二维广义模糊熵图像阈值分割法

针对一维广义模糊熵不能有效处理含噪图像的分割问题,在二维灰度直方图上定义了图像的二维隶属度函数,提出了二维广义模糊熵阈值分割法.该方法不仅考虑了图像的点灰度值,同时考虑了图像像素的邻域平均灰度值,能更好地利用图像中的信息.为了提高二维广义模糊熵阈值法的运行速度、解决参量选取问题,结合粒子群优化搜索方法,设计了嵌套式的优化过程.实验表明,二维广义模糊熵阈值分割法对噪音图像有更好的适应性.     

二维广义模糊熵图像阈值分割法

针对一维广义模糊熵不能有效处理含噪图像的分割问题,在二维灰度直方图上定义了图像的二维隶属度函数,提出了二维广义模糊熵阈值分割法.该方法不仅考虑了图像的点灰度值,同时考虑了图像像素的邻域平均灰度值,能更好地利用图像中的信息.为了提高二维广义模糊熵阈值法的运行速度、解决参量选取问题,结合粒子群优化搜索方法,设计了嵌套式的优化过程.实验表明,二维广义模糊熵阈值分割法对噪音图像有更好的适应性.     

二维直方图θ划分最大Shannon熵图像阈值分割

鉴于常用二维直方图区域直分法存在错分,最近提出的斜分法不具普遍性,提出了适用面更广的基于二维直方图θ划分和最大Shannon熵的图像阈值分割算法.首先给出了二维直方图θ划分方法,采用四条平行斜线及一条其法线与灰度级轴成θ角的直线划分二维直方图区域,按灰度级和邻域平均灰度级的加权和进行阈值分割,斜分法可视为该方法中θ=45°的特例;然后导出了二维直方图θ-划分最大Shannon熵阈值选取公式及其快速递推算法;最后给出了θ取不同值时的分割结果及运行时间,θ取较小值时,边界形状准确性较高,θ取较大值时,抗噪性较强,应用时可根据实际图像特点及需求合理选取θ的值.与常规二维直方图直分最大Shannon熵法相比,本文提出的方法所得分割结果更为准确,抵抗噪声更为稳健,且所需运行时间及存储空间也大为减小.     

二维Arimoto熵直线型阈值分割法

Arimoto熵是一种广义熵形式.本文首先指出了已提出的二维Arimoto熵阈值分割法的表述错误,给出了正确的二维Arimoto熵阈值分割法;然后提出了二维Arimoto熵直线型阈值分割法,并给出了快速递推公式;对Arimoto熵公式中参量的选择进行了探讨,并基于标准图像进行了分割性能评估.大量分割实验表明,二维Arimoto熵直线型阈值法至少与二维Arimoto熵和二维Renyi熵直线型阈值法分割效果相当;在图像边缘和噪音信息丰富的情况下,二维Arimoto熵直线型阈值法的分割效果优于二维Arimoto熵和二维Renyi熵直线型阈值法,是一种有效的图像阈值方法.     

融合改进直方图PDE和二维Tsallis熵多阈值SAR分割

针对合成孔径雷达(SAR)图像中存在大量的相干斑噪声,对SAR图像进行分割易出现分割不精、边缘模糊等问题,融合改进的直方图PDE和二维Tsallis熵多阈值,提出了一种SAR图像分割算法。根据PDE直方图均衡化方法,将图像去噪与图像增强加权融合,利用各自权值调整去噪项与图像增强项;同时将二维Tsallis熵单阈值分割方法扩展到多阈值分割, 建立基于多阈值的选取方法,并引入萤火虫算法来求解最优阈值对,实现了二维Tsallis熵多阈值对去噪增强SAR图像的有效分割。仿真结果表明:与其他3种分割算法相比,该文算法在处理噪声大、灰度差值小的图像时具有较高的分割精度,PRI至少提升2.53%、VOI降低8.48%、GCE降低11.14%。     

基于二维最小Tsallis交叉熵的图像阈值分割方法

利用Tsallis熵的非广延性,提出了二维最小Tsallis交叉熵阈值分割方法.首先给出了二维Tsallis交叉熵的定义,并以最小二维Tsallis交叉熵为准则,利用粒子群优化算法来搜索最优二维阈值向量.该方法不仅进一步考虑了像素之间的空间邻域信息,而且考虑了目标和背景之间的相互关系,其分割性能优于基于Shannon熵的交叉熵阈值法和一维最小Tsallis交叉熵阈值法,并且具有很强的抗噪声能力.实验结果表明,该方法可以实现快速、准确的分割. 关键词： Tsallis交叉熵 二维直方图 粒子群优化算法 图像分割     

灰度图像的二维交叉熵阈值分割法

在解释和说明Li与 Lee提出的一维交叉熵阈值分割方法的基础上,将其推广到二维灰度直方图上,提出了二维交叉熵图像分割算法.为了克服二维空间上运算复杂性高、运算量大的缺点,给出了二维交叉熵阈值法的快速递推公式.与二维Otsu法相比,二维交叉熵阈值法能够更好地适应目标和背景方差相差较大的情形,是一种有效的阈值分割方法.     

基于改进的二维指数熵及混沌粒子群的阈值分割

鉴于现常用的灰度级—平均灰度级二维直方图区域划分存在明显的不足,提出了基于灰度级—梯度二维直方图的指数熵阈值选取方法,给出了基于改进的二维直方图的指数熵阈值选取公式,并利用混沌粒子群优化算法寻找最佳分割阈值,采用递推方式降低迭代过程中适应度函数的计算代价。实验结果表明,与现有的有关算法相比,该方法不仅使分割后的图像区域内部更均匀、边界形状更准确、特征细节更清晰,而且使计算效率及粒子群的收敛精度得到提高。     

基于蚁群算法的二维最大熵分割算法

由于二维最大熵分割法不仅考虑了像素的灰度信息,而且还充分利用了像素的空间邻域信息,因此能够取得较好的分割效果.但是,该方法的计算量巨大,不利于红外图像的快速处理.蚁群算法于20世纪90年代初提出,是受到蚁群集体行为的启发而提出的一种基于种群的模拟进化算法,属于随机搜索算法.该算法已经成功应用于旅行商等离散问题.将蚁群算法应用于二维最大熵法,提出了基于蚁群算法的二维最大熵分割算法.与传统的穷尽搜索法相比,求解速度提高了60倍左右.仿真实验表明,该方法快速、简单、有效.     

利用二维属性直方图的最大熵的图像分割方法

提出二维属性直方图的概念。它是一种由先验知识约束的二维直方图,可以使一些图像处理方法得到简化和变得可行。在此基础上提出一种基于二维属性直方图的图像分割方法。该方法步骤是构造图像的属性集,确定相应的二维属性直方图,然后利用二维属性直方图的最大熵法确定灰度阈值。为了说明该方法的性能,将其用于一种海底小目标图像分割。同时,也使用一维属性直方图的最大熵分割法。结果表明该方法比一维属性直方图的最大熵法抗干扰性更强,分割效果更好。二维属性直方图的概念具有理论意义与应用价值。该方法适用于图像有某种先验知识的场合。     

Parameter Analysis of Multiscale Two-Dimensional Fuzzy and Dispersion Entropy Measures Using Machine Learning Classification

Two-dimensional fuzzy entropy, dispersion entropy, and their multiscale extensions (MFuzzyEn2D and MDispEn2D, respectively) have shown promising results for image classifications. However, these results rely on the selection of key parameters that may largely influence the entropy values obtained. Yet, the optimal choice for these parameters has not been studied thoroughly. We propose a study on the impact of these parameters in image classification. For this purpose, the entropy-based algorithms are applied to a variety of images from different datasets, each containing multiple image classes. Several parameter combinations are used to obtain the entropy values. These entropy values are then applied to a range of machine learning classifiers and the algorithm parameters are analyzed based on the classification results. By using specific parameters, we show that both MFuzzyEn2D and MDispEn2D approach state-of-the-art in terms of image classification for multiple image types. They lead to an average maximum accuracy of more than 95% for all the datasets tested. Moreover, MFuzzyEn2D results in a better classification performance than that extracted by MDispEn2D as a majority. Furthermore, the choice of classifier does not have a significant impact on the classification of the extracted features by both entropy algorithms. The results open new perspectives for these entropy-based measures in textural analysis.     

Principle of Maximum Entropy and Reduced Dynamics

A new method to obtain a series of reduced dynamics at various stages of coarse-graining is proposed. This ranges from the most coarse-grained one which agrees with the deterministic time evolution equation for averages of the relevant variables to the least coarse-grained one which is the generalized Fokker-Planck equation for the probability distribution function of the relevant variables. The method is based on the extention of the Kawasaki-Gunton operator with the help of the principle of maximum entropy.     

Uncertainty of Interval Type-2 Fuzzy Sets Based on Fuzzy Belief Entropy

Interval type-2 fuzzy sets (IT2 FS) play an important part in dealing with uncertain applications. However, how to measure the uncertainty of IT2 FS is still an open issue. The specific objective of this study is to present a new entropy named fuzzy belief entropy to solve the problem based on the relation among IT2 FS, belief structure, and Z-valuations. The interval of membership function can be transformed to interval BPA [Bel,Pl]. Then, Bel and Pl are put into the proposed entropy to calculate the uncertainty from the three aspects of fuzziness, discord, and nonspecificity, respectively, which makes the result more reasonable. Compared with other methods, fuzzy belief entropy is more reasonable because it can measure the uncertainty caused by multielement fuzzy subsets. Furthermore, when the membership function belongs to type-1 fuzzy sets, fuzzy belief entropy degenerates to Shannon entropy. Compared with other methods, several numerical examples are demonstrated that the proposed entropy is feasible and persuasive.     

Calibration Invariance of the MaxEnt Distribution in the Maximum Entropy Principle

The maximum entropy principle consists of two steps: The first step is to find the distribution which maximizes entropy under given constraints. The second step is to calculate the corresponding thermodynamic quantities. The second part is determined by Lagrange multipliers’ relation to the measurable physical quantities as temperature or Helmholtz free energy/free entropy. We show that for a given MaxEnt distribution, the whole class of entropies and constraints leads to the same distribution but generally different thermodynamics. Two simple classes of transformations that preserve the MaxEnt distributions are studied: The first case is a transform of the entropy to an arbitrary increasing function of that entropy. The second case is the transform of the energetic constraint to a combination of the normalization and energetic constraints. We derive group transformations of the Lagrange multipliers corresponding to these transformations and determine their connections to thermodynamic quantities. For each case, we provide a simple example of this transformation.     

Research on Nickel Material Trade Redistribution Strategy Based on the Maximum Entropy Principle

In the double carbon background, riding the wind of new energy vehicles and the battery high nickelization, nickel resources rise along with the trend. In recent years, due to the influence of geopolitical conflicts and emergencies, as well as the speculation and control of international capital with its advantages and rules, the world may face price and security supply risks to a certain extent. Therefore, to obtain the most objective trade redistribution strategy, this paper first constructs the nickel material trade network, identifies the core trading countries and the main trade relations of nickel material trade, and finds that the flow of nickel material mainly occurred between a few countries. On this basis, a trade redistribution model is constructed based on the maximum entropy principle. Taking Indonesia, the largest exporter, and the largest trade relationship (Indonesia exports to China) as examples, the nickel material redistribution between countries when different supply risks occur are simulated. The results can provide an important reference for national resource recovery after the risk of the nickel trade.     

A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems

Two well-known drawbacks in fuzzy clustering are the requirement of assigning in advance the number of clusters and random initialization of cluster centers. The quality of the final fuzzy clusters depends heavily on the initial choice of the number of clusters and the initialization of the clusters, then, it is necessary to apply a validity index to measure the compactness and the separability of the final clusters and run the clustering algorithm several times. We propose a new fuzzy C-means algorithm in which a validity index based on the concepts of maximum fuzzy energy and minimum fuzzy entropy is applied to initialize the cluster centers and to find the optimal number of clusters and initial cluster centers in order to obtain a good clustering quality, without increasing time consumption. We test our algorithm on UCI (University of California at Irvine) machine learning classification datasets comparing the results with the ones obtained by using well-known validity indices and variations of fuzzy C-means by using optimization algorithms in the initialization phase. The comparison results show that our algorithm represents an optimal trade-off between the quality of clustering and the time consumption.     

The Concavity of Entropy and Extremum Principles in Thermodynamics

We revisit the concavity property of the thermodynamic entropy in order to formulate a general proof of the minimum energy principle as well as of other equivalent extremum principles that are valid for thermodynamic potentials and corresponding Massieu functions under different constraints. The current derivation aims at providing a coherent formal framework for such principles which may be also pedagogically useful as it fully exploits and highlights the equivalence between different schemes. We also elucidate the consequences of the extremum principles for the general shape of thermodynamic potentials in relation to first-order phase transitions.