems in various constructions like highways, airport pavements, railways, pipelines and building foundations in the urban cold regions of the world. This thesis contains a survey of the rigid ice model, which is the most complete model of ..."
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. We also outline how to write a Matlab program for implementation of the rigid ice model. [12] and [10] give...
Gaussian processes for machine learning
 International Journal of Neural Systems
, 2004
"... Gaussian processes (GPs) are natural generalisations of multivariate Gaussian random variables to infinite (countably or continuous) index sets. GPs have been applied in a large number of fields to a diverse range of ends, and very many deep theoretical analyses of various properties are available. ..."
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Cited by 93 (14 self)
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Gaussian processes (GPs) are natural generalisations of multivariate Gaussian random variables to infinite (countably or continuous) index sets. GPs have been applied in a large number of fields to a diverse range of ends, and very many deep theoretical analyses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level with special emphasis on characteristics relevant in machine learning. It draws explicit connections to branches such as spline smoothing models and support vector machines in which similar ideas have been investigated. Gaussian process models are routinely used to solve hard machine learning problems. They are attractive because of their flexible nonparametric nature and computational simplicity. Treated within a Bayesian framework, very powerful statistical methods can be implemented which offer valid estimates of uncertainties in our predictions and generic model selection procedures cast as nonlinear optimization problems. Their main drawback of heavy computational scaling has recently been alleviated by the introduction of generic sparse approximations [13, 78, 31]. The mathematical literature on GPs is large and often uses deep
QuasiRandom Sequences and Their Discrepancies
 SIAM J. Sci. Comput
, 1994
"... Quasirandom (also called low discrepancy) sequences are a deterministic alternative to random sequences for use in Monte Carlo methods, such as integration and particle simulations of transport processes. The error in uniformity for such a sequence of N points in the sdimensional unit cube is meas ..."
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Cited by 92 (6 self)
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Quasirandom (also called low discrepancy) sequences are a deterministic alternative to random sequences for use in Monte Carlo methods, such as integration and particle simulations of transport processes. The error in uniformity for such a sequence of N points in the sdimensional unit cube is measured by its discrepancy, which is of size (log N) s N \Gamma1 for large N , as opposed to discrepancy of size (log log N) 1=2 N \Gamma1=2 for a random sequence (i.e. for almost any randomlychosen sequence). Several types of discrepancy, one of which is new, are defined and analyzed. A critical discussion of the theoretical bounds on these discrepancies is presented. Computations of discrepancy are presented for a wide choice of dimension s, number of points N and different quasirandom sequences. In particular for moderate or large s, there is an intermediate regime in which the discrepancy of a quasirandom sequence is almost exactly the same as that of a randomly chosen sequence...
Distance Regularized Level Set Evolution and Its Application to Image Segmentation
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2010
"... Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, ..."
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Cited by 72 (1 self)
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Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore
Practical Steps fo Dynamic Mode Spectroscopy i ransient Changes:
"... functional NIRS signals are delayed with respect to cbf(t) cmro2(t) as a result of the blood transit time in the microvasculature. In the frequency domain, we have identified physiological parameters (e.g., blood transit time, cutoff frequency of autoregulation) that can be Functional brain studie ..."
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functional NIRS signals are delayed with respect to cbf(t) cmro2(t) as a result of the blood transit time in the microvasculature. In the frequency domain, we have identified physiological parameters (e.g., blood transit time, cutoff frequency of autoregulation) that can be Functional brain
Minimization of RegionScalable Fitting Energy for Image Segmentation
 IEEE TRANS. ON IMAGE PROCESSING
, 2008
"... Intensity inhomogeneities often occur in realworld images and may cause considerable difficulties in image segmentation. In order to overcome the difficulties caused by intensity inhomogeneities, we propose a regionbased active contour model that draws upon intensity information in local regions ..."
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Cited by 66 (2 self)
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at a controllable scale. A data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour. This energy is then incorporated into a variational level set formulation with a level set regularization term, from
DISCRETE FRACTIONAL CALCULUS: NONEQUIDISTANT GRIDS AND VARIABLE STEP LENGTH
"... In this paper we further develop Podlubny’s matrix approach to discretization of integrals and derivatives of arbitrary real order. Numerical integration and differentiation on a set of nonequidistant nodes is described and illustrated by several examples of numerical solution of fractional diffe ..."
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differential equations. In this paper, for the first time, we present a variable step length approach that we call “the method of large steps”, since it is applied in combination with the matrix approach for each “large step”. This new method is also illustrated by an example. The presented approach allows
Results 11  20
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