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.     

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.     

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.     

用于脑部核磁共振图像分割的具有抗噪能力的BCFCM算法

脑部核磁共振成像(MRI)是脑疾病临床诊断的重要手段,而脑组织的准确分割则是其中一个重要的环节。然而MRI图像中普遍存在的噪声和偏移场给脑组织的准确分割造成了很大的困难。在MRI图像分割算法中,偏移场矫正模糊C-均值算法(BCFCM)在模糊C-均值聚类算法(FCM)的基础上增加了对偏移场的估计和空间信息的使用,可以很好地消除图像偏移场对分割造成的影响。但是BCFCM算法由于没有考虑到噪声对偏移场估计的影响,因此对高噪声图像的分割效果欠佳。针对MRI脑组织分割,在图像预处理过程中提出一种快速的分割方法来去除颅骨及其附属物。此外,提出基于BCFCM的改进算法,该改进算法在迭代过程中可以通过对噪声强度的估计来自适应地改变目标函数窗口的大小。同时,该算法引入高斯核函数对偏移场进行平滑处理,并通过阈值限制偏移场的估计值,以有效地避免偏移场的错误估计对分割结果的影响。实验结果表明,改进后的算法不仅可以有效准确地 分割脑组织,而且具有较强的抗噪声和处理偏移场的能力。     

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.     

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。     

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.     

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。     

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.     

A two-stage fuzzy multi-objective framework for segmentation of 3D MRI brain image data

Segmentation of Magnetic Resonance Imaging (MRI) brain image data has a significant impact on the computer guided medical image diagnosis and analysis. However, due to limitation of image acquisition devices and other related factors, MRI images are severely affected by the noise and inhomogeneity artefacts which lead to blurry edges in the intersection of the intra-organ soft tissue regions, making the segmentation process more difficult and challenging. This paper presents a novel two-stage fuzzy multi-objective framework (2sFMoF) for segmenting 3D MRI brain image data. In the first stage, a 3D spatial fuzzy c-means (3DSpFCM) algorithm is introduced by incorporating the 3D spatial neighbourhood information of the volume data to define a new local membership function along with the global membership function for each voxel. In particular, the membership functions actually define the underlying relationship between the voxels of a close cubic neighbourhood and image data in 3D image space. The cluster prototypes thus obtained are fed into a 3D modified fuzzy c-means (3DMFCM) algorithm, which further incorporates local voxel information to generate the final prototypes. The proposed framework addresses the shortcomings of the traditional FCM algorithm, which is highly sensitive to noise and may stuck into a local minima. The method is validated on a synthetic image volume and several simulated and in-vivo 3D MRI brain image volumes and found to be effective even in noisy data. The empirical results show the supremacy of the proposed method over the other FCM based algorithms and other related methods devised in the recent past.     

Kernel generalized fuzzy c-means clustering with spatial information for image segmentation

The generalized fuzzy c-means clustering algorithm with improved fuzzy partition (GFCM) is a novel modified version of the fuzzy c-means clustering algorithm (FCM). GFCM under appropriate parameters can converge more rapidly than FCM. However, it is found that GFCM is sensitive to noise in gray images. In order to overcome GFCM?s sensitivity to noise in the image, a kernel version of GFCM with spatial information is proposed. In this method, first a term about the spatial constraints derived from the image is introduced into the objective function of GFCM, and then the kernel induced distance is adopted to substitute the Euclidean distance in the new objective function. Experimental results show that the proposed method behaves well in segmentation performance and convergence speed for gray images corrupted by 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.     

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.     

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.     

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.     

Brain tissue segmentation based on spatial information fusion by Dempster-Shafer theory

As a result of noise and intensity non-uniformity,automatic segmentation of brain tissue in magnetic resonance imaging (MRI) is a challenging task.In this study a novel brain MRI segmentation approach is presented which employs Dempster-Shafer theory (DST) to perform information fusion.In the proposed method,fuzzy c-mean (FCM) is applied to separate features and then the outputs of FCM are interpreted as basic belief structures.The salient aspect of this paper is the interpretation of each FCM output as a belief structure with particular focal elements.The results of the proposed method are evaluated using Dice similarity and Accuracy indices.Qualitative and quantitative comparisons show that our method performs better and is more robust than the existing method.     

图像分割中的模糊聚类方法

模糊聚类算法是近年来图像分割技术领域的研究热点之一。在对模糊C均值聚类算法分析的基础上,结合目前在图像分割中的应用研究,对模糊C均值聚类算法的测度方式进行了比较分析,从单分辨率、多分辨率以及与其他算法结合3个方面,评述改进的模糊C均值聚类算法优缺点。最后,讨论模糊C均值聚类算法目前存在的问题及未来发展方向。     

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.     

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。     

Automatic segmentation of clustered quantum dots based on improved watershed transformation

Automated analysis of the quantum dots (QDs) images is very important in the field of material science. In this frame, efficient QDs segmentation is prerequisite. In this paper, we propose an algorithm of automatic detection and segmentation of the QDs, especially the clustered ones. We depend on fuzzy c-means (FCM) method for initial segmentation of the QDs from the substrate background. Then we present a modified watershed algorithm with markers and a novel marking function. The markers are extracted by adaptive H-minima transformation. Then a marking function based on Quasi-Euclidean distance transform is introduced to accurately and rapidly separate the clustered QDs. We demonstrate the comparisons of our method with the existing approaches. The experimental results show that the proposed method is efficient and accurate with very little running time and has a high quality on QDs segmentation.