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.     

基于小波图像融合算法和改进FCM聚类的MR脑部图像分割算法

针对很多基于模糊C均值(FCM)的图像分割算法存在对噪声敏感和分割轮廓不清晰等问题,提出一种基于小波变换图像融合算法和FCM聚类算法的MR医学图像分割算法。在图像分割系统的第一阶段,利用Haar小波多分辨率特性保持像素间的空间信息;第二阶段,利用小波图像融合算法对得到的多分辨率图像和原始图像进行融合,进而增强被处理图像的清晰度并降低噪声;第三阶段,利用改进型FCM技术对所处理的图像进行分割。在BrainWeb数据集上进行实验,与现有相关算法相比,提出的算法具有较高的分割精度,且对噪声的鲁棒性比较强,处理时间也没有明显增加。     

Fast and robust fuzzy c-means clustering algorithms incorporating local information for image segmentation

Fuzzy c-means (FCM) algorithms with spatial constraints (FCM_S) have been proven effective for image segmentation. However, they still have the following disadvantages: (1) although the introduction of local spatial information to the corresponding objective functions enhances their insensitiveness to noise to some extent, they still lack enough robustness to noise and outliers, especially in absence of prior knowledge of the noise; (2) in their objective functions, there exists a crucial parameter α used to balance between robustness to noise and effectiveness of preserving the details of the image, it is selected generally through experience; and (3) the time of segmenting an image is dependent on the image size, and hence the larger the size of the image, the more the segmentation time. In this paper, by incorporating local spatial and gray information together, a novel fast and robust FCM framework for image segmentation, i.e., fast generalized fuzzy c-means (FGFCM) clustering algorithms, is proposed. FGFCM can mitigate the disadvantages of FCM_S and at the same time enhances the clustering performance. Furthermore, FGFCM not only includes many existing algorithms, such as fast FCM and enhanced FCM as its special cases, but also can derive other new algorithms such as FGFCM_S1 and FGFCM_S2 proposed in the rest of this paper. The major characteristics of FGFCM are: (1) to use a new factor S_ij as a local (both spatial and gray) similarity measure aiming to guarantee both noise-immunity and detail-preserving for image, and meanwhile remove the empirically-adjusted parameter α; (2) fast clustering or segmenting image, the segmenting time is only dependent on the number of the gray-levels q rather than the size N(?q) of the image, and consequently its computational complexity is reduced from O(NcI₁) to O(qcI₂), where c is the number of the clusters, I₁ and are the numbers of iterations, respectively, in the standard FCM and our proposed fast segmentation method. The experiments on the synthetic and real-world images show that FGFCM algorithm is effective and efficient.     

快速鲁棒核空间模糊聚类分割

目的 传统模糊C-均值聚类应用于图像分割仅考虑像素本身的聚类问题,无法克服噪声干扰对图像分割结果的影响,不利于受到噪声干扰的工业图像、医学影像和高分遥感影像等进行目标提取、识别和解译。嵌入像素空间邻域信息或局部信息的鲁棒模糊C-均值聚类分割算法是近年来图像分割理论研究中的热点课题。为此,针对现有的鲁棒核空间模糊聚类算法非常耗时且抑制噪声能力弱、不适合强噪声干扰下大幅面图像快速分割等问题,提出一种快速鲁棒核空间模糊聚类分割算法。方法 利用待分割图像中像素邻域的灰度信息和空间位置等信息构建线性加权滤波图像,对其进行鲁棒核空间模糊聚类。为了进一步提高算法实时性,引入当前聚类像素与其邻域像素均值所对应的2维直方图信息,构造一种基于2维直方图的鲁棒核空间模糊聚类快速分割最优化数学模型,采用拉格朗日乘子法获得图像分割的像素聚类迭代表达式。结果 对大幅面图像添加一定强度的高斯、椒盐以及混合噪声,以及未加噪标准图像的分割测试结果表明,本文算法比基于邻域空间约束的核模糊C-均值聚类等算法的峰值信噪比至少提高1.5 dB,误分率降低约5%,聚类性能评价的划分系数提高约10%,运行速度比核模糊C-均值聚类和基于邻域空间约束的鲁棒核模糊C-均值聚类算法至少提高30%,与1维直方图核空间模糊C-均值聚类算法具有相当的时间开销,所得分割结果具有较好的主观视觉效果。结论 通过理论分析和实验验证,本文算法相比现有空间邻域信息约束的鲁棒核空间模糊聚类等算法具有更强的抗噪鲁棒性、更优的分割性能和实时性,对大幅面遥感、医学等影像快速解译具有积极的促进作用,能更好地满足实时性要求较高场合的图像分割需要。     

基于MRF模型的鲁棒FCM分割算法

FLICM算法是一种基于FCM框架的有效的分割方法。然而,它对于强噪声图像的分割仍然不够准确。本文使用MRF模型的局部先验概率,对FLICM算法从两方面进行了改进。首先,在计算模糊因子时,使用先验概率对距离函数进行加权。改进的模糊因子考虑了更大范围的邻域约束,从而使算法受噪声的影响程度减弱。其次,在分割阶段,进一步使用局部先验概率对FLICM算法的隶属度进行加权。使用改进后的隶属度进行标记判决,使得每一标记的确定需要考虑邻域标记的影响,使分割结果的区域性更好。利用新算法对模拟影像和真实影像进行了分割实验,并与几个考虑空间信息约束的FCM分割算法进行了对比分析,结果证明该算法具有更强的抗噪性能。     

顾及冲突分析的模糊积分非监督变化检测

以模糊积分(Fuzzy integral, FI)为基础, 提出一种顾及冲突分析(Conflict analysis, CA)的全自动遥感变化检测方法CA-based FI, CAFI). CAFI首先选取典型的对比算子, 生成信息互补的差异图(Difference image, DI)集; 其次利用模糊聚类、杰卡德相似系数和FI对差异图进行决策级融合, 得到初步融合变化检测图; 然后通过模糊集理论计算像元的信息冲突程度, 将初步融合检测结果自适应地划分为冲突严重区域和冲突较弱区域; 最后, 对冲突较弱的像元, 将其初步融合结果作为最终检测结果, 对易产生融合错误的冲突严重像元, 利用地统计分析对其重新分类. CAFI能够集成不同信息优势的同时, 很大程度地解决FI融合过程中的信息冲突问题. 三组真实遥感数据的实验结果验证了CAFI的有效性和鲁棒性.     

结合基因表达式编程与空间模糊聚类的图像分割

目的 针对模糊C-均值聚类图像分割方法存在的对初始值敏感及抗噪性能差的问题,提出一种结合基因表达式编程与空间模糊聚类的图像分割方法。方法 首先,利用基因表达式编程算法对图像进行初次分割,即将聚类中心编码成染色体,通过适应度评价引导搜索获得优化的聚类中心;然后在隶属度计算中引入空间函数,以初次分割结果作为初始值,使用空间模糊聚类对图像进行二次分割。结果 对加噪的合成图像和Berkeley图像的分割实验显示,本文方法在聚类划分系数（VPC）、聚类划分熵（VPE）和峰值信噪比（PSNR）等评价指标上总体性能优于经典的模糊C-均值聚类和空间模糊C-均值聚类分割算法,其中VPC值平均高出0.062 4和0.061 1,VPE值平均降低0.117 0和0.101 1,而PSNR值平均提升了约13.312 1 dB和3.308 4 dB;在对Berkeley图像库中的6幅图片的分割实验显示,本文方法对图像分割的VPC值均在0.93以上,相比两种对比方法平均提高0.157 6和0.013 3,VPE值保持在0.1附近,均低于对比方法,PSNR值平均提高2.896 3 dB和1.934 4 dB;在多目标分割实验上,随着聚类数目增加,3种方法的分割性能均有下降,但本文方法性能曲线最为平缓,受聚类数目的影响最小。虽然本文方法所需的运行时间略有增加,但求解所需的迭代次数却极大地减少。结论 本文提出的图像分割方法具有很强的抗噪性、更高的分割精度和稳定性,适用于需要更精确结果、对时间要求不高的分割场景。     

基于二维直方图的图像模糊聚类分割新方法

基于二维直方图的模糊聚类分割算法可以有效地抑制噪声的干扰。但是,FCM算法用于图像数据聚类时的最大缺陷是运算的开销太大,这就限制了这种方法在图像分割中的应用。该文根据FCM算法和灰度图像的特点,提出了一种适用于灰度图像分割的抑制式模糊C-均值聚类算法(S-FCM)。通过调节抑制因子α来提高分割速度和分类的正确率。实验结果表明,新算法对小目标灰度图像的分割效果优于FCM算法。     

Mountain c-regressions method

Since Quandt [The estimation of the parameters of a linear regression system obeying two separate regimes, Journal of the American Statistical Association 53 (1958) 873-880] initiated the research on 2-regressions analysis, switching regression had been widely studied and applied in psychology, economics, social science and music perception. In fuzzy clustering, the fuzzy c-means (FCM) is the most commonly used algorithm. Hathaway and Bezdek [Switching regression models and fuzzy clustering, IEEE Transactions on Fuzzy Systems 1 (1993) 195-204] embedded FCM into switching regression where it was called fuzzy c-regressions (FCR). However, the FCR always depends heavily on initial values. In this paper, we propose a mountain c-regressions (MCR) method for solving the initial-value problem. First, we perform data transformation for the switching regression data set, and then implement the modified mountain clustering on the transformed data to extract c cluster centers. These extracted c cluster centers in the transformed space will correspond to c regression models in the original data set. The proposed MCR method can form well-estimated c regression models for switching regression data sets. According to the properties of transformation, the proposed MCR is also robust to noise and outliers. Several examples show the effectiveness and superiority of our proposed method.     

基于图形处理器的模糊C均值聚类分割算法

针对模糊C均值聚类图像分割算法运算量大、难于实时处理的问题,提出了一种基于图形处理器的加速算法。通过分析模糊C均值聚类算法各阶段可以并行处理的运算部分,利用计算统一设备架构软硬件结构,分别将隶属度矩阵计算、聚类中心计算和像素按隶属度归类3个部分改造成适合图形处理器硬件并行运行的形式。实验结果表明,相对于CPU串行算法,基于图形处理器的加速算法效率提升明显。鉴于大多数图像处理算法均具有可并行处理的部分,利用图形处理器进行加速具有普适性。     

Unsupervised possibilistic clustering

In fuzzy clustering, the fuzzy c-means (FCM) clustering algorithm is the best known and used method. Since the FCM memberships do not always explain the degrees of belonging for the data well, Krishnapuram and Keller proposed a possibilistic approach to clustering to correct this weakness of FCM. However, the performance of Krishnapuram and Keller's approach depends heavily on the parameters. In this paper, we propose another possibilistic clustering algorithm (PCA) which is based on the FCM objective function, the partition coefficient (PC) and partition entropy (PE) validity indexes. The resulting membership becomes the exponential function, so that it is robust to noise and outliers. The parameters in PCA can be easily handled. Also, the PCA objective function can be considered as a potential function, or a mountain function, so that the prototypes of PCA can be correspondent to the peaks of the estimated function. To validate the clustering results obtained through a PCA, we generalized the validity indexes of FCM. This generalization makes each validity index workable in both fuzzy and possibilistic clustering models. By combining these generalized validity indexes, an unsupervised possibilistic clustering is proposed. Some numerical examples and real data implementation on the basis of the proposed PCA and generalized validity indexes show their effectiveness and accuracy.     

A fast and automated segmentation method for detection of masses using folded kernel based fuzzy c-means clustering algorithm

Present study proposes a fast, accurate and automated segmentation approach of mammographic images using kernel based fuzzy c-means (FCM) clustering technique. This approach exploits the significant regional features of mammograms which address the properties of different breast densities. The proposed segmentation approach captures those regional features using appropriate kernel and hence apply fuzzy clustering technique for segmenting the masses. This study also introduces kernel based FCM (KFCM) approach in a folded way to process a combination of significant features simultaneously. Suitable choice of kernel size also assists to collect all possible variations of regional features with minimum blocking effect in the output results. Performances of the proposed methodology are analyzed qualitatively and quantitatively in compare to other clustering-based segmentation techniques. Since the proposed approach is able to resolve uncertain and imprecise characteristics of mammograms, it performs superior to other techniques. Convergence time of the proposed method is also assessed and compared with other conventional clustering techniques. Kernel based approach of the proposed segmentation technique reduces the number of data points for clustering and hence convergence speed improves over the conventional algorithms. This study also shows a variation of convergence speed of the proposed segmentation method with different image sizes.     

Fuzzy spectral clustering with robust spatial information for image segmentation

In recent years, spectral clustering has become one of the most popular clustering algorithms in areas of pattern analysis and recognition. This algorithm uses the eigenvalues and eigenvectors of a normalized similarity matrix to partition the data, and is simple to implement. However, when the image is corrupted by noise, spectral clustering cannot obtain satisfying segmentation performance. In order to overcome the noise sensitivity of the standard spectral clustering algorithm, a novel fuzzy spectral clustering algorithm with robust spatial information for image segmentation (FSC_RS) is proposed in this paper. Firstly, a non-local-weighted sum image of the original image is generated by utilizing the pixels with a similar configuration of each pixel. Then a robust gray-based fuzzy similarity measure is defined by using the fuzzy membership values among gray values in the new generated image. Thus, the similarity matrix obtained by this measure is only dependent on the number of the gray-levels and can be easily stored. Finally, the spectral graph partitioning method can be applied to this similarity matrix to group the gray values of the new generated image and then the corresponding pixels in the image are reclassified to obtain the final segmentation result. Some segmentation experiments on synthetic and real images show that the proposed method outperforms traditional spectral clustering methods and spatial fuzzy clustering in efficiency and robustness.     

Fuzzy clustering algorithms based on resolution and their application in image compression

This paper presents an idea of clustering resolution. On the basis of the idea, fuzzy clustering algorithms based on resolution are deduced, which naturally comprise a set of clustering algorithms. Thus, c-means algorithm and fuzzy c-means algorithms are actually special examples in the set. As an application for codebook design in image compression based on vector quantization, fuzzy clustering algorithms based on multiresolution are developed, which are almost prior to conventional algorithms in all aspects.     

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.     

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。     

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.     

A modified fuzzy C-means image segmentation algorithm for use with uneven illumination patterns

A novel fuzzy C-mean (FCM) algorithm is proposed for use when active or structured light patterns are projected onto a scene. The underlying inhomogeneous illumination intensity due to the point source nature of the projection, surface orientation and curvature has been estimated and its effect on the object segmentation minimized. Firstly, we modified the recursive FCM algorithm to include biased illumination field estimation. New clustering center and fuzzy clustering functions resulted based on the intensity and average intensity of a pixel neighborhood based object function. Finally, a dilation operator was used on the initial segmented image for further refinement. Experimental results showed the proposed method was effective for segmenting images illuminated by patterns containing underlying biased intensity fields. A higher accuracy was obtained than for traditional FCM and thresholding techniques.     

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。     

基于马氏距离的FCM图像分割算法

基于模糊C均值聚类的图像分割是应用较为广泛的方法之一,但大多数模糊C均值聚类方法都是基于欧式距离,且存在运算时间过长等问题。提出了一种基于Mahalanobis距离的模糊C均值聚类图像分割算法。实验分析表明,提出的算法在保证分割质量的前提下,能较快提高分割速度。实验结果表明了该方法的有效性。