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.     

一种自适应的模糊C均值聚类图像分割方法

针对传统的模糊C均值聚类算法(FCM)在图像分割中对噪声十分敏感这一局限性,提出一种自适应的FCM图像分割方法。该方法充分考虑图像像素的灰度信息和空间信息,根据像素的空间位置自适应地计算一个合适的相似度距离来进行聚类分割图像。实验结果表明,与传统的FCM相比,该方法能显著提高分割质量,尤其是能提高对于图像噪声的鲁棒性和分割图像区域边缘的准确性。     

Single point iterative weighted fuzzy C-means clustering algorithm for remote sensing image segmentation

In this paper, a remote sensing image segmentation procedure that utilizes a single point iterative weighted fuzzy C-means clustering algorithm is proposed based upon the prior information. This method can solve the fuzzy C-means algorithm's problem that the clustering quality is greatly affected by the data distributing and the stochastic initializing the centrals of clustering. After the probability statistics of original data, the weights of data attribute are designed to adjust original samples to the uniform distribution, and added in the process of cyclic iteration, which could be suitable for the character of fuzzy C-means algorithm so as to improve the precision. Furthermore, appropriate initial clustering centers adjacent to the actual final clustering centers can be found by the proposed single point adjustment method, which could promote the convergence speed of the overall iterative process and drastically reduce the calculation time. Otherwise, the modified algorithm is updated from multidimensional data analysis to color images clustering. Moreover, with the comparison experiments of the UCI data sets, public Berkeley segmentation dataset and the actual remote sensing data, the real validity of proposed algorithm is proved.     

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.     

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.     

DBCAMM: A novel density based clustering algorithm via using the Mahalanobis metric

In this paper we propose a new density based clustering algorithm via using the Mahalanobis metric. This is motivated by the current state-of-the-art density clustering algorithm DBSCAN and some fuzzy clustering algorithms. There are two novelties for the proposed algorithm: One is to adopt the Mahalanobis metric as distance measurement instead of the Euclidean distance in DBSCAN and the other is its effective merging approach for leaders and followers defined in this paper. This Mahalanobis metric is closely associated with dataset distribution. In order to overcome the unique density issue in DBSCAN, we propose an approach to merge the sub-clusters by using the local sub-cluster density information. Eventually we show how to automatically and efficiently extract not only ‘traditional’ clustering information, such as representative points, but also the intrinsic clustering structure. Extensive experiments on some synthetic datasets show the validity of the proposed algorithm. Further the segmentation results on some typical images by using the proposed algorithm and DBSCAN are presented in this paper and they are shown that the proposed algorithm can produce much better visual results in image segmentation.     

基于FCM聚类的图像分割算法

为提高现有模糊C均值聚类算法(FCM)对噪声图像分割的效果和稳定性,提出一种基于FCM的图像分割算法。利用非局部空间信息构建和图像,根据和图像的直方图,自动选择初始化聚类中心,通过求取目标函数极小值完成图像分割。理论分析和实验结果表明,该算法比现有算法更加有效和稳定,对噪声图像有更强的鲁棒性。     

An adaptive unsupervised approach toward pixel clustering and color image segmentation

This paper proposes an adaptive unsupervised scheme that could find diverse applications in pattern recognition as well as in computer vision, particularly in color image segmentation. The algorithm, named Ant Colony-Fuzzy C-means Hybrid Algorithm (AFHA), adaptively clusters image pixels viewed as three dimensional data pieces in the RGB color space. The Ant System (AS) algorithm is applied for intelligent initialization of cluster centroids, which endows clustering with adaptivity. Considering algorithmic efficiency, an ant subsampling step is performed to reduce computational complexity while keeping the clustering performance close to original one. Experimental results have demonstrated AFHA clustering's advantage of smaller distortion and more balanced cluster centroid distribution over FCM with random and uniform initialization. Quantitative comparisons with the X-means algorithm also show that AFHA makes a better pre-segmentation scheme over X-means. We further extend its application to natural image segmentation, taking into account the spatial information and conducting merging steps in the image space. Extensive tests were taken to examine the performance of the proposed scheme. Results indicate that compared with classical segmentation algorithms such as mean shift and normalized cut, our method could generate reasonably good or better image partitioning, which illustrates the method's practical value.     

一种融入局部信息的直觉模糊C-均值聚类图像分割算法

模糊C-均值(FCM)算法对图像噪声敏感,聚类过程中只考虑图像的数值特征信息而忽略像素间空间约束关系,同时单一隶属度并不能充分描述图像的不确定性,这使得基于FCM的图像分割不够准确.融入局部信息的改进FCM算法虽然对图像噪声有一定鲁棒性,但对图像细节保持不够,难以分割微小区域.针对上述问题,提出一种基于直觉模糊集的改进模糊C-均值(IFS_FCM)图像分割算法.该方法将直觉模糊集理论融入到FCM中,充分考虑图像的不确定性,同时在目标函数中引入空间邻域信息,使得该分割算法对噪声鲁棒性增强的同时还能保持图像细节信息.实验结果表明,IFS_FCM能获得更加理想的图像分割效果.     

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 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.     

Iterative fuzzy image segmentation

The multispectral signature of features has been used for identification of objects in remotely sensed scenes for a number of years. Recently these techniques have been applied to feature selection in natural scenes. Due to the inherent noise and degradation of the input cues to the algorithms, meaningful image segmentation is a difficult process. In an effort to reduce the sensitivity of a system to these problems, we have been led to the development of a iterative fuzzy clustering technique for image segmentation. It is believed that this method represents an image segmentation scheme which can be used as a preprocessor for a multivalued logic based computer vision system.     

基于颜色特征和聚类的马氏距离图像分割法

给出了一种基于颜色特征和聚类的复杂彩图中进行目标图像分割的马氏距离算法.该方法利用目标的颜色进行图像分割.通过对彩图中的物体进行采样和分类,经过对每个像素点进行马氏距离计算和最小值寻找,将图像内的所有像素点进行归类,对目标图像与背景图像进行二值化分割,并对分类后含噪声的目标图像进行自适应滤波.设计了达到以上目的的人机交互式可视化计算机图像处理程序,对在水稻田中试验点上拍摄的水稻照片进行了分析处理,分离出了复杂背景下的水稻植株图像.实验结果表明,该算法能较好地解决复杂彩图中目标图像的分割问题.     

基于微粒群优化的模糊C-均值聚类图像分割

模糊C-均值聚类算法广泛用于图像分割,但存在聚类性能受类中心初始化影响,且计算量大等问题.为此,提出了一种基于微粒群的模糊C-均值聚类图像分割算法,该方法利用微粒群较强的搜索能力搜索聚类中心:由于搜索聚类中心是按密度进行,计算量小,故可以大幅提高模糊C-均值算法的计算速度.实验结果表明,该方法可以使模糊聚类的速度得到明显提高,实现图像的快速分割.     

A novel image segmentation algorithm based on neutrosophic similarity clustering

Segmentation is an important research area in image processing, which has been used to extract objects in images. A variety of algorithms have been proposed in this area. However, these methods perform well on the images without noise, and their results on the noisy images are not good. Neutrosophic set (NS) is a general formal framework to study the neutralities’ origin, nature, and scope. It has an inherent ability to handle the indeterminant information. Noise is one kind of indeterminant information on images. Therefore, NS has been successfully applied into image processing algorithms. This paper proposed a novel algorithm based on neutrosophic similarity clustering (NSC) to segment gray level images. We utilize the neutrosophic set in image processing field and define a new similarity function for clustering. At first, an image is represented in the neutrosophic set domain via three membership sets: T, I and F. Then, a neutrosophic similarity function (NSF) is defined and employed in the objective function of the clustering analysis. Finally, the new defined clustering algorithm classifies the pixels on the image into different groups. Experiments have been conducted on a variety of artificial and real images. Several measurements are used to evaluate the proposed method's performance. The experimental results demonstrate that the NSC method segment the images effectively and accurately. It can process both images without noise and noisy images having different levels of noises well. It will be helpful to applications in image processing and computer vision.     

Learning a Mahalanobis distance metric for data clustering and classification

Distance metric is a key issue in many machine learning algorithms. This paper considers a general problem of learning from pairwise constraints in the form of must-links and cannot-links. As one kind of side information, a must-link indicates the pair of the two data points must be in a same class, while a cannot-link indicates that the two data points must be in two different classes. Given must-link and cannot-link information, our goal is to learn a Mahalanobis distance metric. Under this metric, we hope the distances of point pairs in must-links are as small as possible and those of point pairs in cannot-links are as large as possible. This task is formulated as a constrained optimization problem, in which the global optimum can be obtained effectively and efficiently. Finally, some applications in data clustering, interactive natural image segmentation and face pose estimation are given in this paper. Experimental results illustrate the effectiveness of our algorithm.     

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.     

SAR image segmentation based on quantum-inspired multiobjective evolutionary clustering algorithm

The segmentation task in the feature space of an image can be formulated as an optimization problem. Recent researches have demonstrated that the clustering techniques, using only one objective may not obtain suitable solution because the single objective function just can provide satisfactory result to one kind of corresponding data set. In this letter, a novel multiobjective clustering approach, named a quantum-inspired multiobjective evolutionary clustering algorithm (QMEC), is proposed to deal with the problem of image segmentation, where two objectives are simultaneously optimized. Based on the concepts and principles of quantum computing, the multi-state quantum bits are used to represent individuals and quantum rotation gate strategy is used to update the probabilistic individuals. The proposed algorithm can take advantage of the multiobjective optimization mechanism and the superposition of quantum states, and therefore it has a good population diversity and search capabilities. Due to a set of nondominated solutions in multiobjective clustering problems, a simple heuristic method is adopted to select a preferred solution from the final Pareto front and the results show that a good image segmentation result is selected. Experiments on one simulated synthetic aperture radar (SAR) image and two real SAR images have shown the superiority of the QMEC over three other known algorithms.     

A new fuzzy relational clustering algorithm based on the fuzzy C-means algorithm

In this paper, we show how one can take advantage of the stability and effectiveness of object data clustering algorithms when the data to be clustered are available in the form of mutual numerical relationships between pairs of objects. More precisely, we propose a new fuzzy relational algorithm, based on the popular fuzzy C-means (FCM) algorithm, which does not require any particular restriction on the relation matrix. We describe the application of the algorithm to four real and four synthetic data sets, and show that our algorithm performs better than well-known fuzzy relational clustering algorithms on all these sets.     

A fast recursive algorithm based on fuzzy 2-partition entropy approach for threshold selection

The fuzzy c-partition entropy approach for threshold selection is an effective approach for image segmentation. The approach models the image with a fuzzy c-partition, which is obtained using parameterized membership functions. The ideal threshold is determined by searching an optimal parameter combination of the membership functions such that the entropy of the fuzzy c-partition is maximized. It involves large computation when the number of parameters needed to determine the membership function increases. In this paper, a recursive algorithm is proposed for fuzzy 2-partition entropy method, where the membership function is selected as S-function and Z-function with three parameters. The proposed recursive algorithm eliminates many repeated computations, thereby reducing the computation complexity significantly. The proposed method is tested using several real images, and its processing time is compared with those of basic exhaustive algorithm, genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO) and simulated annealing (SA). Experimental results show that the proposed method is more effective than basic exhaustive search algorithm, GA, PSO, ACO and SA.