结合[k]-means的自动FCM图像分割方法

针对图像分割中模糊C均值算法（FCM）无法自动确定聚类中心,不考虑像素邻域信息的问题,提出一种结合[k]-means的自动FCM图像分割方法。该方法先由图像的灰度直方图确定聚类数目,使用一种改进的快速FCM方法产生初始聚类中心。即通过一步[k]-means算法对大隶属度灰度更新模糊聚类中心,同时仅对小隶属度灰度使用快速FCM?方法进行隶属度更新,迭代后得到初始聚类中心。利用改进隶属度的FCM算法进行最终聚类。实验表明,该方法获取初始聚类中心接近最终值,加速图像分割,并对噪声具有一定的鲁棒性。     

A multivariate fuzzy c-means method

Fuzzy c-means (FCMs) is an important and popular unsupervised partitioning algorithm used in several application domains such as pattern recognition, machine learning and data mining. Although the FCM has shown good performance in detecting clusters, the membership values for each individual computed to each of the clusters cannot indicate how well the individuals are classified. In this paper, a new approach to handle the memberships based on the inherent information in each feature is presented. The algorithm produces a membership matrix for each individual, the membership values are between zero and one and measure the similarity of this individual to the center of each cluster according to each feature. These values can change at each iteration of the algorithm and they are different from one feature to another and from one cluster to another in order to increase the performance of the fuzzy c-means clustering algorithm. To obtain a fuzzy partition by class of the input data set, a way to compute the class membership values is also proposed in this work. Experiments with synthetic and real data sets show that the proposed approach produces good quality of clustering.     

广义洛伦兹内核函数在模糊C均值聚类中的应用研究

模糊C均值(FCM)算法是数据聚类分析的主要算法。但在嘈杂环境下,对于抽样大小不一的聚类,数目越多准确性越低,上述弊端可通过替代性FCM(AFCM)的高斯内核映射来解决。鉴于AFCM的不足,提出了针对模糊C均值聚类的广义洛伦兹内核函数。利用该算法对鸢尾数据库进行聚类,将其划分成山鸢尾、变色鸢尾和维吉尼亚鸢尾3类。实验结果表明,广义洛伦兹模糊C均值(GLFCM)可实现对离群聚类和大小不等的聚类数据的分类,其结果优于K均值、FCM、替代性C均值(AFCM)、Gustafson-Kessel(GK)和 Gath-Geva(GG)方法,收敛迭代次数比AFCM的更少,其分区索引(SC)效果也好于其他方法。     

Automatic detection of Moroccan coastal upwelling zones using sea surface temperature images

An efficient unsupervised method is developed for automatic segmentation of the area covered by upwelling waters in the coastal ocean of Morocco using the Sea Surface Temperature (SST) satellite images. The proposed approach first uses the two popular unsupervised clustering techniques, k-means and fuzzy c-means (FCM), to provide different possible classifications to each SST image. Then several cluster validity indices are combined in order to determine the optimal number of clusters, followed by a cluster fusion scheme, which merges consecutive clusters to produce a first segmentation of upwelling area. The region-growing algorithm is then used to filter noisy residuals and to extract the final upwelling region. The performance of our algorithm is compared to a popular algorithm used to detect upwelling regions and is validated by an oceanographer over a database of 92 SST images covering each week of the years 2006 and 2007. The results show that our proposed method outperforms the latter algorithm, in terms of segmentation accuracy and computational efficiency.     

A local-spectral fuzzy segmentation for MSG multispectral images

In this article, a segmentation approach for cloud detection in Meteosat Second Generation (MSG) multispectral images is proposed. The proposed algorithm uses recursive segmentation that dynamically reduces the number of classes. This algorithm consists of two steps. First, an initial segmentation of the image is obtained using local fuzzy clustering. The clustering algorithm is formulated by modifying the similarity measure of the standard fuzzy c-means (FCM) algorithm. The new similarity function includes the spectral information as well as the homogeneity and spatial clustering information of each considered pixel. In the second step, a hierarchical region-merging process is used to reduce the number of image clusters. At each iteration, the segmentation algorithm proceeds with a new partition until the final result of the segmentation is obtained. The proposed method has been tested using synthetic and MSG images. It yields a compact and coherent segmentation map, with a satisfactory reproduction of the image contours. Moreover, the different types of clouds are well detected and separated with appropriate accuracy.     

A fuzzy data reduction cluster method based on boundary information for large datasets

The fuzzy c-means algorithm (FCM) is aimed at computing the membership degree of each data point to its corresponding cluster center. This computation needs to calculate the distance matrix between the cluster center and the data point. The main bottleneck of the FCM algorithm is the computing of the membership matrix for all data points. This work presents a new clustering method, the bdrFCM (boundary data reduction fuzzy c-means). Our algorithm is based on the original FCM proposal, adapted to detect and remove the boundary regions of clusters. Our implementation efforts are directed in two aspects: processing large datasets in less time and reducing the data volume, maintaining the quality of the clusters. A significant volume of real data application (> 10⁶ records) was used, and we identified that bdrFCM implementation has good scalability to handle datasets with millions of data points.

     

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.     

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.     

基于数据间内在关联性的自适应模糊聚类模型

提出了一种新的模糊聚类模型(Fuzzy C-means clustering model, FCM), 称为自适应模糊聚类(Adaptive FCM, AFCM). 和现有的大多数模糊聚类方法不同的是, AFCM考虑了数据集中全体数据的内在关联性, 模型中引入了自适应度向量W和自适应指数p. 其中, W在迭代过程中是自适应的, p是一个给定参数. W和p共同作用调控聚类过程. AFCM同时输出三组参数: 模糊隶属度集U, 自适应度向量W, 以及聚类原型集V. 本文给出了两组数据实验验证AFCM的性能. 第1组实验验证AFCM的聚类性能, 以FCM为比较对象. 实验表明 AFCM可以得到更好的聚类质量, 而且通过合理选择自适应指数p, AFCM和FCM在时间复杂性上保持同一水平. 第2组实验检验了AFCM的离群点挖掘性能, 以目前常用的基于密度的LOF为比较对象. 实验表明AFCM算法具有极大的计算效率优势, 且AFCM得到的离群点是全局的, 反映的是离群点和整个数据集的关系, 离群点涵盖的信息也更丰富. 文章指出, AFCM在挖掘大数据集和实时数据中的离群点应用方面, 以及获得高质量的聚类结果的应用方面, 特别在聚类的同时需要挖掘离群点的应用方面具有独特的优势.     

Color image segmentation—an innovative approach

In this paper we describe a color image segmentation system that performs color clustering in a color space and then color region segmentation in the image domain. For color segmentation, we developed a fuzzy clustering algorithm that iteratively generates color clusters using a uniquely defined fuzzy membership function and an objective function for clustering optimization. The fuzzy membership function represents belief value of a color belonging to a color cluster and the mutual interference of neighboring clusters. The region segmentation algorithm merges clusters in the image domain based on color similarity and spatial adjacency. We developed three different methods for merging regions in the image domain. Unlike many existing clustering algorithms, the image segmentation system does not require the knowledge about the number of the color clusters to be generated at each stage and the resolution of the color regions can be controlled by one single parameter, the radius of a cluster. The color image segmentation system has been implemented and tested on a variety of color images including satellite images, car and face images. The experiment results are presented and the performance of each algorithm in the segmentation system is analyzed. The system has shown to be both effective and efficient.     

Robust fuzzy clustering-based image segmentation

The fuzzy clustering algorithm fuzzy c-means (FCM) is often used for image segmentation. When noisy image segmentation is required, FCM should be modified such that it can be less sensitive to noise in an image. In this correspondence, a robust fuzzy clustering-based segmentation method for noisy images is developed. The contribution of the study here is twofold: (1) we derive a robust modified FCM in the sense of a novel objective function. The proposed modified FCM here is proved to be equivalent to the modified FCM given by Hoppner and Klawonn [F. Hoppner, F. Klawonn, Improved fuzzy partitions for fuzzy regression models, Int. J. Approx. Reason. 32 (2) (2003) 85–102]. (2) We explore the very applicability of the proposed modified FCM for noisy image segmentation. Our experimental results indicate that the proposed modified FCM here is very suitable for noisy image segmentation.     

基于可靠性的鲁棒模糊聚类

相比于k-means算法,模糊C均值(FCM)通过引入模糊隶属度,考虑不同数据簇之间的相互作用,进而避免了聚类中心趋同性问题.然而模糊隶属度具有拖尾和翘尾的结构特征,因此使得FCM算法对噪声点和孤立点很敏感;此外,由于FCM算法倾向于将各数据簇均等分,因此算法对数据簇大小也很敏感,对非平衡数据簇聚类效果不佳.针对这些问题,本文提出了基于可靠性的鲁棒模糊聚类算法(RRFCM).该算法基于当前的聚类结果,对样本点进行可靠性分析,利用样本点的可靠性和局部近邻信息,突出不同数据簇之间的可分性,从而提高了算法对噪声的鲁棒性,并且降低了对非平衡数据簇大小的敏感性,得到了泛化性能更好的聚类结果.与相关算法进行对比,RRFCM算法在人造数据集,UCI真实数据集以及图像分割实验中均取得最优的结果.     

A fast and robust image segmentation using FCM with spatial information

Automated segmentation of images has been considered an important intermediate processing task to extract semantic meaning from pixels. In general, the fuzzy c-means approach (FCM) is highly effective for image segmentation. But for the conventional FCM image segmentation algorithm, cluster assignment is based solely on the distribution of pixel attributes in the feature space, and the spatial distribution of pixels in an image is not taken into consideration. In this paper, we present a novel FCM image segmentation scheme by utilizing local contextual information and the high inter-pixel correlation inherent. Firstly, a local spatial similarity measure model is established, and the initial clustering center and initial membership are determined adaptively based on local spatial similarity measure model. Secondly, the fuzzy membership function is modified according to the high inter-pixel correlation inherent. Finally, the image is segmented by using the modified FCM algorithm. Experimental results showed the proposed method achieves competitive segmentation results compared to other FCM-based methods, and is in general faster.     

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.     

A fuzzy clustering algorithm based on evolutionary programming

In this paper, a fuzzy clustering method based on evolutionary programming (EPFCM) is proposed. The algorithm benefits from the global search strategy of evolutionary programming, to improve fuzzy c-means algorithm (FCM). The cluster validity can be measured by some cluster validity indices. To increase the convergence speed of the algorithm, we exploit the modified algorithm to change the number of cluster centers dynamically. Experiments demonstrate EPFCM can find the proper number of clusters, and the result of clustering does not depend critically on the choice of the initial cluster centers. The probability of trapping into the local optima will be very lower than FCM.     

A multi-agent-based approach for fuzzy clustering of large image data

Data clustering usually requires extensive computations of similarity measures between dataset members and cluster centers, especially for large datasets. Image clustering can be an intermediate process in image retrieval or segmentation, where a fast process is critically required for large image databases. This paper introduces a new approach of multi-agents for fuzzy image clustering (MAFIC) to improve the time cost of the sequential fuzzy \(c\)-means algorithm (FCM). The approach has the distinguished feature of distributing the computation of cluster centers and membership function among several parallel agents, where each agent works independently on a different sub-image of an image. Based on the Java Agent Development Framework platform, an implementation of MAFIC is tested on 24-bit large size images. The experimental results show that the time performance of MAFIC outperforms that of the sequential FCM algorithm by at least four times, and thus reduces the time needed for the clustering process.     

Fuzzy C-means based clustering for linearly and nonlinearly separable data

In this paper we present a new distance metric that incorporates the distance variation in a cluster to regularize the distance between a data point and the cluster centroid. It is then applied to the conventional fuzzy C-means (FCM) clustering in data space and the kernel fuzzy C-means (KFCM) clustering in a high-dimensional feature space. Experiments on two-dimensional artificial data sets, real data sets from public data libraries and color image segmentation have shown that the proposed FCM and KFCM with the new distance metric generally have better performance on non-spherically distributed data with uneven density for linear and nonlinear separation.     

An adaptive spatially constrained fuzzy c-means algorithm for multispectral remotely sensed imagery clustering

This paper presents a novel adaptive spatially constrained fuzzy c-means (ASCFCM) algorithm for multispectral remotely sensed imagery clustering by incorporating accurate local spatial and grey-level information. In this algorithm, a novel weighted factor is introduced considering spatial distance and membership differences between the centred pixel and its neighbours simultaneously. This factor can adaptively estimate the accurate spatial constrains from neighbouring pixels. To further enhance its robustness to noise and outliers, a novel prior probability function is developed by integrating the mutual dependency information in the neighbourhood to obtain accurate spatial contextual information. The proposed algorithm is free of any experimentally adjusted parameters and totally adaptive to the local image content. Not only the neighbourhood but also the centred pixel terms of the objective function are all accurately estimated. Thus, the ASCFCM enhances the conventional fuzzy c-means (FCM) algorithm by producing homogeneous regions and reducing the edge blurring artefact simultaneously. Experimental results using a series of synthetic and real-world images show that the proposed ASCFCM outperforms the competing methodologies, and hence provides an effective unsupervised method for multispectral remotely sensed imagery clustering.     

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。     

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。