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.     

Fuzzy c-means clustering with weighted image patch for image segmentation

Fuzzy c-means (FCM) clustering has been widely used in image segmentation. However, in spite of its computational efficiency and wide-spread prevalence, the FCM algorithm does not take the spatial information of pixels into consideration, and hence may result in low robustness to noise and less accurate segmentation. In this paper, we propose the weighted image patch-based FCM (WIPFCM) algorithm for image segmentation. In this algorithm, we use image patches to replace pixels in the fuzzy clustering, and construct a weighting scheme to able the pixels in each image patch to have anisotropic weights. Thus, the proposed algorithm incorporates local spatial information embedded in the image into the segmentation process, and hence improve its robustness to noise. We compared the novel algorithm to several state-of-the-art segmentation approaches in synthetic images and clinical brain MR studies. Our results show that the proposed WIPFCM algorithm can effectively overcome the impact of noise and substantially improve the accuracy of image segmentations.     

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 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.     

多描述子活动轮廓模型的医学图像分割

目的 医学图像分割结果可帮助医生进行预测、诊断及制定治疗方案。医学图像在采集过程中受多种因素影响,同一组织往往具有不同灰度,且伴有强噪声。现有的针对医学图像的分割方法,对图像的灰度分布描述不够充分,不足以为精确的分割图像信息,且抗噪性较差。为实现医学图像的精确分割,提出一种多描述子的活动轮廓（MDAC）模型。方法 首先,引入图像的熵,结合图像的局部均值和方差共同描述图像的灰度分布。其次,在贝叶斯框架下,引入灰度偏移因子,建立活动轮廓模型的能量泛函。最后,利用梯度下降流法得到水平集演化公式,演化的最后在完成分割的同时实现偏移场的矫正。结果 利用合成图像和心脏、血管和脑等医学图像进行了仿真实验。利用MDAC模型对加噪的灰度不均图像进行分割,结果显示,在完成精确分割的同时实现了纠偏。通过对比分割前后图像的灰度直方图,纠偏图像只包含对应两相的两个峰,且界限更加清晰;与经典分割算法进行对比,MDAC在视觉效果和定量分析中,分割效果最好,比LIC的分割精度提高了30%多。结论 实验结果表明,利用均值、方差和局部熵共同描述图像灰度分布,保证了算法的精度。局部熵的引入,在保证算法精度的同时,提高了算法的抗噪性。能泛中嵌入偏移因子,保证算法精确分割的同时实现偏移场纠正,进一步提高分割精度。     

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.     

Efficient inhomogeneity compensation using fuzzy c-means clustering models

Intensity inhomogeneity or intensity non-uniformity (INU) is an undesired phenomenon that represents the main obstacle for magnetic resonance (MR) image segmentation and registration methods. Various techniques have been proposed to eliminate or compensate the INU, most of which are embedded into classification or clustering algorithms, they generally have difficulties when INU reaches high amplitudes and usually suffer from high computational load. This study reformulates the design of c-means clustering based INU compensation techniques by identifying and separating those globally working computationally costly operations that can be applied to gray intensity levels instead of individual pixels. The theoretical assumptions are demonstrated using the fuzzy c-means algorithm, but the proposed modification is compatible with a various range of c-means clustering based INU compensation and MR image segmentation algorithms. Experiments carried out using synthetic phantoms and real MR images indicate that the proposed approach produces practically the same segmentation accuracy as the conventional formulation, but 20-30 times faster.     

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。     

肺实质CT图像细化分割

目的 由于肺部CT图像中各组织结构复杂、灰度分布不均匀,造成肺实质部分难以准确分割和提取。为了提高肺实质分割的准确率,本文提出了一种基于超像素的细化分割与模糊C均值聚类相结合的自动分割算法。方法 该算法充分利用肺部CT图像的灰度、纹理特征,同时为了正确标记超像素的分类,引入一种空间邻域信息来增强空间约束进而有效地解决灰度不均匀的问题,它能够对肺实质进行分割并除去其周围的主血管,然后利用形态学知识去除肺部的分支血管。结果 在临床患有四类疾病的患者CT图像数据集上采用改进的图像特征,使得肺实质分割的准确率提高了0.8%。同时,算法准确率提高到99.46%。结论 实验结果表明,本文算法能够实现肺部CT图像肺实质的自动细化分割,结果准确适用。该算法鲁棒性好、速度快,是一种精确有效的自动肺实质分割方法。     

Soft fuzzy rough set-based MR brain image segmentation

Fuzzy sets, rough sets are efficient tools to handle uncertainty and vagueness in the medical images and are widely used for medical image segmentation. Soft sets are a new mathematical approach to uncertainty and vagueness. In this paper, a hybrid segmentation algorithm based on soft sets namely soft fuzzy rough c-means is proposed to extract the white matter, gray matter and the cerebro spinal fluid from MR brain image with bias field correction. In this algorithm, soft fuzzy rough approximations are applied to obtain the rough regions of image. These approximations are free from defining thresholds, weight parameters and are less complex compared to the existing rough set based algorithms. Soft sets use similarity coefficients to find the similarity of the clusters formed in present and previous step. The proposed algorithm does not involve any negative region, hence all the pixels participate in clustering avoiding clustering mistakes. Also, the histogram based centroids choose the centroids close to the ground truth that in turn effect the definition of approximations, standardizing the clusters. The proposed algorithm evaluated through simulation, compared it with existing k-means, rough k-means, fuzzy c-means and other hybrid algorithms. The soft fuzzy rough c-means algorithm outperforms the considered algorithms in all analyzed scenarios even in extracting the tumor from the brain tissue.     

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。     

A robust active contour model driven by fuzzy c-means energy for fast image segmentation

In this paper, we propose a robust region-based active contour model driven by fuzzy c-means energy that draws upon the clustering intensity information for fast image segmentation. The main idea of fuzzy c-means energy is to quickly compute the two types of cluster center functions for all points in image domain by fuzzy c-means algorithm locally with a proper preprocessing procedure before the curve starts to evolve. The time-consuming local fitting functions in traditional models are substituted with these two functions. Furthermore, a sign function and a Gaussian filtering function are utilized to replace the penalty term and the length term in most models, respectively. Experiments on several synthetic and real images have proved that the proposed model can segment images with intensity inhomogeneity efficiently and precisely. Moreover, the proposed model has a good robustness on initial contour, parameters and different kinds of noise.     

Unsupervised segmentation of noisy and inhomogeneous images using global region statistics with non-convex regularization

Improving the segmentation of magnetic resonance (MR) images remains challenging because of the presence of noise and inhomogeneous intensity. In this paper, we present an unsupervised, multiphase segmentation model based on a Bayesian framework for both MR image segmentation and bias field correction in the presence of noise. In our model, global region statistics are utilized as segmentation criteria in order to classify regions with similar mean intensities but different variances. Additionally, we propose an edge indicator function based on a guided filter (instead of a Gaussian filter) that can preserve the underlying edges of the image obscured by noise. The proposed edge indicator function is integrated with non-convex regularization to overcome the influence of noise, resulting in more accurate segmentation. Furthermore, the proposed model utilizes a Markov random field to model the spatial correlation between neighboring pixels, which increases the robustness of the model under high-noise conditions. Experimental results demonstrate significant advantages in terms of both segmentation accuracy and bias field correction for inhomogeneous images in the presence of noise.     

基于改进像素相关性模型的图像分割算法

图像分割是计算机视觉中的研究热点和难点.基于局部信息的模糊聚类算法(FLICM)在一定程度上提升了模糊聚类算法的鲁棒性,但噪声强度较大时无法获得较好的图像分割效果.针对传统的模糊聚类算法分割精度不佳等问题,提出了改进像素相关性模型的图像分割算法.首先通过分析像素的局部统计特征,设计了一种新型的像素相关性模型,在此基础上...     

局部区域拟合的快速水平集图像分割方法

目的 由于灰度不均匀图像在不同目标区域的灰度分布存在严重的重叠,对其进行分割仍然是一个难题;同时,图像中的噪声严重降低了图像分割的准确性。因此,传统水平集方法无法鲁棒、精确、快速地对具有灰度不均匀性和噪声的图像进行分割。针对这一问题,提出一种基于局部区域信息的快速水平集图像分割方法。方法 灰度不均匀图像通常被描述为一个分段常数图像乘以一个缓慢变化的偏移场。首先,通过一个经过微调的多尺度均值滤波器来估计图像的偏移场,并对图像进行预处理以减轻图像的不均匀性;然后,利用基于偏移场校正的方法和基于局部区域信息拟合的方法分别构建能量项,并利用演化曲线轮廓内外图像灰度分布的重叠程度,构建权重函数自适应调整两个能量项之间的权重;最后,引入全方差规则项对水平集进行约束,增强了数值计算的稳定性和对噪声的鲁棒性,并通过加性算子分裂策略实现水平集快速演化。结果 在具有不同灰度不均匀性和噪声图像上的分割结果表明,所提方法不但对初始轮廓的位置、灰度不均匀性和各种噪声具有较强的鲁棒性,而且具有高达94.5%的分割精度和较高的分割效率,与传统水平集方法相比分割精度至少提高了20.6%,分割效率是LIC（local intensity clustering）模型的9倍;结论 本文提出一种基于局部区域信息的快速水平集图像分割方法。实验结果表明,与传统水平集方法相比具有较高的分割精度和分割效率,可以很好地应用于具有灰度不均匀和噪声的医学、红外和自然图像等的分割。     

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。     

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。     

Intensity standardization simplifies brain MR image segmentation

Typically, brain MR images present significant intensity variation across patients and scanners. Consequently, training a classifier on a set of images and using it subsequently for brain segmentation may yield poor results. Adaptive iterative methods usually need to be employed to account for the variations of the particular scan. These methods are complicated, difficult to implement and often involve significant computational costs. In this paper, a simple, non-iterative method is proposed for brain MR image segmentation. Two preprocessing techniques, namely intensity-inhomogeneity-correction, and more importantly MR image intensity standardization, used prior to segmentation, play a vital role in making the MR image intensities have a tissue-specific numeric meaning, which leads us to a very simple brain tissue segmentation strategy.Vectorial scale-based fuzzy connectedness and certain morphological operations are utilized first to generate the brain intracranial mask. The fuzzy membership value of each voxel within the intracranial mask for each brain tissue is then estimated. Finally, a maximum likelihood criterion with spatial constraints taken into account is utilized in classifying all voxels in the intracranial mask into different brain tissue groups. A set of inhomogeneity corrected and intensity standardized images is utilized as a training data set. We introduce two methods to estimate fuzzy membership values. In the first method, called SMG (for simple membership based on a gaussian model), the fuzzy membership value is estimated by fitting a multivariate Gaussian model to the intensity distribution of each brain tissue whose mean intensity vector and covariance matrix are estimated and fixed from the training data sets. The second method, called SMH (for simple membership based on a histogram), estimates fuzzy membership value directly via the intensity distribution of each brain tissue obtained from the training data sets. We present several studies to evaluate the performance of these two methods based on 10 clinical MR images of normal subjects and 10 clinical MR images of Multiple Sclerosis (MS) patients. A quantitative comparison indicates that both methods have overall better accuracy than the k-nearest neighbors (kNN) method, and have much better efficiency than the Finite Mixture (FM) model-based Expectation-Maximization (EM) method. Accuracy is similar for our methods and EM method for the normal subject data sets, but much better for our methods for the patient data sets.     

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.