Optimal-selection-based suppressed fuzzy c-means clustering algorithm with self-tuning non local spatial information for image segmentation

Suppressed fuzzy c-means clustering algorithm (S-FCM) is one of the most effective fuzzy clustering algorithms. Even if S-FCM has some advantages, some problems exist. First, it is unreasonable to compulsively modify the membership degree values for all the data points in each iteration step of S-FCM. Furthermore, duo to only utilizing the spatial information derived from the pixel’s neighborhood window to guide the process of image segmentation, S-FCM cannot obtain satisfactory segmentation results on images heavily corrupted by noise. This paper proposes an optimal-selection-based suppressed fuzzy c-means clustering algorithm with self-tuning non local spatial information for image segmentation to solve the above drawbacks of S-FCM. Firstly, an optimal-selection-based suppressed strategy is presented to modify the membership degree values for data points. In detail, during each iteration step, all the data points are ranked based on their biggest membership degree values, and then the membership degree values of the top r ranked data points are modified while the membership degree values of the other data points are not changed. In this paper, the parameter r is determined by the golden section method. Secondly, a novel gray level histogram is constructed by using the self-tuning non local spatial information for each pixel, and then fuzzy c-means clustering algorithm with the optimal-selection-based suppressed strategy is executed on this histogram. The self-tuning non local spatial information of a pixel is derived from the pixels with a similar neighborhood configuration to the given pixel and can preserve more information of the image than the spatial information derived from the pixel’s neighborhood window. This method is applied to Berkeley and other real images heavily contaminated by noise. The image segmentation experiments demonstrate the superiority of the proposed method over other fuzzy algorithms.     

Robust color image segmentation using fuzzy c-means with weighted hue and intensity

In this paper we propose a novel method for color image segmentation. This method uses only hue and intensity components (which are chosen rationally) of image and combines those by adaptive tuned weights in a specially defined fuzzy c-means cost function. The tuned weights indicate how informative every color component (hue and intensity) is. Obtaining tuned weights begins with finding peaks of hue and intensity's histograms and continues by obtaining the table of the frequencies of hue and intensity values and computing entropy and contrast of every color component. Also this method specifies proper initial values for cluster centers with the aim of reducing the overall number of iterations and avoiding converging of FCM to wrong centroids. Experimental results demonstrate that our algorithm achieves better segmentation performance and also runs faster than similar methods.     

An adaptive spatial information-theoretic fuzzy clustering algorithm for image segmentation

This paper presents an adaptive spatial information-theoretic fuzzy clustering algorithm to improve the robustness of the conventional fuzzy c-means (FCM) clustering algorithms for image segmentation. This is achieved through the incorporation of information-theoretic framework into the FCM-type algorithms. By combining these two concepts and modifying the objective function of the FCM algorithm, we are able to solve the problems of sensitivity to noisy data and the lack of spatial information, and improve the image segmentation results. The experimental results have shown that this robust clustering algorithm is useful for MRI brain image segmentation and it yields better segmentation results when compared to the conventional FCM approach.     

Robust spatially constrained fuzzy c-means algorithm for brain MR image segmentation

Objective

Accurate brain tissue segmentation from magnetic resonance (MR) images is an essential step in quantitative brain image analysis, and hence has attracted extensive research attention. However, due to the existence of noise and intensity inhomogeneity in brain MR images, many segmentation algorithms suffer from limited robustness to outliers, over-smoothness for segmentations and limited segmentation accuracy for image details. To further improve the accuracy for brain MR image segmentation, a robust spatially constrained fuzzy c-means (RSCFCM) algorithm is proposed in this paper.

Method

Firstly, a novel spatial factor is proposed to overcome the impact of noise in the images. By incorporating the spatial information amongst neighborhood pixels, the proposed spatial factor is constructed based on the posterior probabilities and prior probabilities, and takes the spatial direction into account. It plays a role as linear filters for smoothing and restoring images corrupted by noise. Therefore, the proposed spatial factor is fast and easy to implement, and can preserve more details. Secondly, the negative log-posterior is utilized as dissimilarity function by taking the prior probabilities into account, which can further improve the ability to identify the class for each pixel. Finally, to overcome the impact of intensity inhomogeneity, we approximate the bias field at the pixel-by-pixel level by using a linear combination of orthogonal polynomials. The fuzzy objective function is then integrated with the bias field estimation model to overcome the intensity inhomogeneity in the image and segment the brain MR images simultaneously.

Results

To demonstrate the performances of the proposed algorithm for the images with/without skull stripping, the first group of experiments is carried out in clinical 3T-weighted brain MR images which contain quite serious intensity inhomogeneity and noise. Then we quantitatively compare our algorithm to state-of-the-art segmentation approaches by using Jaccard similarity on benchmark images obtained from IBSR and BrainWeb with different level of noise and intensity inhomogeneity. The comparison results demonstrate that the proposed algorithm can produce higher accuracy segmentation and has stronger ability of denoising, especially in the area with abundant textures and details.

Conclusion

In this paper, the RSCFCM algorithm is proposed by utilizing the negative log-posterior as the dissimilarity function, introducing a novel factor and integrating the bias field estimation model into the fuzzy objective function. This algorithm successfully overcomes the drawbacks of existing FCM-type clustering schemes and EM-type mixture models. Our statistical results (mean and standard deviation of Jaccard similarity for each tissue) on both synthetic and clinical images show that the proposed algorithm can overcome the difficulties caused by noise and bias fields, and is capable of improving over 5% segmentation accuracy comparing with several state-of-the-art algorithms.     

Fast global kernel fuzzy c-means clustering algorithm for consonant/vowel segmentation of speech signal

We propose a novel clustering algorithm using fast global kernel fuzzy c-means-F（FGKFCM-F）, where F refers to kernelized feature space. This algorithm proceeds in an incremental way to derive the near-optimal solution by solving all intermediate problems using kernel-based fuzzy c-means-F（KFCM-F） as a local search procedure. Due to the incremental nature and the nonlinear properties inherited from KFCM-F, this algorithm overcomes the two shortcomings of fuzzy c-means（FCM）： sen- sitivity to initialization and inability to use nonlinear separable data. An accelerating scheme is developed to reduce the compu-tational complexity without significantly affecting the solution quality. Experiments are carried out to test the proposed algorithm on a nonlinear artificial dataset and a real-world dataset of speech signals for consonant/vowel segmentation. Simulation results demonstrate the effectiveness of the proposed algorithm in improving clustering performance on both types of datasets.     

Measuring the congruence of fuzzy partitions in fuzzy c-means clustering

We propose an internal cluster validity index for a fuzzy c-means algorithm which combines a mathematical model for the fuzzy c-partition and a heuristic search for the number of clusters in the data. Our index resorts to information theoretic principles, and aims to assess the congruence between such a model and the data that have been observed. The optimal cluster solution represents a trade-off between discrepancy and the complexity of the underlying fuzzy c-partition. We begin by testing the effectiveness of the proposed index using two sets of synthetic data, one comprising a well-defined cluster structure and the other containing only noise. Then we use datasets arising from real life problems. Our results are compared to those provided by several available indices and their goodness is judged by an external measure of similarity. We find substantial evidence supporting our index as a credible alternative to the cluster validation problem, especially when it concerns structureless data.     

基于信息增益的模糊K-prototypes聚类算法

K-prototypes聚类算法结合了K-means算法和K-modes算法,可用于分析混合属性的数据对象。传统的K-prototypes聚类算法在计算数据对象的相异度时,未考虑各个属性对于最终聚类结果的影响程度,而现实世界中,各属性的重要程度是不同的。使用了信息论中信息增益的计算方法,来获得各个属性的权值。在计算各属性的差异度时,乘以这些权值,从而可以获得更为准确的聚类结果。为了增加算法处理模糊问题的能力,本算法引用了模糊理论,从而使其具有较好的抗干扰能力和处理不确定性问题的能力。通过对四个UCI数据集的聚类分析实验,表明了本算法的有效性。     

基于均值漂移与空间信息的导向模糊C均值遥感图像分割算法

作为图像数据结构分割的重要工具,模糊C均值已被广泛应用于计算机视觉领域。然而模糊C均值在图像分割过程中不能有效地保留边缘和抑制噪声,往往得不到理想的分割结果。为解决这一问题,本文利用导向滤波器推导出一种新的改进模糊C均值算法。该算法的第一个创新点是其线性平移不变滤波过程,利用边缘保持平滑特性来保留分割中的边缘结构。第二个创新点是该技术通过将空间信息引入目标函数来改善对噪声的鲁棒性,空间信息通过导向滤波的平均输出获得。为了解决聚类算法中初始聚类中心问题,在图像分割过程中使用均值漂移算法选取初始聚类中心。本文方法的主要优点在于其对边缘保留和噪声具有鲁棒性,进而提高分割精度。基于合成图像和真实遥感图像的实验结果表明,与其他主流分割算法相比,该方法在分割性能方面表现出了良好的性能。     

基于空间信息的可能性模糊C均值聚类遥感图像分割

可能性模糊C均值(PFCM)聚类算法作为模糊C均值(FCM)聚类算法的一种改进算法,能在一定程度上克服FCM算法对噪声的敏感性;但由于PFCM没有考虑像元间的空间信息,对含有较大噪声的图像分割效果依然不理想。为此,提出一种新的基于空间信息的PFCM算法(SPFCM),克服了PFCM算法对含有较大噪声的图像分割效果不佳的缺点。通过对人工图像和IKONOS遥感图像进行分析,结果表明,SPFCM算法无论是在视觉上还是在分割正确率上都优于传统的FCM算法、PFCM算法及两种加入空间信息的FCM算法;对于含有高斯噪声和盐椒噪声的图像,平均分割正确率高达99.71%,是一种去噪效果较好的图像分割算法。     

A new ECG beat clustering method based on kernelized fuzzy c-means and hybrid ant colony optimization for continuous domains

The kernelized fuzzy c-means algorithm uses kernel methods to improve the clustering performance of the well known fuzzy c-means algorithm by mapping a given dataset into a higher dimensional space non-linearly. Thus, the newly obtained dataset is more likely to be linearly seprable. However, to further improve the clustering performance, an optimization method is required to overcome the drawbacks of the traditional algorithms such as, sensitivity to initialization, trapping into local minima and lack of prior knowledge for optimum paramaters of the kernel functions. In this paper, to overcome these drawbacks, a new clustering method based on kernelized fuzzy c-means algorithm and a recently proposed ant based optimization algorithm, hybrid ant colony optimization for continuous domains, is proposed. The proposed method is applied to a dataset which is obtained from MIT–BIH arrhythmia database. The dataset consists of six types of ECG beats including, Normal Beat (N), Premature Ventricular Contraction (PVC), Fusion of Ventricular and Normal Beat (F), Artrial Premature Beat (A), Right Bundle Branch Block Beat (R) and Fusion of Paced and Normal Beat (f). Four time domain features are extracted for each beat type and training and test sets are formed. After several experiments it is observed that the proposed method outperforms the traditional fuzzy c-means and kernelized fuzzy c-means algorithms.     

融合全局最好和声搜索算法的模糊C均值聚类图像分割

针对传统模糊C均值(FCM)聚类算法聚类数目难以确定,迭代速度慢,易陷入局部最优以及对聚类中心初始值的设置敏感等问题,提出一种融合全局最好和声搜索模糊C均值(GBHS-FCM)聚类算法。首先,利用全局最好和声搜索(GBHS)算法的全局性和鲁棒性的优点,得到初始聚类中心和聚类个数,再将其作为传统FCM聚类算法的初始聚类中心和聚类个数;其次,提出一种新颖的模糊聚类目标函数,将图像像素点邻域依赖特性考虑进来,与像素点灰度信息共同作用,增强了分割结果空间的连续性;此外,还采用了一种新颖的距离公式代替欧氏距离公式,增强了新算法对噪声的鲁棒性。仿真结果表明,新算法有效避免了传统FCM算法因初始聚类中心设置敏感而收敛到局部最优解,在聚类精度、速度和鲁棒性上均比传统FCM算法有所提高,针对具有不同特征的图像分割取得了较好的结果。     

A fuzzy c-means based hybrid evolutionary approach to the clustering of supply chain

This paper describes the work that adapts group technology and integrates it with fuzzy c-means, genetic algorithms and the tabu search to realize a fuzzy c-means based hybrid evolutionary approach to the clustering of supply chains. The proposed hybrid approach is able to organise supply chain units, transportation modes and work orders into different unit-transportation-work order families. It can determine the optimal clustering parameter, namely the number of clusters, c, and weighting exponent, m, dynamically, and is able to eliminate the necessity of pre-defining suitable values for these clustering parameters. A new fuzzy c-means validity index that takes into account inter-cluster transportation and group efficiency is formulated. It is employed to determine the promise level that estimates how good a set of clustering parameters is. The capability of the proposed hybrid approach is illustrated using three experiments and the comparative studies. The results show that the proposed hybrid approach is able to suggest suitable clustering parameters and near optimal supply chain clusters can be obtained readily.     

基于邻域信息的改进模糊c均值脑MRI分割

在脑图像分割中,噪声或异常值的干扰往往会使得图像的质量下降。而传统的模糊c均值算法存在一定的缺限,容易受初始值的影响,这给医生准确识别和提取脑组织带来很大的麻烦。针对这些问题,提出一种基于用马尔可夫模型构建的图像像素点邻域的改进模糊c均值图像分割方法。首先,用遗传算法（GA）确定初始的聚类中心;然后,改变目标函数的表达方式,通过在目标函数中添加修正项来改变隶属度矩阵的计算方式,并用约束系数对其来调节;最后,由马尔可夫随机域来表达邻域像素的标号信息,并利用马尔可夫随机场（MRF）的最大化条件概率来表示像素的邻域,增强了抗噪性。实验结果显示,该方法拥有较好的抗噪性,可以降低误分割率,在对脑图像分割时具备较高的分割精度。分割后的图像平均精度可达：JS（Jaccard Similarity）指标为82.76%,Dice指标为90.45%,Sensitivity指标为90.19%;同时,对脑图像边界处的分割更加清晰,分割后的图像更加接近于标准分割图像。     

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.     

Segmentation of ultrasound images of the carotid using RANSAC and cubic splines

A new algorithm is proposed for the semi-automatic segmentation of the near-end and the far-end adventitia boundary of the common carotid artery in ultrasound images. It uses the random sample consensus method to estimate the most significant cubic splines fitting the edge map of a longitudinal section. The consensus of the geometric model (a spline) is evaluated through a new gain function, which integrates the responses to different discriminating features of the carotid boundary: the proximity of the geometric model to any edge or to valley shaped edges; the consistency between the orientation of the normal to the geometric model and the intensity gradient; and the distance to a rough estimate of the lumen boundary.A set of 50 longitudinal B-mode images of the common carotid and their manual segmentations performed by two medical experts were used to assess the performance of the method. The image set was taken from 25 different subjects, most of them having plaques of different classes (class II to class IV), sizes and shapes.The quantitative evaluation showed promising results, having detection errors similar to the ones observed in manual segmentations for 95% of the far-end boundaries and 73% of the near-end boundaries.     

基于 K-center和信息增益的 Web搜索结果聚类方法 *

基于 K-center和信息增益的概念 ,将改进后的 FPF( furthest-point-first)算法用于 Web搜索结果聚类 ,提出了聚类标志方法 ,使得聚类呈现出的结果更易于用户理解 ,给出了评价聚类质量的模型。将该算法与 Lingo, K-means算法进行比较 ,其结果表明 ,本算法能够较好地平衡聚类质量和速度 ,更加适用于 Web检索聚类。     

Segmentation of the carotid intima-media region in B-mode ultrasound images

This paper proposes a new approach for the segmentation of both near-end and far-end intima-media regions of the common carotid artery in ultrasound images. The method requires minimal user interaction and is able to segment the near-end wall in arteries with large, hypoechogenic and irregular plaques, issues usually not considered previously due to the increased segmentation difficulty.     

Evaluating suppliers to include green supplier development programs via fuzzy c-means and VIKOR methods

Green supplier development has became necessity as organizations increasingly compete on environmental supply chain capabilities. This paper aims to determine green/environmental performance of supplier, and define which suppliers need to improve their conditions about environmental issues, and identify which suppliers should be included to green supplier development programs to enhance their environmental performance. Therefore, primarily, performance criteria and green supplier evaluation criteria were determined via a survey, then factor analysis was conducted to evaluate validity of factors. Then two step clustering was performed by using c-means clustering method. In the first step of clustering, all suppliers of a firm performing in automobile industry were clustered according to criteria-delivery, quality, cost and service. Thus best performing suppliers were determined. In the second step of clustering, best performing suppliers determined in the first step of clustering were evaluated with environmental/green criteria. As a result of clustering, best performing suppliers were splitted to three groups according to green criteria-good, medium, poor. Lastly, suppliers within the poor group were sequenced by using VIKOR method in order to include green supplier development programs.     

互信息与模糊C均值聚类集成的特征优选方法

针对大型数据中大量冗余特征的存在可能降低数据分类性能的问题,提出了一种基于互信息(MI)与模糊C均值(FCM)聚类集成的特征自动优选方法FCC-MI。首先分析了互信息特征及其相关度函数,根据相关度对特征进行排序;然后按照最大相关度对应的特征对数据进行分组,采用FCM聚类方法自动确定最优特征数目;最后基于相关度对特征进行了优选。在UCI机器学习数据库的7个数据集上进行实验,并与相关文献中提出的基于类内方差与相关度结合的特征选择方法(WCMFS)、基于近似Markov blanket和动态互信息的特征选择算法(B-AMBDMI)及基于互信息和遗传算法的两阶段特征选择方法(T-MI-GA)进行对比。理论分析和实验结果表明,FCC-MI不但提高了数据分类的效率,而且在有效保证分类精度的同时能自动确定最优特征子集,减少了数据集的特征数目,适用于海量、数据特征相关性大的特征约简及数据分析。     

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。