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.     

A study on fuzzy clustering for magnetic resonance brain image segmentation using soft computing approaches

This paper presents a novel idea of intracranial segmentation of magnetic resonance (MR) brain image using pixel intensity values by optimum boundary point detection (OBPD) method. The newly proposed (OBPD) method consists of three steps. Firstly, the brain only portion is extracted from the whole MR brain image. The brain only portion mainly contains three regions–gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF). We need two boundary points to divide the brain pixels into three regions on the basis of their intensity. Secondly, the optimum boundary points are obtained using the newly proposed hybrid GA–BFO algorithm to compute final cluster centres of FCM method. For a comparison, other soft computing techniques GA, PSO and BFO are also used. Finally, FCM algorithm is executed only once to obtain the membership matrix. The brain image is then segmented using this final membership matrix. The key to our success is that we have proposed a technique where the final cluster centres for FCM are obtained using OBPD method. In addition, reformulated objective function for optimization is used. Initial values of boundary points are constrained to be in a range determined from the brain dataset. The boundary points violating imposed constraints are repaired. This method is validated by using simulated T1-weighted MR brain images from IBSR database with manual segmentation results. Further, we have used MR brain images from the Brainweb database with additional noise levels to validate the robustness of our proposed method. It is observed that our proposed method significantly improves segmentation results as compared to other methods.     

胎儿脑磁共振图像分割研究进展

医学影像是产前筛查、诊断、治疗引导和评估的重要工具,能有效避免胎儿脑的发育异常。近年来,磁共振成像在产前诊断中愈加重要,而实现自动、定量、精确地分析胎儿脑磁共振图像依赖于可靠的图像分割。因此,胎儿脑磁共振图像分割具有十分重要的临床意义与研究价值。由于胎儿图像中存在组织器官多、图像质量差及结构变化快等问题,胎儿脑磁共振图像的分割面临着巨大的困难与挑战。目前,尚未有文献对该领域的方法进行系统性的总结和分析,尤其是基于深度学习的方法。本文针对胎儿脑磁共振图像分割方法进行综述,首先,对胎儿脑磁共振图像的主要公开图谱/数据集进行详细说明;接着,对脑实质提取、组织分割和病灶分割方法进行全面的分类与分析;最后,对胎儿脑磁共振图像分割面临的挑战及未来的研究方向进行总结与展望。     

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.     

Chest X-ray enhancement to interpret pneumonia malformation based on fuzzy soft set and Dempster–Shafer theory of evidence

Image enhancement algorithms are commonly used to increase the contrast and visual quality of low-dose x-ray images. This paper proposes an automated enhancement method using soft fuzzy sets with a new decision-making scheme based on Dempster-Shafer theory of evidence for the visual interpretation of pneumonia malformation in low-dose x-ray images, called as XEFSDS. The XEFSDS model first generates an original source x-ray image into a complementary image, then each original and complement image is applied to the characterized image object and background areas of fuzzy space. The S-function is utilized to define fuzzy soft sets for the classification of gray level ambiguity in both images, and hence a decision criterion via Dempster-Shafer approach and fuzzy interval has been adapted to discriminate uncertainties on the pixel intensity and the spatial information. Modified membership grade operations have been performed on each object/background area, and Werner’s AND/OR operator (an aggregation operator) has been utilized to build a new membership function from two modified membership functions. Finally, an enhanced image is obtained from the new membership function via defuzzification. Experiments on different pneumonia X-ray images demonstrate that the XEFSDS scheme produces better results than the existing methods. To show the advantages of the XEFSDS scheme, we have executed a segmentation based examination on enhanced image for the detection of pneumonia malformation as well as abnormal lobe (lobar pneumonia) or bronchopneumonia.     

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.     

基于MS-FCM算法的MR图像分割方法

针对传统模糊C-均值(FCM)聚类算法在分割低信噪比图像时准确性较差的问题,提出一种用于MR图像分割的改进算法MS-FCM。针对脑部MR图像相邻像素属于同一分类的模糊隶属度相近的特性,在迭代过程中对隶属度数据集进行滤波,以降低噪声对聚类精度的影响。模拟脑部MR图像和临床脑部MR图像的分割实验证明,该算法可以提高图像分割精度。     

Fusion of images interpreted by a new fuzzy classifier

This paper presents a global system for the fusion of images segmented by various methods and interpreted by a fuzzy classifier. A set of complementary segmentation operators is applied to the image. Each region of the segmented images is interpreted by the fuzzy classifier, through membership degrees to classes. The fuzzy classifier builds the classes automatically from examples, even in the case of complex data sets. Interpreted images are then merged by a fusion operator from the fuzzy set theory. Several fusion operators are compared. They trust more high membership degrees to classes, which are considered as reliability degrees. The fusion of the interpreted images improves the segmentation, and gives solutions to segmentation and interpretation evaluation.     

基于隶属度光滑约束的模糊C均值聚类算法

传统的FCM聚类算法未利用图像的空间信息,在分割叠加了噪声的MR图像时分割效果不理想。本文考虑到脑部MR图像真实的灰度值具有分片为常数的特性,按照合理利用图像空间信息的原则,对传统的FCM聚类算法进行了改进,增加了使隶属度趋向于分片光滑的约束项,得到了新的聚类算法。通过对模拟脑部MR图像和临床脑部MR图像的分割实验结果表明,本文提出的新算法比传统的FCM算法等多种图像分割算法有更精确的图像分割能力,并且运算简单、运算速度快、稳健性好。     

An image segmentation method based on maximizing fuzzy correlation and its fast recursive algorithm

In this paper, an image segmentation method is proposed that integrates fuzzy 2-partition into Yen’s maximum correlation thresholding method. A fuzzy 2-partition of the image is obtained by transforming the image into fuzzy domain by means of two parameterized membership functions. Fuzzy correlation is defined to measure the appropriateness of the fuzzy 2-partition. An ideal threshold is calculated from the optimal membership functions’ parameters, which make the corresponding fuzzy 2-partition have maximum fuzzy correlation. In the process of searching the optimal parameters of membership functions, a fast recursive algorithm is presented in order to reduce the computation complexity. Experimental results on synthetic image, brain magnetic resonance (MR) images and casting images show that the proposed method has a satisfactory performance.     

A new segmentation system for brain MR images based on fuzzy techniques

This work concerns a new method called fuzzy membership C-means (FMCMs) for segmentation of magnetic resonance images (MRI), and an efficient program implementation of it to the segmentation of MRI. Classical unsupervised clustering methods including the FCM by Bezdek, suffer many problems that can be partially treated with a proper rule to construct the initial membership matrix to clusters. This work develops a specific method to construct the initial membership matrix to clusters in order to improve the strength of the clusters. The new FMCM is tested on a set of benchmarks and then the application to the segmentation of MR images is presented and compared with the results obtained using FCM.     

A framework with modified fast FCM for brain MR images segmentation

Intensity inhomogeneity, noise and partial volume (PV) effect render a challenging task for segmentation of brain magnetic resonance (MR) images. Most of the current MR image segmentation methods focus on only one or two of the effects listed above. In this paper, a framework with modified fast fuzzy c-means for brain MR images segmentation is proposed to take all these effects into account simultaneously and improve the accuracy of image segmentations. Firstly, we propose a new automated method to determine the initial values of the centroids. Secondly, an adaptive method to incorporate the local spatial continuity is proposed to overcome the noise effectively and prevent the edge from blurring. The intensity inhomogeneity is estimated by a linear combination of a set of basis functions. Meanwhile, a regularization term is added to reduce the iteration steps and accelerate the algorithm. The weights of the regularization terms are all automatically computed to avoid the manually tuned parameter. Synthetic and real MR images are used to test the proposed framework. Improved performance of the proposed algorithm is observed where the intensity inhomogeneity, noise and PV effect are commonly encountered. The experimental results show that the proposed method has stronger anti-noise property and higher segmentation precision than other reported FCM-based techniques.     

Fuzzy Markovian Segmentation in Application of Magnetic Resonance Images

In this paper, we present a fuzzy Markovian method for brain tissue segmentation from magnetic resonance images. Generally, there are three main brain tissues in a brain dataset: gray matter, white matter, and cerebrospinal fluid. However, due to the limited resolution of the acquisition system, many voxels may be composed of multiple tissue types (partial volume effects). The proposed method aims at calculating a fuzzy membership in each voxel to indicate the partial volume degree, which is statistically modeled. Since our method is unsupervised, it first estimates the parameters of the fuzzy Markovian random field model using a stochastic gradient algorithm. The fuzzy Markovian segmentation is then performed automatically. The accuracy of the proposed method is quantitatively assessed on a digital phantom using an absolute average error and qualitatively tested on real MRI brain data. A comparison with the widely used fuzzy C-means algorithm is carried out to show numerous advantages of our method.     

基于模糊马尔可夫场的脑部MR图像分割算法

在传统马尔可夫场模型的基础上,建立了模糊马尔可夫场模型。通过对模型的分析得出图像像素对不同类的隶属度计算公式,提出了一种高效、无监督的图像分割算法,从而实现了对脑部MR图像的精确分割。通过对模拟脑部MR图像和临床脑部MR图像分割实验,表明新算法比传统的基于马尔可夫场的图像分割算法和模糊C-均值等图像分割算法有更精确的图像分割能力。     

基于有偏场的适配模糊聚类分割算法

近年来提出了许多监督和非监督模式识别技术用于磁共振图象的组织分类和定量分析。但是，这些方法的精度受到图象灰度不均匀性的严重影响。对于那些受灰度不均匀性影响的图象，如磁共振图象（MRI），提出了一种新的基于有偏场适配模糊聚类算法（BAFCM）来产生它们的分割结果。该算法通过修改C－means模糊算法中的目标方程，引入了描述灰度不均匀性的增益场，通过将增益场经为有偏场的计算，避免了AFCM中为保证增益场平滑缓慢变化引入的第一阶和第二阶正则项空间改变的二阶差分方程的复杂计算。其不仅对图象的灰度不均匀性进行了校正，而且实现了脑组织图象的快速全自动分割。     

基于模糊聚类的脑磁共振图像分割算法综述

磁共振成像（Magnetic resonance imaging, MRI） 技术以其非介入、无损伤以及不受目标运动影响等特点,已成为临床诊断的重要辅助手段。精确的脑MR图像分割对生物医学研究和临床应用具有重要的指导意义。在实际应用中,脑MR图像中存在的噪声、灰度不均匀性、部分容积效应和低对比度等缺陷,都给脑MR图像的 精确分割带来了巨大困难和挑战。本文基于模糊聚类模型的脑MR图像分割问题,从聚类类别数的确定、模型初始化、克服噪声、估计偏移场、克服部分容积效应、数据不确定性描述以及模型扩展7个方面深入阐述了国内外发展现状、应对技巧及改进策略,并分析存在的不足 ,指出进一步的研究方向。     

结合灰度直方图和细胞自动机的多模态MRI脑胶质瘤分割

为了解决脑胶质瘤边界模糊、复杂而导致的分割不准确问题,提出了一种将灰度直方图（gray level histogram,GLH）与改进的细胞自动机相结合的脑胶质瘤分割算法。首先,对脑胶质瘤的T2加权图像和液体衰减反转（FLAIR）图像进行融合;然后,利用灰度直方图特性增强脑胶质瘤区域;最后,以加权距离为特征向量用改进的细胞自动机进行分割,并得到脑胶质瘤各组织分割结果。在20组BraTS2015（brain tumor segmentation）数据库数据和10组临床脑胶质瘤数据上进行分割实验,整个肿瘤区域及核心肿瘤区域的平均分割准确率分别达到90.76%和89.73%。实验结果表明,相对于对比方法,所提算法不仅能更好地分割出对比度明显的胶质瘤区域,还在一定程度上解决了模糊胶质瘤区域分割不准确的问题。该算法在保持不增加算法复杂度的同时,亦提高了算法分割的准确性和鲁棒性。     

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.     

基于视觉注意和改进隶属度的FSVM彩色图像分割

针对SVM进行图像分割时存在对噪声和孤立点较敏感导致分割结果不佳和抗造性能低下等问题,提出一种基于视觉注意和改进隶属度的FSVM (Modified fuzzy SVM,MFSVM)彩色图像分割方法.该方法在考虑人类视觉显著性检测机制因素的同时,对标准的模糊SVM算法进行改进,新的隶属度函数综合考虑了样本点距离类中心的远近以及样本点的疏密程度,从而有效惩罚噪声点并增强了支持向量的作用.通过彩色图像分割进行验证,结果显示与标准的SVM及基于样本疏密程度隶属度的FSVM分割方法相比,本文方法能够对复杂场景下的彩色进行有效分割,同时呈现出良好的抗噪能力.