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您的检索式：作者名="Remco Duits"
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| 1 | Numerical Schemes for Linear and Non-Linear Enhancement of DW-MRI显示文摘We consider the linear and non-linear enhancement of diffusion weighted magnetic resonance images(DW-MRI)to use contextual information in denoising and inferring fiber crossings.We describe the space of DW-MRI images in a moving frame of reference,attached to fiber fragments which allows for convection-diffusion along the fibers.Because of this approach,our method is naturally able to handle crossings in data.We will perform experiments showing the ability of the enhancement to infer information about crossing structures,even in diffusion tensor images(DTI)which are incapable of representing crossings themselves.We will present a novel non-linear enhancement technique which performs better than linear methods in areas around ventricles,thereby eliminating the need for additional preprocessing steps to segment out the ventricles.We pay special attention to the details of implementation of the various numeric schemes. | Eric Creusen Remco Duits Anna Vilanova Luc Florack | 2013 | Numerical Mathematics(Theory,Methods and Applications)2013，6，1： | 1 |
| 2 | Numerical Approaches for Linear Left-invariant Diffusions on SE(2), their Comparison to Exact Solutions, and their Applications in Retinal Imaging显示文摘Left-invariant PDE-evolutions on the roto-translation group SE(2)(and their resolvent equations)have been widely studied in the fields of cortical model-ing and image analysis.They include hypo-elliptic diffusion(for contour enhance-ment)proposed by Citti&Sarti,and Petitot,and they include the direction process(for contour completion)proposed by Mumford.This paper presents a thorough study and comparison of the many numerical approaches,which,remarkably,are missing in the literature.Existing numerical approaches can be classified into 3 categories:Finite difference methods,Fourier based methods(equivalent to SE(2)-Fourier methods),and stochastic methods(Monte Carlo simulations).There are also 3 types of exact solutions to the PDE-evolutions that were derived explicitly(in the spatial Fourier domain)in previous works by Duits and van Almsick in 2005.Here we provide an overview of these 3 types of exact solutions and explain how they relate to each of the 3 numerical approaches.We compute relative errors of all nu-merical approaches to the exact solutions,and the Fourier based methods show us the best performance with smallest relative errors.We also provide an improvement of Mathematica algorithms for evaluating Mathieu-functions,crucial in implemen-tations of the exact solutions.Furthermore,we include an asymptotical analysis of the singularities within the kernels and we propose a probabilistic extension of un-derlying stochastic processes that overcomes the singular behavior in the origin of time-integrated kernels.Finally,we show retinal imaging applications of combining left-invariant PDE-evolutions with invertible orientation scores. | Jiong Zhang Remco Duits Gonzalo Sanguinetti Bart Mter Haar Romeny | 2016 | Numerical Mathematics(Theory,Methods and Applications)2016，9，1： | 0 |
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