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1.
Arjan Kuijper reas Schwarzkopf Thomas Kalbe Chandrajit Bajaj Stefan Roth & Michael Goesele 《高等学校计算数学学报(英文版)》2013,6(1):72-94
We present an efficient implementation of volumetric anisotropic image diffusion filters on
modern programmable graphics processing units (GPUs), where the mathematics behind volumetric diffusion is effectively reduced to the diffusion in 2D images.
We hereby avoid the computational bottleneck of a time consuming eigenvalue decomposition in $\mathbb{R}^3$.
Instead, we use a projection of the Hessian matrix along the surface normal onto the tangent plane of
the local isodensity surface and solve for the remaining two tangent space eigenvectors.
We derive closed formulas to achieve this and prevent the GPU code from branching.
We show that our most complex volumetric anisotropic diffusion filters gain a speed up of more than 600 compared to a CPU solution. 相似文献
2.
A. Kuijper 《PAMM》2007,7(1):1011201-1011202
Minimizing the integral ∫Ω1/p |∇L |p d Ω for an image L under suitable boundary conditions gives PDEs that are well-known for p = 1, 2, namely Total Variation evolution and Laplacian diffusion (also known as Gaussian scale space and heat equation), respectively. Without fixing p, one obtains a framework related to the p -Laplace equation. The partial differential equation describing the evolution can be simplified using gauge coordinates (directional derivatives), yielding an expression in the two second order gauge derivatives and the norm of the gradient. Ignoring the latter, one obtains a series of PDEs that form a weighted average of the second order derivatives, with Mean Curvature Motion as a specific case. Both methods have the Gaussian scale space in common. Using singularity theory, one can use properties of the heat equation (namely. the role of scale) in the full L ( x , t) space and obtain a framework for topological image segmentation. In order to be able to extend image analysis aspects of Gaussian scale space in future work, relations between these methods are investigated, and general numerical schemes are developed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
This note concerns a class of Wiener-Hopf operators on a finite interval, acting between Sobolev multi-index spaces. Necessary and sufficient conditions for such an operator to be Fredholm are given, as well as a formula for the index. The argument is based on a reduction procedure of convolution operators on a finite interval to operators of the same type on the half-line.supported by the Netherlands organization for scientific research (NWO)supported in part by NSF Grant 9101143 相似文献
4.
H. F. Kuijper 《Fresenius' Journal of Analytical Chemistry》1883,22(1):347-357
Ohne Zusammenfassung 相似文献
5.
The level scheme of97Tc has been investigated by observing theγ-rays following the decay of 2.9-d97Ru.γ-singles andγγ-coincidence measurements were carried out with Ge(Li)-detectors. The time difference of coincident γ-rays was measured as a third parameter. From the coincidence events, the intensities ofγγ-cascades were extracted. The97Ru decay gives rise to 18γ-lines which could be fitted into a level scheme of97Tc consisting of 9 levels. Spin and parity assignments of the levels were made from log(ft) values andγ-ray branching ratios. Discrepancies concerning the energy of the first 3/2? state and the existence of a 946 keV level are discussed. 相似文献
6.
The construction of shortest feedback shift registers for a finite sequence \(S_1,\ldots ,S_N\) is considered over finite chain rings, such as \({\mathbb Z}_{p^r}\). A novel algorithm is presented that yields a parametrization of all shortest feedback shift registers for the sequence of numbers \(S_1,\ldots ,S_N\), thus solving an open problem in the literature. The algorithm iteratively processes each number, starting with \(S_1\), and constructs at each step a particular type of minimal basis. The construction involves a simple update rule at each step which leads to computational efficiency. It is shown that the algorithm simultaneously computes a similar parametrization for the reverse sequence \(S_N,\ldots ,S_1\). The complexity order of the algorithm is shown to be \(O(r N^2)\). 相似文献
7.
A. B. Kuijper 《Integral Equations and Operator Theory》1991,14(1):146-152
This note deals with a class of convolution operators of the first kind on a finite interval. Necessary and sufficient conditions for such an operator to be Fredholm are given. The argument is based on a process of reduction of convolution-type operators on a finite interval to operators of the same type on the half line.Research supported by the Netherlands organization for scientific research (NWO). 相似文献
8.
Margreta Kuijper Jan Willem Polderman 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(4):429-443
Recently it has been shown that list decoding of Reed-Solomon codes may be translated into a bivariate interpolation problem. The data consist of pairs in a finite field and the aim is to find a bivariate polynomial that interpolates the given pairs and is minimal with respect to some criterion. We present a systems theoretic approach to this interpolation problem. With the data points we associate a set of time series, also called trajectories. For this set of trajectories we construct the Most Powerful Unfalsified Model (MPUM). This is the smallest possible model that explains these trajectories. The bivariate polynomial is then derived from a specific polynomial representation of the MPUM. 相似文献
9.
We focus on Gröbner bases for modules of univariate polynomial vectors over a ring. We identify a useful property, the “predictable leading monomial (PLM) property” that is shared by minimal Gröbner bases of modules in F[x]q, no matter what positional term order is used. The PLM property is useful in a range of applications and can be seen as a strengthening of the wellknown predictable degree property (= row reducedness), a terminology introduced by Forney in the 70’s. Because of the presence of zero divisors, minimal Gröbner bases over a finite ring of the type Zpr (where p is a prime integer and r is an integer >1) do not necessarily have the PLM property. In this paper we show how to derive, from an ordered minimal Gröbner basis, a so-called “minimal Gröbner p-basis” that does have a PLM property. We demonstrate that minimal Gröbner p-bases lend themselves particularly well to derive minimal realization parametrizations over Zpr. Applications are in coding and sequences over Zpr. 相似文献
10.
Abstract The Melting line of the WCA L-J reference system, i.e. the part of the L-J potential representing the repulsive forces, is determined by means of Monte Carlo calculations. The Gibbs free energy of the fluid is calculated by thermodynamic integration and that of the solid by using the Einstein-crystal method of Frenkel and Ladd (1984). 相似文献