快速模糊C均值聚类彩色图像分割方法

模糊C均值(FCM)聚类用于彩色图像分割具有简单直观、易于实现的特点，但存在聚类性能受中心点初始化影响且计算量大等问题，为此，提出了一种快速模糊聚类方法(FFCM)。这种方法利用分层减法聚类把图像数据分成一定数量的色彩相近的子集，一方面，子集中心用于初始化聚类中心点；另一方面，利用子集中心点和分布密度进行模糊聚类，由于聚类样本数量显著减少以及分层减法聚类计算量小，故可以大幅提高模糊C均值算法的计算速度，进而可以利用聚类有效性分析指标快速确定聚类数目。实验表明，这种方法不需事先确定聚类数目并且在优化聚类性能不变的前提下，可以使模糊聚类的速度得到明显提高，实现彩色图像的快速分割。     

基于改进的FCM的人脑MR图像分割

传统模糊C均值广泛应用于图像分割,它是一种经典的模棚聚类分析方法,但是FCM算法对于初始值的选择都是采取随机的方法,强烈依赖于初始值的选择,收敛结果容易陷入局部最小值,并且FCM并没有考虑图像的空间信息,因而对噪声十分敏感。提出改进的FCM方法,采用新的方法确定初始值的选择,然后考虑空间信息,利用Gibbs随机场的性质引入先验邻域约束信息,重新确定像素的模糊隶属度值,同时再进一步地调整距离矩阵。通过实验可以表明,此改进的方法具有很好的分割效果,同时对噪声具有较强的鲁棒性。     

一种快速的模糊C均值聚类彩色图像分割方法

FCM用于彩色图像分割存在聚类数目需要事先确定、计算速度慢的问题,为此,提出一种快速的模糊C均值聚类方法（FFCM）。首先,对原始彩色图像进行基于梯度图的分水岭变换,从而把原始彩色图像数据分成一些具有色彩一致性的子集;然后,利用这些子集的大小和中心点进行模糊聚类。由于FFCM聚类样本数量显著减小,因此可以大幅提高模糊C均值聚类算法的计算速度,进而可以采用聚类有效性指标确定聚类数目。实验表明,这种方法不需要事先确定聚类数目,在聚类有效性能不变的前提下,可以使模糊聚类的速度得到明显提高,实现了彩色图像的快速分割。     

基于HSI空间模糊聚类的彩色图像分割新方法

模糊C均值(FCM)被广泛应用于彩色图像分割中,但传统的模糊C均值由于没有考虑空间信息,因此对噪声特别敏感。针对此问题,提出了一种在HIS颜色空间结合像素邻域空间信息的模糊聚类新方法。实验结果表明,此方法对高噪声图像有较好的处理结果。     

HSI颜色模型下基于空间信息的FCM算法

针对提花毛皮样片的花型识别技术,在HSI颜色模型下提出了一种基于空间信息的FCM图像分割算法。算法在HSI颜色模型下获得FCM算法的初始聚类中心,并采用了基于空间信息的模糊C均值聚类方法对图像进行分割。经C++编程验证,算法能有效去除花型图像中的噪声,获得较理想的花型识别结果。     

Regularized Linear Fuzzy Clustering and Probabilistic PCA Mixture Models

Fuzzy$c$-means (FCM)-type fuzzy clustering approaches are closely related to Gaussian mixture models (GMMs) and EM-like algorithms have been used in FCM clustering with regularized objective functions. Especially, FCM with regularization by Kullback–Leibler information (KLFCM) is a fuzzy counterpart of GMMs. In this paper, we propose to apply probabilistic principal component analysis (PCA) mixture models to linear clustering following a discussion on the relationship between local PCA and linear fuzzy clustering. Although the proposed method is a kind of the constrained model of KLFCM, the algorithm includes the fuzzy$c$-varieties (FCV) algorithm as a special case, and the algorithm can be regarded as a modified FCV algorithm with regularization by K–L information. Numerical experiments demonstrate that the proposed clustering algorithm is more flexible than the maximum likelihood approaches and is useful for capturing local substructures properly.     

基于免疫克隆选择的模糊聚类分析

模糊c-均值聚类(FCM)应用广泛,但它容易陷入局部最优,且对初始值很敏感。提出了一种基于免疫克隆选择算法的模糊聚类方法,首先,用克隆选择算法对模糊聚类中心的个数和聚类中心的选取进行指导,然后,利用FCM进行聚类,是一种有监督学习和无监督学习结合的一种算法,实验结果表明:该方法在一定程度上避免FCM算法对初始值敏感和容易陷入局部最优解的缺陷,使聚类更有效,更合理。     

彩色地图分色算法的改进及实现

在加权模糊c-均值（FCM）聚类算法的基础上,对分色算法进行了改进．首先进行色彩空间模型转换,然后对基于样本加权的FCM算法进行改进,对隶属度进行调整,把二维彩色直方图引入加权系数中．对于模糊c-均值算法,当隶属度接近时,分类会变得模糊,而且对于不同的样本矢量,聚类效果有所不同,本算法兼顾到了这两点．该方法已用Visual C＋＋6．0编程实现,效果比较理想．     

一种基于三角模糊数多指标信息的FCM 聚类算法

针对一类具有不确定性三角模糊数多指标信息的聚类分析问题，基于传统的数值信息FCM聚类算法，提出一种新的聚类分析算法．首先描述了具有三角模糊数多指标信息的聚类分析问题，提出并证明了基于三角模糊数多指标信息的关于最优划分和最优聚类中心确定的两个定理；然后根据这两个定理，进一步给出了基于三角模糊数信息的FCM聚类算法的迭代步骤；最后通过一个算例说明了该聚类算法的具体应用．     

关于模糊C-均值（FCM）聚类算法的改进

针对模糊C-均值（FCM）聚类算法的容易收敛于局部极值的不足,提出了一种改进的模糊FCM聚类算法,此新算法在聚类中心选取和优化过程中进行了充分的考虑,是一种用于确定最佳聚类数的聚类算法,并且利用了分阶段思想,结合动态直接聚类算法和标准聚类算法,来尽量避免模糊C-均值（FCM）聚类算法的不足。新算法与传统（FCM）聚类算法方法相比,提高了算法的寻优能力,并且迭代次数更少,在准确度上也有较大的提高,具有很好的实际应用价值。     

FCM与马氏空间约束条件下的快速图像分割技术研究*

提出了一种FCM与马氏空间约束的快速图像分割技术.在FCM图像分割算法的基础上,引入了Markov 随机场用以描述图像分割中的空间约束信息,并通过多级级联的方式获得最后的图像分割结果.这样既克服了传统模糊C均值聚类算法只考虑图像中的数值特征信息,忽略像素间的空间约束关系的缺点,又最大限度地保证了分割算法计算的简单有效性.实验证明,与其他模糊C均值聚类算法相比,本文方法有更好的可靠性与有效性.     

Fuzzy clustering algorithms incorporating local information for change detection in remotely sensed images

In this paper we have used two fuzzy clustering algorithms, namely fuzzy c-means (FCM) and Gustafson–Kessel clustering (GKC) along with local information for unsupervised change detection in multitemporal remote sensing images. In conventional FCM and GKC no spatio-contextual information is taken into account and thus the result is not so much robust to small changes. Since the pixels are highly correlated with their neighbors in image space (spatial domain), incorporation of local information enhances the performance of the algorithms. In this work we have introduced a new technique for incorporation of local information. Change detection maps are obtained by separating the pixel-patterns of the difference image into two groups. Hybridization of FCM and GKC with two other optimization techniques, genetic algorithm (GA) and simulated annealing (SA), is made to further enhance the performance. To show the effectiveness of the proposed technique, experiments are conducted on two multispectral and multitemporal remote sensing images. Two fuzzy cluster validity measures (Xie–Beni and fuzzy hypervolume) have been used to quantitatively evaluate the performance. Results are compared with those of existing state of the art Markov random field (MRF) and neural network based algorithms and found to be superior. The proposed technique is less time consuming and unlike MRF does not require any a priori knowledge of distributions of changed and unchanged pixels.     

基于GFCMA算法的医学彩色图像分割

医学图像分割是医学图像分析的关键步骤,经典的模糊C-均值聚类算法(FCM)是常用方法,但其依赖于初始聚类中心的选择,通常存在局部收敛的缺陷。通过与遗传算法(GA)结合而成的遗传模糊C-均值聚类算法(GFCMA),采用RGB颜色空间,能够得到全局最优解,并在此基础上实现了医学彩色图像分割和特定目标提取,取得良好分割效果。     

Fuzzy clustering algorithms for unsupervised change detection in remote sensing images

In this paper, we propose a context-sensitive technique for unsupervised change detection in multitemporal remote sensing images. The technique is based on fuzzy clustering approach and takes care of spatial correlation between neighboring pixels of the difference image produced by comparing two images acquired on the same geographical area at different times. Since the ranges of pixel values of the difference image belonging to the two clusters (changed and unchanged) generally have overlap, fuzzy clustering techniques seem to be an appropriate and realistic choice to identify them (as we already know from pattern recognition literatures that fuzzy set can handle this type of situation very well). Two fuzzy clustering algorithms, namely fuzzy c-means (FCM) and Gustafson-Kessel clustering (GKC) algorithms have been used for this task in the proposed work. For clustering purpose various image features are extracted using the neighborhood information of pixels. Hybridization of FCM and GKC with two other optimization techniques, genetic algorithm (GA) and simulated annealing (SA), is made to further enhance the performance. To show the effectiveness of the proposed technique, experiments are conducted on two multispectral and multitemporal remote sensing images. A fuzzy cluster validity index (Xie-Beni) is used to quantitatively evaluate the performance. Results are compared with those of existing Markov random field (MRF) and neural network based algorithms and found to be superior. The proposed technique is less time consuming and unlike MRF does not require any a priori knowledge of distributions of changed and unchanged pixels.     

一种特征加权FCM算法的图像重建技术研究

针对传统FCM(Fuzzy C-means)算法中初始聚类中心选取的随机性以及对初始值敏感的问题,提出一种基于进化策略的色彩空间加权的FCM聚类算法.通过在RGB(Red Green Blue)色彩空间矢量中设置加权矩阵来补偿各色彩的非均匀性,并采用一种类内最小距离最大的统计聚类算法来初始化聚类中心.实验结果表明,该算法能有效减少颜色量化后的均方差值,保持重建图像的整体层次和局部特征细节,对研究图像处理技术有较强的实际意义.

Abstract：

Aiming at a defect on randomness of the initial clustering center choosing and sensitivity of initial value in tradition FCM(fuzzy C-means) algorithm, a clustering algorithm about FCM of weighted color space based on evolutionary strategy is proposed. By interposing weighted matrix in RGB(Red Green Blue) color space, the color's inhomogeneous is compensated. And by using a statistics clustering algorithm of minimal maximal distance, clustering center is initiated. The experimental results show that the algorithm can decrease effectively the mean square deviation of color quantization, keep overall arrangement of ideas and part characteristic detail in image reconstruction, and has practical value to the study of the image process technology.     

一种扩展的条件模糊C-均值聚类算法

在综合分析标准的模糊C-均值聚类算法和条件模糊C-均值聚类算法基础上,对模糊划分空间进行修改,进一步弱化模糊划分矩阵的约束,给出一种扩展的条件模糊C-均值聚类算法。算法的划分矩阵和原型不依赖于背景约束及模糊划分矩阵的隶属度总和。实验结果表明：该算法可以得到不同的聚类原型,并具有很好的聚类效果。     

自适应快速FCM彩色图像分割研究

模糊C均值聚类算法（FCM）广泛用于彩色图像分割,但该算法存在需要预先指定聚类数目、计算量大、耗时长且易陷入局部最优等缺点。提出一种自适应快速模糊C均值彩色图像分割方法,该方法首先运用蚁群算法,自动获取初始聚类中心和聚类数目,然后使用基于梯度的分水岭算法对原始彩色图像进行预分割,得到一系列由色彩特征空间具有一致性的点构成的子集,最后对这些子集的中心进行模糊聚类。实验结果表明：由于子集数量远小于原始图像像素数目,使聚类样本数量显著减少,大大提高了聚类速度,同时在聚类中以特征距离代替欧式距离,增强了算法的鲁棒性。     

An interval number distance- and ranking-based method for remotely sensed image fuzzy clustering

ABSTRACT

Fuzzy c-means clustering is an important non-supervised classification method for remote-sensing images and is based on type-1 fuzzy set theory. Type-1 fuzzy sets use singleton values to express the membership grade; therefore, such sets cannot describe the uncertainty of the membership grade. Interval type-2 fuzzy c-means (IT2FCM) clustering and relevant methods are based on interval type-2 fuzzy sets. Real vectors are used to describe the clustering centres, and the average values of the upper and lower membership grades are used to determine the classification of each pixel. Thus, the width information for interval clustering centres and interval membership grades are ignored. The main contribution of this article is to propose an improved IT2FCM* algorithm by adopting interval number distance (IND) and ranking methods, which use the width information of interval clustering centres and interval membership grades, thus distinguishing this method from existing fuzzy clustering methods. Three different IND definitions are tested, and the distance definition proposed by Li shows the best performance. The second contribution of this work is that two fuzzy cluster validity indices, FS- and XB-, are improved using the IND. Three types of multi/hyperspectral remote-sensing data sets are used to test this algorithm, and the experimental results show that the IT2FCM* algorithm based on the IND proposed by Li performs better than the IT2FCM algorithm using four cluster validity indices, the confusion matrix, and the kappa coefficient (κ). Additionally, the improved FS- index has more indicative ability than the original FS- index.     

Color image segmentation using feedforward neural networks with FCM

This paper proposes a hybrid technique for color image segmentation. First an input image is converted to the image of CIE L*a*b* color space. The color features “a” and “b” of CIE L*a*b* are then fed into fuzzy C-means (FCM) clustering which is an unsupervised method. The labels obtained from the clustering method FCM are used as a target of the supervised feed forward neural network. The network is trained by the Levenberg-Marquardt back-propagation algorithm, and evaluates its performance using mean square error and regression analysis. The main issues of clustering methods are determining the number of clusters and cluster validity measures. This paper presents a method namely co-occurrence matrix based algorithm for finding the number of clusters and silhouette index values that are used for cluster validation. The proposed method is tested on various color images obtained from the Berkeley database. The segmentation results from the proposed method are validated and the classification accuracy is evaluated by the parameters sensitivity, specificity, and accuracy.     

Fuzzy order statistics and their application to fuzzy clustering

The median and the median absolute deviation (MAD) are robust statistics based on order statistics. Order statistics are extended to fuzzy sets to define a fuzzy median and a fuzzy MAD. The fuzzy c-means (FCM) clustering algorithm is defined for any p-norm (pFCM), including the l₁-norm (1FCM), The 1FCM clustering algorithm is implemented via the alternating optimization (AO) method and the clustering centers are shown to be the fuzzy median. The resulting AO-1FCM clustering algorithm is called the fuzzy c-medians (FCMED) clustering algorithm. An example illustrates the robustness of the FCMED