A fast recursive algorithm based on fuzzy 2-partition entropy approach for threshold selection

The fuzzy c-partition entropy approach for threshold selection is an effective approach for image segmentation. The approach models the image with a fuzzy c-partition, which is obtained using parameterized membership functions. The ideal threshold is determined by searching an optimal parameter combination of the membership functions such that the entropy of the fuzzy c-partition is maximized. It involves large computation when the number of parameters needed to determine the membership function increases. In this paper, a recursive algorithm is proposed for fuzzy 2-partition entropy method, where the membership function is selected as S-function and Z-function with three parameters. The proposed recursive algorithm eliminates many repeated computations, thereby reducing the computation complexity significantly. The proposed method is tested using several real images, and its processing time is compared with those of basic exhaustive algorithm, genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO) and simulated annealing (SA). Experimental results show that the proposed method is more effective than basic exhaustive search algorithm, GA, PSO, ACO and SA.     

模糊熵的区域合并和图割的快速矿岩分割

目的 针对现有区域合并和图割的结合算法没有考虑矿岩图像模糊特性,导致分割精度和运行效率较低,模糊边缘无法有效分割的问题,利用快速递推计算的最大模糊2-划熵信息设置以区域为顶点的图割模型似然能来解决。方法 首先利用双边滤波器和分水岭算法对矿岩图像进行预处理,并将其划分为若干一致性较好的区域;然后利用图像在计算最大模糊2-划分熵时,目标和背景的模糊隶属度函数来设计图割能量函数似然能,使得能量函数更接近模糊图像的真实情况,期间为了提高最大模糊2-划分熵值的搜索效率,提出了时间复杂度为O（n²）的递推算法将模糊熵的计算转化为递推过程,并保留不重复的递推结果用于后续的穷举搜索;最后利用设计的图割算法对区域进行标号,以完成分割。结果 本文算法的分割精度较其他区域合并和图割结合算法提高了约23%,分割后矿岩颗粒个数的统计结果相对于人工统计结果,其误差率约为2%,运行时间较其他算法缩短了约60%。结论 本文算法确保精度同时,有效提高矿岩图像的分割效率,为自动化矿岩图像高效分割的工程实践提供重要指导依据。     

基于最大模糊熵和微粒群的双阈值图像分割

基于最大模糊熵准则和微粒群算法,提出了一种新的双阈值图像分割方法.该方法通过定义3种模糊隶属度函数,将图像模糊划分为暗、灰和亮3个不同的区域.同时采用微粒群算法搜索最大模糊准则下模糊参数的最优组合,进而确定图像的两个最佳分割阈值.仿真结果表明,该算法具有良好的分割效果和较强的实时处理能力.     

Recursive algorithm based on fuzzy 2-partition entropy for 2-level image thresholding

The fuzzy c-partition entropy approach for threshold selection behaves well in segmenting images. But the size of search space increases very rapidly when the number of parameters needed to determine the membership function increases. The computation complexity of the fuzzy 2-partition entropy approach is bounded by O(L³). In this paper, a recursive scheme which decreases the computation complexity of the basic algorithm to O(L²) is proposed. The approach does not need the calculation of the membership function. The processing time of each image is reduced from more than 5 min to less than 20 s.     

模糊Renyi熵与QGA结合的快速图像分割

针对非模糊熵的阈值分割方法不能较好地反映数字图像本质上具有的模糊特性,提出一种新的基于模糊熵的图像阈值分割方法。通过模糊隶属度函数将图像直方图信息转换到模糊域,利用模糊Renyi熵计算目标与背景的信息熵。根据最大熵原理,引入量子遗传算法对隶属度函数参数进行寻优,进而得到图像的最佳分割阈值。与典型的阈值法进行对比实验,表明该方法能获得更好的分割结果,满足实时性需求。     

基于模糊Havrda-Charvát熵与混沌PSO算法的红外人体图像分割

针对红外人体图像成像质量较差的问题,提出一种基于模糊Havrda-Charvát熵的快速阈值分割方法.首先应用Z形及S形隶属度函数把图像灰度直方图信息转换到模糊域,定义图像背景与目标的模糊Havrda-Charvát熵;然后提出一种基于Tent映射的混沌粒子群优化算法,把隶属度函数参数组合作为粒子,根据最大熵原理确定参数的最佳组合,再由最佳隶属度函数参数计算得到图像的最佳分割阈值.在真实红外人体图像集上与几种经典的图像阈值方法进行对比实验的结果,说明了该方法的有效性和鲁棒性.     

基于最优模糊变换和Retinex理论的静脉图像增强方法

一种新的结合模糊变换和retinex理论静脉图像增强方法,可以解决近红外静脉图像所存在的低对比度,动态范围狭窄和强度分布不对称问题。最优模糊变换用于加强全局对比度,引入的Retinex方法可以增强图像细节信息,弥补最优模糊变换的细节缺失。由于图像从空间域向模糊域转换时使用一个参数优化隶属函数,处理的图像不具有最佳性,文中提出一种双参数的隶属函数的优化方法,同时提出一种自适应的选择控制参数方法。实验结果表明,该方法可以有效提高静脉图像与背景的对比度,与其他方法的实验结果相比较,可以看出该办法具有更好的图像增强性能。     

基于模糊理论的2维隶属划分Renyi熵分割算法

基于信息论中最大熵原理,提出了一种2维直方图模糊划分Renyi熵分割算法。首先介绍了模糊划分的原理,由于Renyi熵是Shannon熵的广义形式,因此用模糊概率和条件概率来定义模糊划分Renyi熵。然后在向量空间内搜索最优参数组合,利用隶属函数实现图像分割。选用3幅不同类型的图像进行MATLAB仿真实验,结果表明该方法对噪声及杂散点等干扰的抑制性能较理想,且显著优于对比方法所得结果。     

Design of fuzzy PID controllers using modified triangular membership functions

A design method for fuzzy proportional-integral-derivative (PID) controllers is investigated in this study. Based on conventional triangular membership functions used in fuzzy inference systems, the modified triangular membership functions are proposed to improve a system’s performance according to knowledge-based reasonings. The parameters of the considered controllers are tuned by means of genetic algorithms (GAs) using a fitness function associated with the system’s performance indices. The merits of the proposed controllers are illustrated by considering a model of the induction motor control system and a higher-order numerical model.     

Generating fuzzy edge images from gradient magnitudes

The representation and processing of edges in images based on notions from fuzzy set theory has become popular in recent years. There are several reasons for this direction, from the vague definition of edges to the inherent uncertainty of digital images. Here, we study the transition from a gradient image, a popular intermediate representation, to a fuzzy edge image. We consider different parametric membership functions to transform the gradients into membership degrees. A histogram-based strategy is then introduced for automatically determining the value of those parameters, adapting the membership functions to the characteristics of each image. The functions are applied on the Canny method for edge detection, resulting in an improvement compared to the classical normalizing approach.     

广义模糊熵阈值法中基于粒子群优化的参数选取

针对广义模糊熵图像阈值分割法中参数m的选取问题,提出一种利用优化算法自适应选取参数的广义模糊熵阔值分割方法.该方法通过粒子群优化算法,依据图像分割质量评价准则对参数m在(0,1)区间进行全局寻优,并依据广义模糊熵最大准则对S型隶属度函数中的3个参数(a,b,d)进行全局组合寻优,从而实现了广义模糊熵图像阈值分割方法的自动阈值选取.实验结果表明,该方法对光照不均匀图像具有更好的分割效果.     

No-reference image quality assessment using interval type 2 fuzzy sets

Image quality assessment of distorted or decompressed images without any reference to the original image is challenging from computational point of view. Quality of an image is best judged by human observers without any reference image, and evaluated using subjective measures. The paper aims at designing a generic no-reference image quality assessment (NR-IQA) method by incorporating human visual perception in assigning quality class labels to the images. Using fuzzy logic approach, we consider information theoretic entropies of visually salient regions of images as features and assess quality of the images using linguistic values. The features are transformed into fuzzy feature space by designing an algorithm based on interval type-2 (IT2) fuzzy sets. The algorithm measures uncertainty present in the input–output feature space to predict image quality accurately as close to human observations. We have taken a set of training images belonging to five different pre-assigned quality class labels for calculating foot print of uncertainty (FOU) corresponding to each class. To assess the quality class label of the test images, maximum of T-conorm applied on the lower and upper membership functions of the test images belonging to different classes is calculated. Our proposed image quality metric is compared with other no-reference quality metrics demonstrating more accurate results and compatible with subjective mean opinion score metric.     

模糊马尔可夫随机场理论在阴影检测中的应用

阴影的检测是目标检测、目标跟踪、视频监控等领域的一个关键问题。提出了一种基于模糊马尔可夫随机场的阴影检测算法。该算法把阴影检测问题看做是一个求最优化的像素点分类问题。对于输入的视频,提取背景图像,找出阴影和前景目标物体区域。通过计算阴影概率分布,前景概率分布,隶属度函数,建立模糊马尔可夫随机场。应用贝叶斯准则,最大后验(MAP)估计和条件迭代模式(ICM)算法,寻找最优化的模糊马尔可夫随机场,并利用最大隶属度原则消除模糊性,得到阴影检测的结果。实验证明,文中算法具有较好的阴影检测率和目标检测率。     

Image segmentation based on histogram analysis utilizing the cloud model

Both the cloud model and type-2 fuzzy sets deal with the uncertainty of membership which traditional type-1 fuzzy sets do not consider. Type-2 fuzzy sets consider the fuzziness of the membership degrees. The cloud model considers fuzziness, randomness, and the association between them. Based on the cloud model, the paper proposes an image segmentation approach which considers the fuzziness and randomness in histogram analysis. For the proposed method, first, the image histogram is generated. Second, the histogram is transformed into discrete concepts expressed by cloud models. Finally, the image is segmented into corresponding regions based on these cloud models. Segmentation experiments by images with bimodal and multimodal histograms are used to compare the proposed method with some related segmentation methods, including Otsu threshold, type-2 fuzzy threshold, fuzzy C-means clustering, and Gaussian mixture models. The comparison experiments validate the proposed method.     

An improved medical image enhancement scheme using Type II fuzzy set

A contrast enhancement of medical images using Type II fuzzy set theory is suggested. Fuzzy set theory considers uncertainty in the form of membership function but to have better information on uncertainty on the membership function, Type II fuzzy set is considered. Type II fuzzy set considers fuzziness in the membership function. Hamacher T co norm is used as an aggregation operator to form a new membership function using the upper and lower membership function of Type II fuzzy set. The image with the new membership function is an enhanced image. As medical images contain lot of uncertainties, Type II fuzzy set may be a good tool for medical image analysis. To show the effectiveness of the proposed method, the results are compared with fuzzy, intuitionistic fuzzy, and existing Type II fuzzy methods. Experiments on several images show that the proposed Type II fuzzy method performs better than the existing methods. To show the advantage of the proposed enhancement method, detection or extraction of abnormal lesions or blood vessels has been carried out on enhanced images of all the methods. It is observed that the segmented results on the proposed enhanced images are better.     

基于微粒群和最大模糊熵的图像分割

提出了一种基于微粒群和最大模糊熵的图像分割方法.将图像分为目标和背景,并分别建立相应的模糊隶属函数来描述图像各个灰度级属于目标和背景的模糊特性,进而给出图像模糊熵的描述.在此基础上,根据最大模糊熵准则采用微粒群算法搜索模糊参数的最优组合,确定区分目标和背景的最佳阈值.为了验证方法的有效性,对比进行了图像分割实验,并与双峰法、迭代法和最大类间方差法进行了比较,实验结果表明,效果良好,能够自动、有效地选取阈值,分割效果优于其它三种算法,具有很好的鲁棒性和自适应性.     

基于模糊理论的SAR图像分割算法研究与实现

SAR图像存在强烈的相干斑噪声,传统方法不能很好对其分割。文章基于模糊理论,通过选择图像特征,构造模糊集,借助最大隶属度原则进行了SAR图像分割算法的设计,并借助SAR图像分别进行了参数调节和窗口选择的实验,获得了满意的分割结果。实验结果表明．该算法对于SAR图像分割可行有效。     

A two-stage fuzzy multi-objective framework for segmentation of 3D MRI brain image data

Segmentation of Magnetic Resonance Imaging (MRI) brain image data has a significant impact on the computer guided medical image diagnosis and analysis. However, due to limitation of image acquisition devices and other related factors, MRI images are severely affected by the noise and inhomogeneity artefacts which lead to blurry edges in the intersection of the intra-organ soft tissue regions, making the segmentation process more difficult and challenging. This paper presents a novel two-stage fuzzy multi-objective framework (2sFMoF) for segmenting 3D MRI brain image data. In the first stage, a 3D spatial fuzzy c-means (3DSpFCM) algorithm is introduced by incorporating the 3D spatial neighbourhood information of the volume data to define a new local membership function along with the global membership function for each voxel. In particular, the membership functions actually define the underlying relationship between the voxels of a close cubic neighbourhood and image data in 3D image space. The cluster prototypes thus obtained are fed into a 3D modified fuzzy c-means (3DMFCM) algorithm, which further incorporates local voxel information to generate the final prototypes. The proposed framework addresses the shortcomings of the traditional FCM algorithm, which is highly sensitive to noise and may stuck into a local minima. The method is validated on a synthetic image volume and several simulated and in-vivo 3D MRI brain image volumes and found to be effective even in noisy data. The empirical results show the supremacy of the proposed method over the other FCM based algorithms and other related methods devised in the recent past.     

基于局部隶属度和邻域信息的GIFP-FCM图像分割算法

基于一般化的模糊划分GIFP-FCM聚类算法是模糊C均值算法(FCM)的一种改进算法,一定程度上克服了FCM算法对噪声的敏感性,但由于其没有考虑图像的邻域信息,对含有较大噪声的图像分割效果不理想。为此,提出将局部隶属度和局部邻域信息等引入到GIFP-FCM算法的目标函数中,通过重新计算每个像素的局部隶属度和邻域信息,较好地克服了噪声影响。利用该算法对合成图像、脑图分割的实验结果表明,对于含有高斯噪声、椒盐噪声和混合噪声的图像,新算法得到的划分系数值最大,划分熵最小,是一种去噪效果较好的图像分割算法。