An automatic fuzzy c-means algorithm for image segmentation

Fuzzy c-means (FCM) algorithm is one of the most popular methods for image segmentation. However, the standard FCM algorithm must be estimated by expertise users to determine the cluster number. So, we propose an automatic fuzzy clustering algorithm (AFCM) for automatically grouping the pixels of an image into different homogeneous regions when the number of clusters is not known beforehand. In order to get better segmentation quality, this paper presents an algorithm based on AFCM algorithm, called automatic modified fuzzy c-means cluster segmentation algorithm (AMFCM). AMFCM algorithm incorporates spatial information into the membership function for clustering. The spatial function is the weighted summation of the membership function in the neighborhood of each pixel under consideration. Experimental results show that AMFCM algorithm not only can spontaneously estimate the appropriate number of clusters but also can get better segmentation quality.     

空间模糊C均值聚类的神经切片图像分割方法

周围神经切片显微图像具有背景复杂、区域不连续和光照不均匀等特点,应用经典的图像分割算法难以取得有效的分割结果。通过结合初始隶属度概率函数和空间距离来设计空间函数而得到的SFCM聚类算法,并提出SFCM彩色图像分割方法。把图像从RGB颜色空间转换到HIS颜色空间。采用聚类有效性分析指标在直方图快速FCM算法中为HSI各分量确定分类数目和获取SFCM初始化参数。对HIS各分量分别进行SFCM聚类,合并各分量并转换回RGB彩色空间以显示结果。实验结果表明,与标准FCM聚类分割算法相比,新方法能更有效地分割区域不连续的神经切片显微图像。     

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.     

结合类内和类间距离的可能聚类分割算法

目的 为了进一步提高噪声图像分割的抗噪性和准确性,提出一种结合类内距离和类间距离的改进可能聚类算法并将其应用于图像分割。方法 该算法避免了传统可能性聚类分割算法中仅仅考虑以样本点到聚类中心的距离作为算法的测度,将类内距离与类间距离相结合作为算法的新测度,即考虑了类内紧密程度又考虑了类间离散程度,以便对不同的聚类结构有较强的稳定性和更好的抗噪能力,并且将直方图融入可能模糊聚类分割算法中提出快速可能模糊聚类分割算法,使其对各种较复杂图像的分割具有即时性。结果 通过人工合成图像和实际遥感图像分割测试结果表明,本文改进可能聚类算法是有效的,其分割轮廓清晰,分类准确且噪声较小,其误分率相比其他算法至少降低了2个百分点,同时能获得更满意的分割效果。结论 针对模糊C-均值聚类分割算法和可能性聚类分割算法对于背景和目标颜色相近的图像分类不准确的缺陷,将类内距离与类间距离相结合作为算法的测度有效的解决了图像分割归类问题,并且结合直方图提出快速可能模糊聚类分割算法使其对于大篇幅复杂图像也具有适用性。     

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K-L变换和模糊集理论的彩色字符图像分割

根据彩色印刷字符图像的特点,在Lab颜色空间下提取a分量,将彩色图像转换为灰度图像。根据模糊逻辑和阈值分割方法将图像分为目标区域、背景区域以及模糊区域。用K-L变换组合邻域的区域隶属信息和灰度信息,将灰度域换成模糊域,在该模糊域上进行分割。经实践,该算法在工业环境中对复杂背景的彩色印刷图像可以得到较好的分割效果,其时间复杂度不高于传统的阈值分割算法,并且在分割的精确度上要优于传统的阈值分割算法。     

基于模糊规则的印刷图像专色分色研究

现有印刷图像专色分色技术已经不能满足印前处理效率和印刷质量要求,针对这一现状,提出了一种模糊C-均值聚类算法(FCM)。该算法基于像素分类,它首先对图像的灰度级进行模糊聚类,得到图像的聚类中心,然后根据每个像素点的灰度级,依照最大隶属度原则将各个像素点归于相应的类别中。实验证明,采用FCM 对印刷图像进行分割具有直观、易于实现的特点,实现了较好的分割效果。     

基于对偶树复小波变换的模糊纹理分割

提出了一种基于对偶树复小波变换的模糊纹理图像分割算法,该方法包括纹理特征提取和纹理分类两个阶段,其中,特征提取在对偶树复小波变换的基础上进行;纹理分类可以直接用模糊C均值算法进行聚类从而完成纹理的分割,但由于该算法中隶属度函数是基于样本到类中心的距离设计的,这对非球形分布数据很不合理,针对该问题,引入样本与样本的紧致度来度量类中各个样本之间的关系从而修正隶属度函数,并将其用于纹理分类。实验结果表明与模糊C均值算法在运行时间上相差不大的情况下,改进的方法在分割精度、边缘准确性和区域一致性上都得到了明显的改善。     

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。     

Generalized rough fuzzy c-means algorithm for brain MR image segmentation

Fuzzy sets and rough sets have been widely used in many clustering algorithms for medical image segmentation, and have recently been combined together to better deal with the uncertainty implied in observed image data. Despite of their wide spread applications, traditional hybrid approaches are sensitive to the empirical weighting parameters and random initialization, and hence may produce less accurate results. In this paper, a novel hybrid clustering approach, namely the generalized rough fuzzy c-means (GRFCM) algorithm is proposed for brain MR image segmentation. In this algorithm, each cluster is characterized by three automatically determined rough-fuzzy regions, and accordingly the membership of each pixel is estimated with respect to the region it locates. The importance of each region is balanced by a weighting parameter, and the bias field in MR images is modeled by a linear combination of orthogonal polynomials. The weighting parameter estimation and bias field correction have been incorporated into the iterative clustering process. Our algorithm has been compared to the existing rough c-means and hybrid clustering algorithms in both synthetic and clinical brain MR images. Experimental results demonstrate that the proposed algorithm is more robust to the initialization, noise, and bias field, and can produce more accurate and reliable segmentations.     

利用包含度和隶属度的遥感影像模糊分割

目的 传统FCM算法及其改进算法均只采用隶属度作为分割判据实现图像分割。然而,在分割过程中聚类中心易受到同质区域内几何噪声的影响,导致此类算法难以有效分割具有几何噪声的图像。为了解决这一类问题,提出一种利用包含度和隶属度的遥感影像模糊分割算法。方法 该算法假设同一聚类对每个像素都有不同程度的包含度,将包含度作为一种新测度来描述聚类与像素间关系,并将包含度纳入目标函数中。该算法通过迭代最小化目标函数来得到最优的隶属度和包含度,然后,通过反模糊化隶属度和包含度之积实现带有几何噪声的遥感图像的分割。结果 采用本文算法分别对模拟图像,真实遥感影像进行分割实验,并与FCM算法和FLICM算法进行对比,定性结果表明,对含有几何噪声的区域,提出算法的用户精度和产品精度均高于FCM算法和FLICM算法,且总精度和Kappa值也高于对比算法。实验结果表明,本文算法能够抵抗几何噪声对图像分割的影响,且分割精度远远高于其他两种算法的分割精度。结论 提出算法通过考虑聚类对像素的包含性,能够有效抵抗几何噪声对图像分割的影响,使得算法具有较高的抗几何噪声能力,进而提高该算法对含有几何噪声图像的分割精度。提出算法适用于包含几何噪声的高分辨率遥感图像,具有很好的抗几何噪声性。     

Effective fuzzy clustering techniques for segmentation of breast MRI

The goal of this work is to segment the breast into different regions, each corresponding to a different tissue, and to identify tissue regions judged abnormal, based on the signal enhancement-time information. There are a number of problems that render this task complex. Breast MRI segmentation based on the differential enhancement of image intensities can assist the clinician to detect suspicious regions. In this paper, we propose an effective segmentation method for breast contrast-enhanced MRI (ce-MRI). The segmentation method is developed based on standard fuzzy clustering techniques proposed by Bezedek. By minimizing the proposed effective objective function, this paper obtains an effective way of predicting membership grades for objects and new method to update centers. Experiments will be done with a synthetic image to show how effectively the new proposed effective fuzzy c-means (FCM) works in obtaining clusters. To show the performance of proposed FCM, this work compares the results with results of standard FCM algorithm on same synthetic image. Then the proposed method was applied to segment the clinical ce-MR images with the help of computer programing language and results have been shown visually.     

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。     

A multiobjective spatial fuzzy clustering algorithm for image segmentation

This article describes a multiobjective spatial fuzzy clustering algorithm for image segmentation. To obtain satisfactory segmentation performance for noisy images, the proposed method introduces the non-local spatial information derived from the image into fitness functions which respectively consider the global fuzzy compactness and fuzzy separation among the clusters. After producing the set of non-dominated solutions, the final clustering solution is chosen by a cluster validity index utilizing the non-local spatial information. Moreover, to automatically evolve the number of clusters in the proposed method, a real-coded variable string length technique is used to encode the cluster centers in the chromosomes. The proposed method is applied to synthetic and real images contaminated by noise and compared with k-means, fuzzy c-means, two fuzzy c-means clustering algorithms with spatial information and a multiobjective variable string length genetic fuzzy clustering algorithm. The experimental results show that the proposed method behaves well in evolving the number of clusters and obtaining satisfactory performance on noisy image segmentation.     

基于模糊熵和RPCL的彩色图像聚类分割

提出了一种基于模糊熵和RPCL(rival penalized competitive learn ing)的彩色图像聚类分割算法。该算法可以自动确定图像的颜色类数目和初始类中心,从而提高了聚类的收敛速度,并且能够解决模糊熵阈值化分割算法所造成的过度分割问题。首先,计算彩色图像各颜色分量的模糊熵,获得分量模糊熵曲线,并根据模糊熵原理确定各分量的分割区域及聚类中心;然后,对各分量的聚类中心进行组合,形成彩色图像可能的聚类中心。但是,组合的聚类中心数目会多于实际的聚类数目,造成过度分割。因此,本文采用RPCL算法,对这些组合的聚类中心颜色进行学习来确定实际的颜色类数目以及聚类中心,并用学习后的聚类中心对原图像进行聚类分割。实验结果表明,该算法能有效地分割彩色图像,无需事先给定聚类数目和初始类中心。     

自适应烟花算法下多维模糊C均值彩色图像分割

针对图像分割在自然场景中,分割精度不高和细节保持不够敏感,提出一种自适应烟花算法下的多维模糊C均值彩色图像分割算法。结合动态时间弯曲思想,以邻域像素相似特点构造弯曲曲线,得到多维相似距离和新的目标函数。在自适应烟花寻优算法下,找到最优聚类中心,最终达到对图像分割效果。实验表明,该算法与同类算法相比,对彩色图像有良好的分割效果,对图像的细节保持也不错。     

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.     

分水岭分割的方向迭代后处理算法

为了提取彩色图像中线目标，该文提出了一种新的彩色图像分割算法，首先对图像进行分水岭分割得到初始过分割图像，并通过模糊聚类方法得到区域分类概率，然后根据图像的边缘信息和空间特性，得到区域的线方向邻接区域，最后通过迭代的方法，利用线方向邻接区域信息更新区域的分类概率。实验结果显示了很好的提取效果。     

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.     

Color image segmentation based on multiobjective artificial bee colony optimization

This paper presents a new color image segmentation method based on a multiobjective optimization algorithm, named improved bee colony algorithm for multi-objective optimization (IBMO). Segmentation is posed as a clustering problem through grouping image features in this approach, which combines IBMO with seeded region growing (SRG). Since feature extraction has a crucial role for image segmentation, the presented method is firstly focused on this manner. The main features of an image: color, texture and gradient magnitudes are measured by using the local homogeneity, Gabor filter and color spaces. Then SRG utilizes the extracted feature vector to classify the pixels spatially. It starts running from centroid points called as seeds. IBMO determines the coordinates of the seed points and similarity difference of each region by optimizing a set of cluster validity indices simultaneously in order to improve the quality of segmentation. Finally, segmentation is completed by merging small and similar regions. The proposed method was applied on several natural images obtained from Berkeley segmentation database. The robustness of the proposed ideas was showed by comparison of hand-labeled and experimentally obtained segmentation results. Besides, it has been seen that the obtained segmentation results have better values than the ones obtained from fuzzy c-means which is one of the most popular methods used in image segmentation, non-dominated sorting genetic algorithm II which is a state-of-the-art algorithm, and non-dominated sorted PSO which is an adapted algorithm of PSO for multi-objective optimization.