A numerical method for diffusion-convection equation using high-order difference schemes

In this paper, we propose a simple general form of high-order approximation of O(c²+ch²+h⁴) to solve the two-dimensional parabolic equation αuxx+βuyy=F(x,y,t,u,ux,uy,ut), where α and β are positive constants. We apply the compact form for solving diffusion-convection equation. The results of numerical experiments are presented and compared with analytical solutions to confirm the higher accuracy of the presented scheme.     

A total color difference measure for segmentation in color images

A single-value total color difference (TCD) measurement for scene segmentation is proposed and evaluated experimentally. Both chrominance and luminance difference criteria are considered. The luminance component is defined by a unit in luminance change expressed in terms of MacAdam's Just Noticeable Difference, JND. The chromaticity component is derived directly from JND. Experiments using both pixel and region analysis show that the proposed TCD can effectively indicate object boundaries over a wide range of luminance changes. The results have been evaluated both subjectively and quantitatively. For comparison purposes, results have been obtained in several color spaces.     

A fuzzy algorithm for color quantization of images

In this paper, we review a number of techniques for fuzzy color quantization. We show that the fuzzy membership paradigm is particularly suited to color quantization, where color cluster boundaries are not well defined. We propose a new fuzzy color quantization technique which incorporates a term for partition index. This algorithm produces better results than fuzzy C-means at a reduced computational cost. We test the results of the fuzzy algorithms using quality metrics which model the perception of the human visual system and illustrate that substantial quality improvements are achieved.     

A Fast Marching Method for the Area Based Affine Distance

In a previous paper, it was proved that the area based affine distance of a convex region in the plane satisfies a non-homogeneous Monge-Ampère differential equation. Based on this equation, in this paper we propose a fast marching method for the computation of this distance. The proposed algorithm has a lower computational complexity than the direct method and we have proved its convergence. And since the algorithm allows one to obtain a connection from any point of the region to the boundary by a path of decreasing distance, it offers a dynamic point of view for the area based affine distance.

Fast and efficient numerical method for solving the Allen–Cahn equation on the cubic surface

In this study, we present a fast and efficient finite difference method (FDM) for solving the Allen–Cahn (AC) equation on the cubic surface. The proposed method applies appropriate boundary conditions in the two-dimensional (2D) space to calculate numerical solutions on cubic surfaces, which is relatively simpler than a direct computation in the three-dimensional (3D) space. To numerically solve the AC equation on the cubic surface, we first unfold the cubic surface domain in the 3D space into the 2D space, and then apply the FDM on the six planar sub-domains with appropriate boundary conditions. The proposed method solves the AC equation using an operator splitting method that splits the AC equation into the linear and nonlinear terms. To demonstrate that the proposed algorithm satisfies the properties of the AC equation on the cubic surface, we perform the numerical experiments such as convergence test, total energy decrease, and maximum principle.     

Quantale-based autoassociative memories with an application to the storage of color images

In recent years, lattice computing has emerged as a new paradigm for processing lattice ordered data such as intervals, Type-1 and Type-2 fuzzy sets, vectors, images, symbols, graphs, etc. Here, the word “lattice” refers to a mathematical structure that is defined as a special type of a partially ordered set (poset). In particular, a complete lattice is a poset that contains the infimum as well as the supremum of each of its subsets. In this paper, we introduce the quantale-based associative memory (QAM), where the notion of a quantale is defined as a complete lattice together with a binary operation that commutes with the supremum operator. We show that QAMs can be effectively used for the storage and the recall of color images.     

彩色纹理图像恢复的非局部TV模型及其特征保持

基于局部算子的不同形式的TV模型用于彩色图像噪声去除时往往存在边缘模糊、纹理模糊、阶梯效应、Mosaic效应等问题。本文基于非局部算子概念将传统的Tikhonov模型、TV模型、MTV模型、CTV模型推广到NL-CT模型、NL-LTV模型、NL-MTV模型、NL-CTV模型,并通过引入辅助变量和Bregman迭代参数设计了相应的快速Split Bregman算法。实验表明,所提出的非局部TV模型在纹理、边缘、光滑度等特征保持方面具有良好特性,且差异不大,但不同模型的计算效率存在较大差异。     

On the security of a visual cryptography scheme for color images

Hou [Visual cryptography for color images, Pattern Recognition 36 (2003) 1619-1629] proposed a four-share visual cryptography scheme for color images. The scheme splits a dithered eight-color secret image into four shares: the black mask and other three shares. It was claimed that without knowing the black mask, no information about the secret image can be obtained even if all the other three shares are known. In this paper, we show that this may be true for a few specific two-color secret images only. In all other cases, however, security cannot be guaranteed. We show that an attacker can compromise a randomly chosen two-color secret image from any two of the other three shares with probability by completely recovering the shape and pattern of the secret image. The advantage will increase to if all the three shares are known. If the secret image has three or four colors, we show that the attacker can compromise it with probability and , respectively. Finally, we show that our technique can be extended to compromising secret images with more than four colors.     

彩色图像的单应矩阵估计算法

图像间单应矩阵估计是图像配准与图像拼接中的核心问题,传统的估计方法是针对灰度图像的算法。本文以分层运动估计为基础提出了彩色图像的平面单应矩阵的估计算法。此算法采用色度与饱和度不变为约束条件得到彩色图像的光流方程,显著改善了亮度不变约束的不足之处;采用最优导数计算滤波器计算图像导数,提高了算法的精度与稳健性;采用尺度总体最小二乘方法代替最小二乘或总体最小二乘方法来估计模型参数,提高了算法对于图像噪声的适应性。实验结果表明,该算法稳健性好、精度高,而且可以得到稠密的匹配点。     

A new numerical algorithm for the Abel equation of the second kind

An algorithm based on the Taylor matrix method is proposed and applied to the non-linear Abel equation of the second kind. A Padé approximation of the problem is also obtained. The results are compared and tabulated.     

Fast extraction of wavelet-based features from JPEG images for joint retrieval with JPEG2000 images

In this paper, some fast feature extraction algorithms are addressed for joint retrieval of images compressed in JPEG and JPEG2000 formats. In order to avoid full decoding, three fast algorithms that convert block-based discrete cosine transform (BDCT) into wavelet transform are developed, so that wavelet-based features can be extracted from JPEG images as in JPEG2000 images. The first algorithm exploits the similarity between the BDCT and the wavelet packet transform. For the second and third algorithms, the first algorithm or an existing algorithm known as multiresolution reordering is first applied to obtain bandpass subbands at fine scales and the lowpass subband. Then for the subbands at the coarse scale, a new filter bank structure is developed to reduce the mismatch in low frequency features. Compared with the extraction based on full decoding, there is more than 72% reduction in computational complexity. Retrieval experiments also show that the three proposed algorithms can achieve higher precision and recall than the multiresolution reordering, especially around the typical range of compression ratio.     

Surface Lagrangian Remeshing: A new tool for studying long term evolution of continental lithosphere from 2D numerical modelling

In this paper we present a new local remeshing algorithm that is dedicated to the problem of erosion in finite element models whose grid follows the movement of the free surface. The method, which we name Surface Lagrangian Remeshing (SLR), is adapted to 2D Lagrangian models which couple surface erosion with deformation of Earth materials. The remeshing procedure preserves nodes defining the surface submitted to erosion and removes nodes belonging to surface elements whose internal angles or area is critically low. This algorithm is ideally suited to track long term surface evolution. To validate the method we perform a set of numerical tests, using triangular finite elements, which compare the results obtained with the SLR algorithm with global remeshing and with analytical results. The results show good agreements with analytical solutions. Interpolation errors associated with remeshing are generated locally and numerical diffusion is restricted to the remeshed domain itself. In addition this method is computationally costless compared to classical global remeshing algorithm. We propose to couple the SLR method with the Dynamical Lagrangian Remeshing (DLR) algorithm to enable local remeshing only of Lagrangian models coupling large deformation of Earth materials with large erosion.     

A composite numerical scheme for the numerical simulation of coupled Burgers’ equation

In this work, a composite numerical scheme based on finite difference and Haar wavelets is proposed to solve time dependent coupled Burgers’ equation with appropriate initial and boundary conditions. Time derivative is discretized by forward difference and then quasilinearization technique is used to linearize the coupled Burgers’ equation. Space derivatives discretization with Haar wavelets leads to a system of linear equations and is solved using Matlab7.0. Convergence analysis of proposed scheme exhibits that the error bound is inversely proportional to the resolution level of the Haar wavelet. Finally, the adaptability of proposed scheme is demonstrated by numerical experiments and shows that the present composite scheme offers better accuracy in comparison with other existing numerical methods.     

A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems

In this paper a dissipative exponentially-fitted method for the numerical integration of the Schrödinger equation and related problems is developed. The method is called dissipative since is a nonsymmetric multistep method. An application to the the resonance problem of the radial Schrödinger equation and to other well known related problems indicates that the new method is more efficient than the corresponding classical dissipative method and other well known methods. Based on the new method and the method of Raptis and Cash a new variable-step method is obtained. The application of the new variable-step method to the coupled differential equations arising from the Schrödinger equation indicates the power of the new approach.     

A three-dimensional model for the study of the cooling system of submersible electric pumps

We study the cooling system for submersible electric pumps. This study aims to provide some guidelines to improve the existing cooling system of these electric pumps when they work partially or totally not immersed in the service fluid. Note that inefficient cooling systems cannot prevent the rise in temperature of the alternating current (AC) motor of the pump, and the consequent reduction of the service factor.     

Dirichlet feedback control for the stabilization of the wave equation: a numerical approach

In (J. Differential Equations 66 (1987) 340) a uniform stabilization method of the wave equation by boundary control à la Dirichlet has been discussed. In this article, we investigate the numerical implementation of the above stabilization process by a numerical scheme which mimics the energy decay properties of its continuous counterpart. The practical implementation of that scheme leads to a biharmonic problem of a new type which is solved by a method directly inspired by some related work of Glowinski and Pironneau on the solution of the Dirichlet problem for the biharmonic operator (SIAM Rev. 21(2) (1979) 167). Numerical experiments show that the decay properties of the energy are well-preserved by our numerical methodology.     

基于改进SRG法的叠加维吾尔文字提取算法

如何自动选取种子点的位置是基于区域生长法分割文字的关键问题。该算法通过横向线段检测算子提取出文字条中所有的横向线段;统计线段在饱和度、亮度上像素点的分布,根据统计分布使用Otsu法提取出纯净的文字基线,将它作为区域生长种子点的位置;通过生长法则分割文字。实验在四类不同的背景集中测试算法,其中花卉测试集的字母提取率达到72.31%。     

Convergence analysis and numerical implementation of a second order numerical scheme for the three-dimensional phase field crystal equation

In this paper we analyze and implement a second-order-in-time numerical scheme for the three-dimensional phase field crystal (PFC) equation. The numerical scheme was proposed in Hu et al. (2009), with the unique solvability and unconditional energy stability established. However, its convergence analysis remains open. We present a detailed convergence analysis in this article, in which the maximum norm estimate of the numerical solution over grid points plays an essential role. Moreover, we outline the detailed multigrid method to solve the highly nonlinear numerical scheme over a cubic domain, and various three-dimensional numerical results are presented, including the numerical convergence test, complexity test of the multigrid solver and the polycrystal growth simulation.