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As a method based on the deformable surface evolution, brain extraction tools (BET) is widely used for brain extraction on cranial 3D magnetic resonance (MR) images. BET iteratively applies an evolution model depending on local parameters to the deformable surface until it reaches the brain border. In this paper, we propose a modified BET based on the fast model introducing a global parameter, the global mean inter-vertex distance of deformable surface. The surface evolution consists of two steps driven by two models: pre-processing step by the fast model and major step by the original model. We demonstrated our method in the experiments with T₁-weighted and diffusion weighted MR images of 19 normal subjects. The modified BET converged within 300 iterations less than half of about 1000 iterations in the original BET, while reducing substantially the false negative regions and self-intersections. The proposed method may be efficient for high resolution images and large-scale studies.

In this paper, we describe a new algorithm for radar detection based on the Hough transform which employs the slope-intercept parameter space. Unlike the conventional Hough transform, we shift the parameter space cells to perform the transform. The computation burden is reduced. Another advantage is that those straight lines whose intercept are bigger than the radar maximum range can also be detected. In addition, we also investigate the performance of the algorithm we present and show its efficiency with some simulations.

This paper presents a fast fuzzy c-means (FCM) clustering algorithm with two layers, which is a mergence of hard clustering and fuzzy clustering. The result of hard clustering is used to initialize the c cluster centers in fuzzy clustering, and then the number of iteration steps is reduced. The application of the proposed algorithm to image segmentation based on the two dimensional histogram is provided to show its computational efficience.

Direct computation of Legendre orthogonal moments requires huge arithmetic operations, which is very time consuming. Many works have described methods for reducing the computations involved in evaluating Legendre moments. Nevertheless, reduction computational complexity is still an open problem and needs more investigation. Existing algorithms mainly focused on binary images and compute Legendre moments using a set of geometric moments. We propose a fast and efficient method for computation of Legendre moments for binary and gray level images. A recurrence formula of one-dimensional Legendre moments will be established using the recursive property of Legendre polynomials; then the method will be extended to calculate the two-dimensional Legendre moments. This method is completely independent on geometric moment. The complexity analysis shows that the proposed method computes Legendre moments more efficiently than the direct method and the other conventional methods.

By applying the multiscale method to the Möbius transformation function, we construct the multiscale analytic sampling approximation (MASA) to any function in the Hardy space $H^2(𝕋)$. The approximation error is estimated, and it is proved that the MASA is robust to sample error. We prove that the MASA can be expressed by a Hankel matrix, making use of which, a fast algorithm is established to compute the MASA. Since what we acquire in practice may well be the samples on time domain instead of the analytic ones on the unit disc of the complex plane, we establish a fast algorithm for acquiring analytic samples. Numerical experiments are carried out to demonstrate the efficiency of the MASA.

Sample entropy is a widely used tool for quantifying complexity of a biological system. Computing sample entropy directly using its definition requires large computational costs. We propose a fast algorithm based on a k-d tree data structure for computing sample entropy. We prove that the time complexity of the proposed algorithm is and its space complexity is O(N log N), where N is the length of the input time series and m is the length of its pattern templates. We present a numerical experiment that demonstrates significant improvement of the proposed algorithm in computing time.

Due to the successful applications in engineering, physics, biology, finance, etc., there has been substantial interest in fractional diffusion equations over the past few decades, and literatures on developing and analyzing efficient and accurate numerical methods for reliably simulating such equations are vast and fast growing. This paper gives a concise overview on finite element methods for these equations, which are divided into time fractional, space fractional and time-space fractional diffusion equations. Besides, we also involve some relevant topics on the regularity theory, the well-posedness, and the fast algorithm.

Solitary wave motion, which arises in various fields of science and engineering such as hydrodynamics, quantum mechanics, plasma physics, and particle physics, is a nonlinear and weakly dispersive phenomenon generally modeled by a third-order nonlinear partial differential equation called the Korteweg–de Vries (KdV) equation. Our aim is to obtain a numerical solution of the governing KdV equation for shallow water waves using a robust and efficient numerical scheme called differential quadrature method (DQM), which has potential applications in solving higher-order differential equations, generally occurring in solid mechanics. One of the most promising advantages of DQM over standard numerical schemes, such as finite difference, finite element, and finite volume methods, is that it provides a very accurate and stable solution for a partial differential equation (PDE) using very few grid points. In fact, the solution becomes unstable if a large number of grid points are used in contrast to that of the standard numerical schemes, where solution becomes more accurate when spacing between grid points is reduced. This unique property of DQM makes it a fast algorithm for solving PDEs. Standard polynomial-based DQM with unequally spaced Gauss– Lobatto–Chebyshev points are used here for the simulation studies. The suggested numerical scheme is used for solving test problems involving a single solitary wave as well as interactions of two and three solitary waves. To check the accuracy of the newly applied method, the error norms, L₂ and L_∞, have been calculated. A fuzzy differential quadrature has been developed to solve the fuzzy KdV equation, which is formulated by considering the parameters associated with the nonlinear and dispersive terms of the KdV equation as fuzzy variables. The advantage of fuzzy differential quadrature is that we can reach the classical DQM solution from fuzzy DQM.

Up to now, all the wavelet transforms are inner product representation of Hilbert space. In this paper, based on the principle of mathematics and dialectical method, a novel method — VPWT (Vector Product Wavelet Transform) is proposed and studied, it is useful for wavelet theory and signal processing. In this paper, a new signal processing way is also given out. Numerical tests of the new way by optimal control theory suggest that the new method considerably improve the representation capabilities of wavelet expansions. And a novel method for constructing wavelet filters is described in this paper. The method generates a parameterization of wavelet coefficients based on sines and cosines of a set of angles, the angles sum to π/4, enforcing a total sum condition. The orthogonal wavelet filter coefficients with arbitrary length are constructed. When N = 2^{k - 1} and N = 2k, the unified analytic constructions of orthogonal wavelet filters are put forward, respectively. The parameterization is necessary and sufficient for filters of length 2, the method is shown to be sufficient for filter of length 2^{k - 1}. The famous Daubechies filter and some other wavelet filters are tested by the proposed novel method, which is very useful for wavelet theory research and many applications areas such as partern recognition. Based on wavelet analysis, the key theory on information transmission for point to point by the safest way in Internet is studied in this paper. By making full use of the three kinds of features such as computer features, files features and human being features, the mathematic model of information transmission for point to point by the safest way in Internet is set up for the first time. International Centre for Wavelet Analysis and Its Applications of Logistical Engineering University successfully develops the electronic signature system for the security of our country, which based on wavelet analysis with CNC — net.com from the height of the tactics and stratagem, adopting the theory of the fasting wavelet transform and the technology of biology identify. The character of fingerprints is detected, transformed to fingerprint feature codes and embedded into electronic texts in this paper, the security problems of the information transformation is solved completely. The paper may have important influence on the Internet client authentication, information authentication and have the vital contribution to the progressive network security and information security of Internet.