Extended Gaussian kernel version of fuzzy c-means in the problem of data analyzing

Fuzzy c-means clustering with spatial constraints is considered as suitable algorithm for data clustering or data analyzing. But FCM has still lacks enough robustness to employ with noise data, because of its Euclidean distance measure objective function for finding the relationship between the objects. It can only be effective in clustering ‘spherical’ clusters, and it may not give reasonable clustering results for “non-compactly filled” spherical data such as “annular-shaped” data. This paper realized the drawbacks of the general fuzzy c-mean algorithm and it tries to introduce an extended Gaussian version of fuzzy C-means by replacing the Euclidean distance in the original object function of FCM. Firstly, this paper proposes initial kernel version of fuzzy c-means to aim at simplifying its computation and then extended it to extended Gaussian kernel version of fuzzy c-means. It derives an effective method to construct the membership matrix for objects, and it derives a robust method for updating centers from extended Gaussian version of fuzzy C-means. Furthermore, this paper proposes a new prototypes learning method and it obtains initial cluster centers using new mathematical initialization centers for the new effective objective function of fuzzy c-means, so that this paper tries to minimize the iteration of algorithms to obtain more accurate result. Initial experiment will be done with an artificially generated data to show how effectively the new proposed Gaussian version of fuzzy C-means works in obtaining clusters, and then the proposed methods can be implemented to cluster the Wisconsin breast cancer database into two clusters for the classes benign and malignant. To show the effective performance of proposed fuzzy c-means with new initialization of centers of clusters, this work compares the results with results of recent fuzzy c-means algorithm; in addition, it uses Silhouette method to validate the obtained clusters from breast cancer datasets.     

Fuzzy c-means clustering with non local spatial information for noisy image segmentation

As an effective image segmentation method, the standard fuzzy c-means (FCM) clustering algorithm is very sensitive to noise in images. Several modified FCM algorithms, using local spatial information, can overcome this problem to some degree. However, when the noise level in the image is high, these algorithms still cannot obtain satisfactory segmentation performance. In this paper, we introduce a non local spatial constraint term into the objective function of FCM and propose a fuzzy cmeans clustering algorithm with non local spatial information (FCM_NLS). FCM_NLS can deal more effectively with the image noise and preserve geometrical edges in the image. Performance evaluation experiments on synthetic and real images, especially magnetic resonance (MR) images, show that FCM_NLS is more robust than both the standard FCM and the modified FCM algorithms using local spatial information for noisy image segmentation.     

基于改进的直觉模糊核聚类的图像分割方法

针对噪声图像模糊性的本质，提出了基于改进的直觉模糊核聚类的图像分割方法。采用直觉模糊集描述噪声图像包含的不确定性信息，将图像的灰度信息转换到直觉模糊域进行处理；将模糊核聚类拓展为直觉模糊核聚类，在图像的直觉模糊域进行聚类；通过高斯核函数和欧氏距离分别对像素8-邻域的灰度和空间信息进行建模，综合平衡灰度和空间信息对聚类的作用，并将其作为惩罚项加入到直觉模糊核聚类的目标函数中；通过梯度下降法，推导了迭代求解算法；通过典型的合成图像和自然图像分割实例，验证了所提算法的有效性和鲁棒性。     

SOM and fuzzy based color image segmentation

Spatial information enhances the quality of clustering which is not utilized in the conventional FCM. Normally fuzzy c-mean (FCM) algorithm is not used for color image segmentation and also it is not robust against noise. In this paper, we presented a modified version of fuzzy c-means (FCM) algorithm that incorporates spatial information into the membership function for clustering of color images A progressive technique based on SOM is used to automatically find the number of optimal clusters. The results show that our technique outperforms state-of-the art methods.     

基于核与局部信息的多维度模糊聚类图像分割算法

在以聚类分析为背景的图像分割算法中,引入局部信息是为了在保留图像细节的同时尽可能地减少噪声.在模糊C均值算法基础上,提出了一种基于核与局部信息的多维度模糊聚类分析方法来权衡图像中的噪声和细节.该算法引入2个基于局部信息的图像变体,即平滑和锐化处理后的图像,使之与原始图像一起构成多维度的灰度值向量来替换原始单维的灰度值; 再利用核方法提高其鲁棒性; 最后添加一个邻域隶属度差异惩罚项很好地修正和增强了最终的分割效果.在人工合成图片的去噪实验中,所提方法取得了近99%的分割正确率,优于Nystrom归一化分割(NNcut)和基于模糊局部信息C均值(FLICM)算法;同时在自然图片和医学图片的对比实验以及参数调控实验中,展现出了其在处理图像噪声和细节时灵活、稳定、健壮且易于调控的特点.     

Image Segmentation Based on Adaptive Cluster Prototype Estimation

An image segmentation algorithm based on adaptive fuzzy c-means (FCM) clustering is presented in this paper. In the conventional FCM clustering algorithm, cluster assignment is based solely on the distribution of pixel attributes in the feature space, and does not take into consideration the spatial distribution of pixels in an image. By introducing a novel dissimilarity index in the modified FCM objective function, the new adaptive fuzzy clustering algorithm is capable of utilizing local contextual information to impose local spatial continuity, thus exploiting the high inter-pixel correlation inherent in most real-world images. The incorporation of local spatial continuity allows the suppression of noise and helps to resolve classification ambiguity. To account for smooth intensity variation within each homogenous region in an image, a multiplicative field is introduced to each of the fixed FCM cluster prototype. The multiplicative field effectively makes the fixed cluster prototype adaptive to slow smooth within-cluster intensity variation, and allows homogenous regions with slow smooth intensity variation to be segmented as a whole. Experimental results with synthetic and real color images have shown the effectiveness of the proposed algorithm.     

DCT子空间的邻域加权模糊C均值聚类算法

模糊C均值聚类是一种有效的图像分割方法, 但存在因忽略空间上下文信息和结构信息而易为噪声所干扰的现象. 为此提出了DCT子空间的邻域加权模糊C均值聚类方法. 该方法首先结合分块的思想, 对图像块进行离散余弦变换(discrete cosine transform,DCT), 建立了一个基于图像块局部信息的相似性度量模型; 然后定义目标函数中的欧式距离为邻域加权距离; 最后将该方法应用于加噪的人工合成图像、自然图像和MR图像. 实验结果表明, 该方法能够获得较好的分割效果, 同时具有较强的抗噪性.     

基于灰度空间特征的模糊C均值聚类图像分割

模糊C均值(FCM)聚类算法广泛用于图像的自动分割,但是该算法没有考虑像素的灰度和空间特征,对噪声十分敏感.因此提出一种改进的算法,在传统的FCM聚类的基础上,运用邻域像素的灰度相似度和聚类分布统计来构造新的隶属函数,对图像进行聚类分割.该方法不仅有效地抑制了噪声的干扰,而且把错分类的像素很容易的纠正过来.对两种类型的含噪图像的实验结果表明该方法对噪声具有很强的鲁棒性和对像素聚类的正确性.     

Optimality test for generalized FCM and its application to parameter selection

In cluster analysis, the fuzzy c-means (FCM) clustering algorithm is the best known and most widely used method. It was proven to converge to either a local minimum or saddle points by Bezdek et al. Wei and Mendel produced efficient optimality tests for FCM fixed points. Recently, a weighting exponent selection for FCM was proposed by Yu et al. Inspired by these results, we unify several alternative FCM algorithms into one model, called the generalized fuzzy c-means (GFCM). This GFCM model presents a wide variation of FCM algorithms and can easily lead to new and interesting clustering algorithms. Moreover, we construct a general optimality test for GFCM fixed points. This is applied to theoretically choose the parameters in the GFCM model. The experimental results demonstrate the precision of the theoretical analysis.     

基于核函数与马氏距离的FCM图像分割算法

针对模糊聚类算法邻域信息与空间信息利用率低易受噪声影响的问题,提出一种结合核函数与马氏距离的FCM算法,即FCMKM算法。首先,将图像像素点由低维空间通过核函数非线性映射到高维空间;然后,利用马氏距离替换原有的欧氏距离作为高维空间距离量度;最后,利用改进后的算法对图像进行分割。为验证FCMKM算法的性能,选取Bezdek划分系数、Xie-Beni系数、重构错误率、运行时间、迭代次数五个评测指标作为对比实验的评价标准。实验结果表明,与传统FCM算法、基于核函数的FCM算法、基于马氏距离的FCM算法相比,FCMKM算法能有效地提高模糊聚类算法的抗噪性。     

Effective fuzzy c-means clustering algorithms for data clustering problems

Clustering is a well known technique in identifying intrinsic structures and find out useful information from large amount of data. One of the most extensively used clustering techniques is the fuzzy c-means algorithm. However, computational task becomes a problem in standard objective function of fuzzy c-means due to large amount of data, measurement uncertainty in data objects. Further, the fuzzy c-means suffer to set the optimal parameters for the clustering method. Hence the goal of this paper is to produce an alternative generalization of FCM clustering techniques in order to deal with the more complicated data; called quadratic entropy based fuzzy c-means. This paper is dealing with the effective quadratic entropy fuzzy c-means using the combination of regularization function, quadratic terms, mean distance functions, and kernel distance functions. It gives a complete framework of quadratic entropy approaching for constructing effective quadratic entropy based fuzzy clustering algorithms. This paper establishes an effective way of estimating memberships and updating centers by minimizing the proposed objective functions. In order to reduce the number iterations of proposed techniques this article proposes a new algorithm to initialize the cluster centers.In order to obtain the cluster validity and choosing the number of clusters in using proposed techniques, we use silhouette method. First time, this paper segments the synthetic control chart time series directly using our proposed methods for examining the performance of methods and it shows that the proposed clustering techniques have advantages over the existing standard FCM and very recent ClusterM-k-NN in segmenting synthetic control chart time series.     

结合小波变换和改进邻域权值的FCM算法

针对改进的模糊C均值聚类算法在进行图像分割时构建的邻域权值函数未能同时考虑空间结构信息和灰度值域信息,而导致对噪声敏感及边缘纹理信息的处理粗糙的问题,提出了一种结合小波变换和改进邻域权值的FCM算法.该算法首先在原始灰度图像的基础上进行小波多分辨率分析的自适应阈值去噪处理;然后在重构图像上结合双边滤波的思想构建一个基于图像块局部空间邻域信息和灰度值域信息的改进邻域权值函数.实验结果表明,该算法比传统FCM算法以及FCM的改进算法有更高的分割精确度,对强噪声更具鲁棒性,图像边缘也更加平整.     

利用空间信息的核模糊C均值聚类算法

模糊聚类,特别是模糊C均值聚类算法（FCM）广泛地运用到图像的分割中。但是传统的算法未对数据对特征进行优化,亦未考虑图像的空间信息,对噪声图像分割不理想。在FCM目标函数中引入核函数,用内核引导距离代替传统的欧式距离,同时考虑到邻近象素的影响,增加了空间约束项,提出了利用空间信息的核FCM算法。通过对模拟图和仿真脑部MR图像的分割实验证明,该算法可以有效的分割含有噪声图像。     

Strong fuzzy c-means in medical image data analysis

This paper presents a robust fuzzy c-means (FCM) for an automatic effective segmentation of breast and brain magnetic resonance images (MRI). This paper obtains novel objective functions for proposed robust fuzzy c-means by replacing original Euclidean distance with properties of kernel function on feature space and using Tsallis entropy. By minimizing the proposed effective objective functions, this paper gets membership partition matrices and equations for successive prototypes. In order to reduce the computational complexity and running time, center initialization algorithm is introduced for initializing the initial cluster center. The initial experimental works have done on synthetic image and benchmark dataset to investigate the effectiveness of proposed, and then the proposed method has been implemented to differentiate the different region of real breast and brain magnetic resonance images. In order to identify the validity of proposed fuzzy c-means methods, segmentation accuracy is computed by using silhouette method. The experimental results show that the proposed method is more capable in segmentation of medical images than existed methods.     

FCM融合改进的GSA算法在医学图像分割中的研究

医学图像由于具有复杂性,在对其进行图像分割时存在很大的不确定性,为了提高模糊c均值聚类算法(FCM)在处理医学图像分割时的性能,提出一种新的混合方法进行图像分割。利用FCM算法将图像像素分成均匀的区域,融合引力搜索算法,将改进的引力搜索算法纳入模糊c均值聚类算法中,以找到最优聚类中心,使模糊c均值聚类的适应度函数值最小,从而提高分割效果。实验结果表明,相对于传统的聚类算法,所提算法在分割复杂的医学图像方面更具有效性。     

一种快速鲁棒核空间图形模糊聚类分割算法

针对现有鲁棒图形模糊聚类算法难以满足强噪声干扰下大幅面图像快速分割的需要，提出一种快速鲁棒核空间图形模糊聚类分割算法。该算法将欧氏空间样本通过核函数映射至高维空间；采用待分割图像中像素邻域的灰度和空间等信息构建线性加权滤波图像，对其进行鲁棒核空间图形模糊聚类；并引入当前聚类像素与其邻域像素均值所对应的二维直方图信息，获得鲁棒核空间图形模糊聚类快速迭代表达式。对大幅面图像添加高斯和椒盐噪声进行分割测试，实验结果表明:本文算法相比基于图形模糊聚类等分割算法的分割性能、抗噪鲁棒性和实时性有了显著提高。     

A Modified Fuzzy C-Means Algorithm for Brain MR Image Segmentation and Bias Field Correction

In quantitative brain image analysis, accurate brain tissue segmentation from brain magnetic resonance image (MRI) is a critical step. It is considered to be the most important and difficult issue in the field of medical image processing. The quality of MR images is influenced by partial volume effect, noise, and intensity inhomogeneity, which render the segmentation task extremely challenging. We present a novel fuzzy c-means algorithm (RCLFCM) for segmentation and bias field correction of brain MR images. We employ a new gray-difference coefficient and design a new impact factor to measure the effect of neighbor pixels, so that the robustness of anti-noise can be enhanced. Moreover, we redefine the objective function of FCM (fuzzy c-means) by adding the bias field estimation model to overcome the intensity inhomogeneity in the image and segment the brain MR images simultaneously. We also construct a new spatial function by combining pixel gray value dissimilarity with its membership, and make full use of the space information between pixels to update the membership. Compared with other state-of-the-art approaches by using similarity accuracy on synthetic MR images with different levels of noise and intensity inhomogeneity, the proposed algorithm generates the results with high accuracy and robustness to noise.     

A new fuzzy clustering algorithm for the segmentation of brain tumor

This paper introduces a new method of clustering algorithm based on interval-valued intuitionistic fuzzy sets (IVIFSs) generated from intuitionistic fuzzy sets to analyze tumor in magnetic resonance (MR) images by reducing time complexity and errors. Based on fuzzy clustering, during the segmentation process one can consider numerous cases of uncertainty involving in membership function, distance measure, fuzzifier, and so on. Due to poor illumination of medical images, uncertainty emerges in their gray levels. This paper concentrates on uncertainty in the allotment of values to the membership function of the uncertain pixels. Proposed method initially pre-processes the brain MR images to remove noise, standardize intensity, and extract brain region. Subsequently IVIFSs are constructed to utilize in the clustering algorithm. Results are compared with the segmented images obtained using histogram thresholding, k-means, fuzzy c-means, intuitionistic fuzzy c-means, and interval type-2 fuzzy c-means algorithms and it has been proven that the proposed method is more effective.     

Improved spatial fuzzy c-means clustering for image segmentation using PSO initialization,Mahalanobis distance and post-segmentation correction

In this paper, we propose an improvement method for image segmentation using the fuzzy c-means clustering algorithm (FCM). This algorithm is widely experimented in the field of image segmentation with very successful results. In this work, we suggest further improving these results by acting at three different levels. The first is related to the fuzzy c-means algorithm itself by improving the initialization step using a metaheuristic optimization. The second level is concerned with the integration of the spatial gray-level information of the image in the clustering segmentation process and the use of Mahalanobis distance to reduce the influence of the geometrical shape of the different classes. The final level corresponds to refining the segmentation results by correcting the errors of clustering by reallocating the potentially misclassified pixels. The proposed method, named improved spatial fuzzy c-means IFCMS, was evaluated on several test images including both synthetic images and simulated brain MRI images from the McConnell Brain Imaging Center (BrainWeb) database. This method is compared to the most used FCM-based algorithms of the literature. The results demonstrate the efficiency of the ideas presented.     

A clustering algorithm with optimized multiscale spatial texture information: application to SAR image segmentation

An image segmentation method based on optimized spatial texture information is proposed in this article. Spatial information, including the relative position of neighbouring pixels and texture features of the multiscale neighbourhood, is incorporated into the similarity measure of the fuzzy c-means (FCM) clustering algorithm, in which the Gaussian kernel is adopted to diminish the local incorrect segmentation. The FCM clustering is spatially adjusted and optimized by the particle swarm optimization (PSO) algorithm. The purpose of optimization is to obtain the appropriate control parameters influencing spatial information, which can improve segmentation results. Experimental results demonstrate that the proposed method achieves better segmentation performance and is capable of effectively segmenting synthetic images and synthetic aperture radar (SAR) images.