Fast recursive algorithm for two-dimensional Tsallis entropy thresholding method

Recently, a two-dimensional （2-D） Tsallis entropy thresholding method has been proposed as a new method for image segmentation. But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems. A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed. The key variables involved in calculating 2-D Tsallis entropy are written in recursive form. Thus, many repeating calculations are avoided and the computation complexity reduces to O（L2） from O（L4）. The effectiveness of the proposed algorithm is illustrated by experimental results.

Image Thresholding Using Two-Dimensional Tsallis Cross Entropy Based on Either Chaotic Particle Swarm Optimization or Decomposition

The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.

多向加权Tsallis熵最大化导向的自动阈值分割方法

受噪声或随机细节、目标和背景的大小比例、成像时的点扩散等不同因素的影响,许多图像的灰度直方图呈现为无模态、单模态、双模态或者多模态样式.为了在统一框架内处理这4种不同模态情形下的自动阈值选择问题,本文提出了一种多向加权Tsallis熵最大化导向的自动阈值分割方法(Multi-directional Weighted Tsallis Entropy,MWTE).基于新设计的反正切方向性卷积核的多尺度乘积效应,该方法将不同模态的灰度直方图转化为统一的单模态右偏灰度直方图.在4个不同方向上提取出这种特殊的单模态右偏灰度直方图后,通过多向加权策略构建出与原始图像灰度值紧密相关的加权Tsallis熵目标函数,并以该目标函数取最大值时对应的灰度值作为最终分割阈值.本文将提出的方法和3个阈值分割方法、1个软分割方法、1个活动轮廓分割方法以及1个自动聚类分割方法进行了比较.在4种不同模态情形下的4幅合成图像和50幅真实世界图像上的实验结果表明,本文提出的方法虽然在计算效率方面不占有优势,但它对不同模态的测试图像具有更稳健的分割适应性,且在量化分割精度所用的马修斯相关系数方面优于其他6个分割方法.

Tsallis相对熵引导的包裹相位修补

齿轮齿面形貌激光干涉测量中,由于容易受到多种噪声干扰,采集到的包裹相位图中会存在相位质量差的区域,解包路径经过这些区域会造成解包裹错误,降低测量精度。针对这一问题,根据干涉条纹图像的概率分布特点,本文提出一种基于Tsallis相对熵质量评价的包裹相位修补方法。该方法先利用高斯分布拟合阈值处理后的图像,再由Tsallis相对熵评价相位质量,最后修补质量较差的区域以提高相位解包裹质量。设计对比实验验证本方法的有效性,实验结果表明,该方法可以减少40%的相位残差点,并且有效提高了相位质量。该方法使用简单,准确率高,同样适用于其他移相光学领域。

Two-dimensional cross entropy multi-threshold image segmentation based on improved BBO algorithm

In order to improve the global search ability of biogeography-based optimization(BBO)algorithm in multi-threshold image segmentation,a multi-threshold image segmentation based on improved BBO algorithm is proposed.When using BBO algorithm to optimize threshold,firstly,the elitist selection operator is used to retain the optimal set of solutions.Secondly,a migration strategy based on fusion of good solution and pending solution is introduced to reduce premature convergence and invalid migration of traditional migration operations.Thirdly,to reduce the blindness of traditional mutation operations,a mutation operation through binary computation is created.Then,it is applied to the multi-threshold image segmentation of two-dimensional cross entropy.Finally,this method is used to segment the typical image and compared with two-dimensional multi-threshold segmentation based on particle swarm optimization algorithm and the two-dimensional multi-threshold image segmentation based on standard BBO algorithm.The experimental results show that the method has good convergence stability,it can effectively shorten the time of iteration,and the optimization performance is better than the standard BBO algorithm.

On Utilization of K-Means for Determination of <i>q</i>-Parameter for Tsallis-Entropy-Maximized-FCM

In this paper, we consider a fuzzy c-means (FCM) clustering algorithm combined with the deterministic annealing method and the Tsallis entropy maximization. The Tsallis entropy is a q-parameter extension of the Shannon entropy. By maximizing the Tsallis entropy within the framework of FCM, membership functions similar to statistical mechanical distribution functions can be derived. One of the major considerations when using this method is how to determine appropriate q values and the highest annealing temperature, Thigh?, for a given data set. Accordingly, in this paper, a method for determining these values simultaneously without introducing any additional parameters is presented. In our approach, the membership function is approximated by a series of expansion methods and the K-means clustering algorithm is utilized as a preprocessing step to estimate a radius of each data distribution. The results of experiments indicate that the proposed method is effective and both q and Thigh can be determined automatically and algebraically from a given data set.

A New Approach to Time-Dependent Solutions to the Non-Linear Fokker-Planck Equations Related to Arbitrary Functions of Tsallis Entropy: A Mathematical Study and Investigation

The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the authors’ name: Alireza Heidari and Seyedali Vedad. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.5 420-429, 2012, has been removed from this site.

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.

Nonextensivity and Tsallis Entropy in DNA Fragmentation Patterns by Ionizing Radiation

Nonextensive statistical mechanics as in Tsallis formalism was used in this study, along with the dynamical Hamiltonian rod-like DNA model and the maximum entropy criteria for Tsallis’ entropy, so as to obtain length distribution of plasmid fragments, after irradiation with very high doses, assuming that the system reaches metaequilibrium. By intensively working out the Grand Canonical Ensemble (used to take into account the variation of the number of base pairs) a simplified expression for Fragment Size Distribution Function (FSDF) was obtained. This expression is dependent on two parameters only, the Tsallis q value and the minimal length of the fragments. Results obtained from fittings to available experimental data were adequate and the characteristic behavior of the shortest fragments was clearly documented and reproduced by the model, a circumstance never verified from theoretical distributions. The results point to the existence of an entropy which characterizes fragmentation processes and depending only on the q entropic index.

融合量子克隆进化与二维Tsallis熵的医学图像分割算法

针对进化算法用于图像分割时收敛速度慢、易早熟的缺点,提出一种改进的量子克隆进化算法.首先利用量子空间的多样性丰富种群信息,在量子变异中根据适应度的不同对个体施以不同的混沌扰动,以克服量子门旋转方向单一、大小固定的缺陷,避免种群陷入局部早熟;然后利用克隆算子将最优个体信息扩充至下一代,以提高其局部寻优能力,加快收敛速度;最后将此算法用于寻找二维Tsallis熵的最佳阈值,实现了对图像的分割.实验结果表明,该算法有效地解决了进化算法收敛速度慢和容易陷入局部极值的问题,而且在分割速度和精度上得到了较大提高,分割效果良好,可以满足医学图像三维重建要求.

输电线路故障层次化变步长Tsallis小波奇异熵诊断方法

为提高熵方法输电线路故障信号时-频域的特征提取能力,提出层次化变步长Tsallis小波奇异熵(Tsallis Wavelet Singular Entropy,TWSE)方法用于电力系统故障诊断。首先,对采集到的电压信号进行小波分解与单支重构,构建时-频矩阵;之后,将奇异值分解与Tsallis熵理论相结合,对该时-频矩阵求滑动步长为1的Tsallis奇异熵,确定故障发生时刻;然后,对故障发生后1周期内的三相电压重构系数求滑动步长为1/4周期的TWSE,构建用于故障诊断的特征向量;最后,将TWSE特征向量输入到极限学习机(Extremly Learning Machine,ELM)分类器中,实现输电线路故障诊断。仿真结果表明,新方法具有更好的故障暂态信号特征表现能力,且分类结果不受故障时间、过渡电阻和故障位置等因素影响,相较基于小波奇异熵的线路故障诊断方法具有更好的诊断效果。

基于二维Tsallis熵的改进PCNN图像分割

为了改善图像分割的性能,采用改进的脉冲耦合神经网络(PCNN)进行分割,通过对其内部活动项进行空不变的单阈值化分割,来达到对原图像空变阈值化分割效果.另外分割准则也作了修正,通过计算图像二维直方图的Tsallis熵,得到二维Tsallis熵,以此作为图像分割准则.最后,修正了动态门限项的下降速度,使得PCNN收敛更快.实验证明二维Tsallis熵准则优于最大Shannon熵准则与最小交叉熵准则,且改进的PCNN模型比传统PCNN模型收敛更快.

密度泛函活性理论中的Rényi熵,Tsallis熵和Onicescu信息能（英文）

根据密度泛函理论,分子的电子密度确定了该体系基态下的所有性质,其中包括结构和反应活性.如何运用电子密度泛函有效地预测分子反应活性仍然是一个有待解决的难题.密度泛函活性理论(DFRT)倾力打造这样一个理论和概念架构,使得运用电子密度以及相关变量准确地预测分子的反应特性成为可能.信息理论方法的香农熵和费舍尔信息就是这样的密度泛函,研究表明,它们均可作为反应活性的有效描述符.本文将在DFRT框架中介绍和引进三个密切相关的描述符,Rényi熵、Tsallis熵和Onicescu信息能.我们准确地计算了它们在一些中性原子和分子中的数值并讨论了它们随电子数量和电子总能量的变化规律.此外,以第二阶Onicescu信息能为例,在分子和分子中的原子两个层面上,系统地考察了其随乙烷二面角旋转的变化模式.这些新慨念的引入将为我们深入洞察和预测分子的结构和反应活性提供额外的描述工具.

二维直方图准分的Tsallis熵阈值分割及其快速实现

传统二维Tsallis熵阈值法主要由于对二维直方图采用近似假设等原因,导致分割结果不够准确,由此提出了基于二维直方图准分的Tsallis熵快速图像分割方法。首先,准确选择邻域模板构建二维直方图并将Tsallis熵法用于此直方图上以便提高分割性能;然后,舍弃二维直方图中关于主对角区域的概率和近似为1的假设而准确计算使阈值选取更准确;最后,结合Tsallis熵公式对二维直方图进行分析得到其特性和2个定理,利用此特性和2个定理导出新型、快速的递推算法来降低计算复杂度。实验结果表明,与传统二维Tsallis熵法相比,所提出的方法不仅分割更准确和抗噪性更强,而且占用的存储空间和运行时间都更少。

二维直方图斜分Tsallis–Havrda–Charvát熵图像阈值分割

本文指出了现有二维直方图区域直分法中存在明显的错分,提出了二维直方图区域斜分方法,即通过与主对角线平行的四条斜线将直方图分成内点区、边界点区和噪声点区,并按灰度级与邻域平均灰度级之和的大小进行分割。该方法可以运用于所有的基于二维直方图的阈值分割。文中导出了基于二维直方图区域斜分的Tsallis–Havrda–Charvát熵阈值选取公式及其快速递推算法,给出了分割结果和运行时间。与基于二维直方图直分的Tsallis–Havrda–Charvát熵原始算法相比,本文提出的基于二维直方图斜分的Tsallis–Havrda–Charvát熵阈值分割算法,使分割后的图像内部区域均匀,边界形状准确,更有稳健的抗噪性,其运行时间减少了五个数量级。

中值邻域二维最小交叉Tsallis熵的快速图像分割

鉴于邻域窗口影响二维阈值法的分割结果,提出了一种基于中值邻域二维最小交叉Tsallis熵的快速图像分割方法。首先利用中值滤波法构建中值邻域二维直方图;然后将最小交叉Tsallis熵运用在这种直方图上构建中值邻域二维最小交叉Tsallis熵分割法,由于中值滤波后的图像优于均值滤波后的图像,此法能获得更理想的阈值;最后将递推法与定义的数组运算相结合导出快速算法搜索最佳阈值向量,并用此阈值向量对原图像和中值邻域图像进行分割,得到更好的分割结果。实验结果表明:相对于当前均值邻域二维最小交叉Tsallis熵阈值法,该方法不仅分割效果更好,抗噪性更强,而且速度更快。

基于Tsallis熵与层次化混合分类器的含未知故障断路器机械故障诊断

为提高断路器机械振动信号特征提取效率,避免将无训练样本未知类型故障误识别为正常样本或错误已知故障,提出一种断路器机械状态监测与故障诊断新方法。首先,将断路器机械操动机构振动信号进行时域分割,对分割后的各段信号分别直接提取7种特征,构成特征向量;通过散布矩阵分析特征分类能力,确定以Tsallis熵特征分析断路器机械故障。然后,将特征向量输入到基于单类支持向量机(OCSVM)与极限学习机(ELM)的层次化混合分类器中开展故障诊断。在混合分类器中,首先由OCSVM区分正常与故障状态;如为故障状态,则使用ELM识别故障类型,之后再以OCSVM校正ELM识别结果。通过实际断路器振动数据开展实验证明,散布矩阵能够有效分析特征的类可分性,时域分割提取特征效率高,层次化混合分类器不仅能够准确识别断路器机械状态与故障类型,而且可有效识别无训练样本未知故障类型数据。

基于多分辨Tsallis熵的癫痫EEG分析

利用多分辨率 Tsallis熵的方法 ,识别癫痫脑电中的棘波 ,把 EEG信号分解成小波级数 ,在各个尺度上利用多分辨率 Tsallis熵来检测棘波。和申农熵相比 ,多分辨率 Tsallis熵能给出更详细的信息。通过对 6位患者的EEG信号进行处理 ,发现这种方法能够比较准确的检测 EEG中的棘波 。

基于二维对称Tsallis交叉熵的小目标图像阈值分割

现有的阈值分割方法应用于目标与背景面积相差悬殊的小目标图像时,几乎都失效。为此,提出了基于对称Tsallis交叉熵及背景与目标面积差的小目标图像阈值分割方法。对称Tsallis交叉熵准则能确保准确分割时目标和背景内部的灰度均匀,而背景与目标面积差可抑制均等分割的趋势,二者综合构成了更为合理的阈值选取准则函数。首先导出了一维阈值选取公式;然后经推广得到基于二维斜分对称Tsallis交叉熵及背景与目标面积差的阈值选取公式,给出了其快速递推算法及相应的简化方法。大量实验结果表明:与目前性能较优越的二维斜分Otsu、最大熵、非对称交叉熵阈值分割方法相比,所提出的方法在小目标图像分割效果上具有极为明显的优势。

基于NSCT和Tsallis熵的SAR图像快速分割方法

针对小波域SAR图像分割结果粗糙及运算速度低的不足,本文提出一种基于非下采样Contourlet变换(NSCT)和混沌粒子群优化(CPSO)的最大Tsallis熵的SAR图像快速分割方法。首先,利用NSCT提取SAR图像的概貌和细节信息,并建立相应的概貌-细节灰度级矩阵模型;然后,利用Tent映射CPSO算法搜索最优阈值,并提出递推算法大大减少迭代过程中适应度函数的重复计算。实验结果表明,与小波域SAR图像快速分割方法相比,该方法采用了具有多方向性和移不变性的NSCT分解图像,信息提取更为有效,分割结果更佳;同时由于引入混沌序列并以递推方式计算粒子适应度,粒子群搜索的收敛精度更高,运算时间更少。