利用混沌PSO或分解的2维Tsallis灰度熵阈值分割

现有最大Shannon熵或Tsallis熵阈值选取方法没有从类内灰度均匀性出发,而仅依据图像灰度直方图,并且Tsallis熵法的分割效果通常优于Shannon熵法。为此,提出了基于混沌粒子群优化(PSO)和基于分解的两种2维Tsallis灰度熵阈值分割方法。首先,给出了1维Tsallis灰度熵阈值选取方法并将其推广到2维,导出了相应的2维Tsallis灰度熵阈值选取公式及其递推算法;其次,利用混沌PSO算法搜寻2维Tsallis灰度熵法的最佳阈值,并采用递推方式去除迭代过程中适应度函数的冗余运算,大大提高了运行速度;最后,将2维Tsallis灰度熵阈值选取方法的运算转化为两个1维Tsallis灰度熵法的运算,计算复杂度从O(L2)进一步降低到O(L)。实验结果表明,与2维最大Shannon熵法、2维最大Tsallis熵法及2维Tsallis交叉熵法相比,所提出的两种方法可以大幅提高图像分割质量和算法运行速度。     

Renyi熵与Tsallis熵的等价关系

描述了Tsallis熵和Renyi熵的等价关系及其在图像分割领域的应用.Tsallis熵和Renyi熵在图像分割中的应用是两种重要的全局阈值选取方法,是Shannon熵的广义形式,不仅在形式上具有等价关系,而且在应用于图像分割中也具有特殊的等价关系.这种特殊的等价关系应用在图像分割时只需任选一种熵来选取阈值.还讨论了它们自带的参数的取值对阈值选取的影响,这个参数可以针对不同类型的图像进行调节,可以得到很好的分割效果.     

基于灰色Tsallis熵的SAR图像快速分割*

针对SAR图像斑点噪声及分割速度慢的问题,提出一种基于灰色理论和Tsallis熵的SAR图像快速分割方法。该方法首先对待分割图像进行小波变换,将表征图像概貌信息的低频部分重构为概貌图像,表征图像细节和边缘的高频部分重构为细节图像,并建立了相应的概貌—细节共生矩阵模型;然后利用灰色理论和Tsallis熵设计了基于该共生矩阵的灰色Tsallis熵模型,用于求解最优分割阈值;同时,为加快阈值搜索速度,引入群体智能中的粒子群优化算法。实验结果显示,新方法在抗噪性、分割速度和灵活性三个方面均有明显提高。     

分解的二维非对称Tsallis 交叉熵图像阈值选取

现有的Tsallis 交叉熵能够度量图像分割前后的差异,但公式复杂,计算效率不高,据此, 提出了基于分解的二维非对称Tsallis 交叉熵图像阈值选取方法。首先给出了非对称Tsallis 交叉熵的定 义,提出了一维非对称Tsallis 交叉熵阈值选取方法;然后,将其拓展到二维,推导出相应的阈值选取 公式;最后,在此基础上提出了二维非对称Tsallis交叉熵阈值选取的分解算法,使求解二维非对称Tsallis 交叉熵阈值法的运算转化到两个一维空间上,将计算复杂度从O(L4)降低为O(L)。大量实验结果表明, 与基于混沌粒子群优化的二维Tsallis 灰度熵法、二维斜分对称交叉熵法,二维斜分对称Tsallis 交叉熵 法等方法相比,该方法分割性能优,运行时间短,可望满足实际应用系统对分割的实时要求。     

Generation of cubic power-law for high frequency intra-day returns: Maximum Tsallis entropy framework

A theoretical framework based on the maximum Tsallis entropy is proposed to explain the tail behavior of the intra-day stock returns, providing a rationale for the cubic law behavior for high frequency data. The specification of first two time-dependent moment constraints yields a q-Gaussian distribution for the intra-day stock returns. The value of the parameter q is estimated by minimizing appropriately modified Jensen–Shannon (JS) divergence in Tsallis entropy framework between q-Gaussian distribution and empirical NASDAQ 100 data. The estimated value of q yields the well-known empirically observed cubic law tail behavior of the intra-day stock returns which has been observed for high frequency data sets. To validate the cubic law stylized fact, five more data sets from high frequency NASDAQ 100, S&P 500 and NYSE index have been examined and it is found that the cubic law operates.     

Multi-level thresholding based on differential evolution and Tsallis Fuzzy entropy

This paper presents a multilevel image thresholding approach which relies on Tsallis entropy using Fuzzy partition with a novel threshold selection technique. In order to compute the optimal threshold values, Differential Evolution (DE) has been employed. The proposed method can further be exploited in image segmentation which is considered to be a critical step in image processing. Our proposed threshold selection technique is based on Tsallis-Fuzzy entropy and the results are compared with Shannon entropy (or fuzzy entropy) and Tsallis entropy based existing threshold selection techniques. The experiments are performed on two different sets of images and the results have been compared with that of existing state-of-the-art methods, namely, Patch Levy Bees' Algorithm (PLBA), Bacterial Foraging optimization (BFO), modified Bacterial Foraging optimization (MBFO) and Bees' Algorithm (BA). Quantitative analysis is carried out based on three image quality metrics viz SSIM, PSNR and SNR. Standard deviation and CPU time for convergence of the objective function have been calculated for performance evaluation. Furthermore, the statistical significance of our method has been estimated using Friedman test and Wilcoxon test. The experimental results manifest that our method produces results superior to the methods in comparison.     

基于引导滤波和Tsallis熵的SAR图像分割算法

针对合成孔径雷达(SAR)图像易受噪声干扰、分割方法精度低的问题,提出了一种基于频域引导滤波和Tsallis熵的SAR图像多阈值分割算法.利用非下采样Contourlet变换(NSCT)对图像多尺度分解,提取图像各方向的高频信息;通过引导滤波增强高频分量的边缘信息,在保持边缘的同时抑制了相干斑噪声;利用改进的二维Tsallis熵多阈值对增强图像精确分割.实验结果表明:分割算法对噪声不敏感,分割精度和适应性明显提高.     

基于混沌布谷鸟优化的二维Tsallis交叉熵建筑物遥感图像分割

为了进一步提升建筑物遥感图像分割的准确性和运算速度,本文提出了基于混沌布谷鸟优化的二维Tsallis交叉熵的建筑物遥感图像分割方法。首先给出了二维Tsallis交叉熵的阈值选取公式,然后将Logistic混沌映射引入布谷鸟算法,进一步加快布谷鸟算法的收敛速度,最后通过该混沌布谷鸟算法优化基于二维Tsallis交叉熵的阈值寻找过程,并以得到的最优阈值分割建筑物遥感图像。大量实验结果表明,与二维倒数交叉熵法、二维Tsallis熵法、基于混沌粒子群优化的二维Tsallis灰度熵法等方法相比较,本文方法分割的目标更为准确,细节更为清晰,且运算时间更短。     

基于灰度-梯度二维对称Tsallis交叉熵的阈值分割

针对灰度级-平均灰度级直方图的二维Tsallis交叉熵阈值分割法存在错分、计算复杂度较高问题,提出一种基于灰度-梯度二维对称Tsallis交叉熵的阈值分 割方法。构建新的灰度-梯度二维直方图,更加全面地考虑目标点和背景点;导出基于该直方图区域划分的对称Tsallis交叉熵阈值选取公式;采用基于tent映射的 混沌小生境粒子群优化算法搜寻二维最佳阈值向量,并引入快速递推算法降低其适应度函数的计算复杂度。实验结果表明,与基于灰度级-平均灰度级直方图的 二维Tsallis交叉熵阈值分割法相比,该方法能够使分割后的图像边缘更加准确,类内灰度更加均匀,且实时性提高了30倍。     

Interval-valued fuzzy n-ary subhypergroups of n-ary hypergroups

This paper provides a continuation of ideas presented by Davvaz and Corsini (J Intell Fuzzy Syst 18(4):377–382, 2007). Our aim in this paper is to introduce the concept of quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set. This concept is a generalized concept of quasicoincidence of a fuzzy point within a fuzzy set. By using this new idea, we consider the interval-valued (∈, ∈ ∨q)-fuzzy n-ary subhypergroup of a n-ary hypergroup. This newly defined interval-valued (∈, ∈ ∨q)-fuzzy n-ary subhypergroup is a generalization of the usual fuzzy n-ary subhypergroup. Finally, we consider the concept of implication-based interval-valued fuzzy n-ary subhypergroup in an n-ary hypergroup; in particular, the implication operators in ￡ukasiewicz system of continuous-valued logic are discussed.     

快速二维最小交叉Tsallis熵的图像阈值分割

目前二维最小交叉Tsallis熵阈值分割法有较好的分割性能,但由于计算复杂度高,使得分割速度慢。针对此问题,提出了一种基于二维最小交叉Tsallis熵的快速图像分割方法。首先对二维最小交叉Tsallis熵法公式进行推导找出需要递推的几个量,然后对二维直方图投影进行分析得到二维直方图的特性;最后利用此特性导出新型的快速递推算法来减少计算时间。实验结果表明:相对于当前二维最小交叉Tsallis熵阈值法,提出的方法在保持分割效果的情况下,其速度提高了20倍以上,其运行时间小于0.2 s。     

概率分布双向稀疏化下单一Tsallis熵阈值选取方法

现有基于熵最大准则选取阈值的方法涉及两个或两个以上的随机变量, 都忽视了一个约束条件而影响到它们的分割精度和适用范围: 参与随机系统整体熵计算的各随机变量应当相互独立. 提出了一种概率分布双向稀疏化下的单一Tsallis熵最大化导向的自动阈值选取方法, 可以自然规避多个随机变量需要相互独立的约束条件.在多尺度卷积乘变换...     

基于Tsallis熵差的遥感图像边缘检测方法

基于Tsallis熵差和百分位形态变换,提出了一种改进的遥感图像边缘检测方法。该方法通过构造基于百分位形态变换的边缘检测算子和选择不同方向结构元素进行变换来增加图像的边缘信息,并且该方法在百分位形态变换的基础上还改进了百分位变换的评价准则。它利用图像Tsallis熵差来选择边缘检测算子的百位变换值,将选择Tsallis熵差最大的百分位变换作为变换结果。实验结果表明,与传统的基于数学形态学的边缘检测方法相比,该方法可以最大程度上抑制噪声,有效地提高图像的边缘检测效果。     

最大熵和最小交叉熵综合的交互式图像分割

在图像分割中,使用某一种分割方法并不是总有效。最大熵和最小交叉熵阈值化方法是目前常用的两种图像分割方法,但在某些分割应用场合失效。针对此问题,提出基于最大熵和最小交叉熵综合的交互式图像分割方法。首先,利用一种简单的算法将前两种方法有机结合产生一种既满足最大熵原则,又满足最小交叉熵原则的新分割方法,然后通过人机交互,在这三种阈值方法中选择最好的图像分割。仿真实验结果表明,提出的方法不仅分割效果好,算法的普适性增强,而且更实用。     

On construction of the entropy transport model based on the formalism of nonextensive statistics

A new approach to the construction of transport entropy models of distribution based on the formalism of nonextensive statistics is proposed. As an example, a simple entropy model is built for single-purpose travels and for a homogenous group of cars. This approach allows simulation of more complicated non-Gibbs distributions. The fundamental principle of the research is the Tsallis nonextensive entropy and degree distributions dependent on the actual number q which is the measure of nonadditive complex socioeconomic systems.     

Edge detection of noisy digital image using optimization of threshold and self organized map neural network

The purpose of this research is to find a suitable method for detecting the edges of noisy digital images by eliminating the noise effects. The image will be partitioned into equal partitions and the initial threshold of that image partition will be calculated. By applying all these thresholds into the self-organized map (SOM) neural network input optimized for learning and training based optimization algorithm (TLBO), threshold clustering will be performed. The partitioned image will be edge detected by entropy method. Choosing the threshold for image segmentation is of great importance. The mean of the brightness of digital noise images is not a good representative of the initial threshold. Noise causes the mean intensity of the brightness to take distance from the main range of the intensity of the image so the resulting edge detected image will be severely noisy and truncated. By determining the highest frequency of brightness intensity instead of the mean brightness, the above-mentioned weaknesses will be eliminated. This method outperforms many current methods, such as Tsallis entropy, Singh and Kiani and even Canny Edge Detection which demonstrates the effectiveness of the proposed method, In the Table 1 the PSNR of image 5 of the proposed method is 61.4896, but Singh method which is 55.61, Tsallis method which is 53.9234, Kiani method which is 53.9315 the proposed method is less than the other methods.

     

面向医学图像分割的直线截距直方图倒数交叉熵方法

为了进一步 提高医学图像分割的速度和准确度,为临床诊断和辅助治疗提供更为充分有效的依据,本文 提出了一种基于直线截距直方图的倒数交叉熵图像阈值分割方法。首先定义了直线截距直方 图;然后根据医学图像的二维信息,建立该图像的直线截距直方图;最后,推导出基于该直 方图的倒数交叉熵阈值选取准则,并以此对医学图像进行分割。实验结果表明,与基于 混沌小生境粒子群优化(Niche chaotic mutation particle swarm optimization, NCPSO) 的二维倒数熵法、基于分解的二维指数灰度熵法、基于斜分的二维对称交叉熵法及基于粒子 群优化(Particle swarm optimization, PSO)的二维Tsallis交叉熵法相比,本文方法分割 后的图像中目标区域完整准确,边缘细节清晰丰富,且所需运行时间大幅减少,是医学影像 研究中可选择的一种快速有效的图像分割方法。     

基于HSI颜色空间与灰度波动相结合的复杂桥梁蜂窝麻面的图像分割

针对桥梁蜂窝麻面图像经常存在光照不均、多背景并存的干扰问题,提出了基于HSI颜色空间与灰度波动相结合的复杂桥梁蜂窝麻面的图像分割算法。首先,绘制S分量灰度变化曲线;其次,搜索曲线所有潜在的波峰波谷,并求相邻波峰波谷的高度差;然后,基于灰度像素个数差分值的标准差筛选出部分高度差;最后,基于部分高度差的标准差搜索最佳阈值完成图像的阈值分割。实验结果表明,与二维OTSU法、Niblack法、二维Tsallis熵法等几种算法相比,该算法的分割效果和实时性更好。     

Improving a firefly meta-heuristic for multilevel image segmentation using Tsallis entropy

In this paper we show that the non-extensive Tsallis entropy, when used as kernel in the bio-inspired firefly algorithm for multi-thresholding in image segmentation, is more efficient than using the traditional cross-entropy presented in the literature. The firefly algorithm is a swarm-based meta-heuristic, inspired by fireflies-seeking behavior following their luminescence. We show that the use of more convex kernels, as those based on non-extensive entropy, is more effective at \(5\,\%\) of significance level than the cross-entropy counterpart when applied in synthetic spaces for searching thresholds in global minimum.     

一种基于Tsallis熵的逆合成孔径雷达距离对准方法

距离对准是逆合成孔径雷达(ISAR) 成像处理中运动补偿的关键步骤,其对准质量影响最终的ISAR成像质量。在传统的基于Shan non熵的距离对准方法基础上,本文给出一种新的基于Tsallis熵的距离对准方法,即引入非 广延Tsallis熵,来衡量合成距离像的锐化度,并对距离平移量进行估计。详细分析了Tsall is熵的特性和用于距离对准的可行性,并通过仿真和实测数据,来验证基于Tsallis熵的距 离对准方法的性能。结果表明,相比基于Shannon熵的距离对准方法,基于Tsallis熵的距离 对准方法具有较好的抗噪声性能,并且可获得更好的距离对准效果。