Directional weighted spatial fuzzy C-means for segmentation of brain MRI images

Abstract

Brain and its structure are extremely complex with deep levels of details. Applying image processing methods of brain image can be very useful in many practical domains. Magnetic Resonance Imaging (MRI) is widely used imaging technique and has particular advantage by possessing the capability of providing highly detailed images of brain soft tissues than any other imaging techniques. The real challenge at hand for researchers is to perform precise segmentation while overcoming the effects of noise and other imaging artifacts like intensity in homogeneity introduced in medical images during image acquisition process. In this research work, a directional weighted optimized Fuzzy C-Means (dwsFCM) method has been proposed for segmentation of brain MR images. This method works by incorporating the spatial information of the pixels of the images and assigning the directional weights to the neighborhood. In order to validate the proposed segmentation framework, a comprehensive set of experiments have been performed on publically available standard simulated as well as real datasets. The experimental results showed 95% of accuracy and the performance of the proposed segmentation framework is much better and the framework suppress the sufficient amount of noise especially rician noise and reproduce good segmentation by overcoming the effect of intensity in homogeneity.

Keywords

Rician noise directional weighted spatial fuzzy C-mean image segmentation MRI optimal extraction

1 Introduction

The most critical task in many clinical applications is the image segmentation. Segmentation is usually used for quantifying and envisaging the anatomical structures of brain during analysis of MRI images, for analyzing changes in brain, for delineating pathological regions, and for surgical planning and image-guided interventions [1]. The segmentation of an image in a partition consists of the image space into different regions which carry similar pixels within same region and dissimilar from other regions pixels. The segmentation of brain tissues from MRI is an important task. Manual segmentation is a method used by medical experts to diagnose brain tumor and other brain related diseases from MRI and mostly takes three to five hours to complete the task. The multiple phases involving very careful examination make MRI scanning and analysis a very turbulent and time-consuming job. Any wrong diagnosis can result in harmful consequences [2]. But medical experts sometimes face some difficulties in decision making because acquired MR images are imperfect and are often degraded by different kind of noises and other imaging artifacts. In the last few decades, many researchers and scientists developed automated segmentation techniques, but these techniques are subject to differences in MRI acquisition process which can cause difficulties [3]. There are no such algorithms which always generate promising outputs for all types of brain MRI images like T1-weighted and T2-weighted [4]. Automatic segmentation of medical images is important but very difficult and challenging task as medical images are complex in nature and output of segmentation algorithms is affected due to many factors and artifacts like partial volume effect, different noises introduced during image acquisition, intensity in homogeneities, overlapping of different tissue classes in the brain [5].

The numbers of methods to automatically segment brain MR images, which have been applied in various stages of intelligent system in MRI [6], are actually pre-processing and enhancement of images and their segmentation in respective order. Pre-processing and enhancement techniques are used to improve the detection of the suspicious regions in MRI. This stage is the simplest categorization of medical image processing which is employed for highlighting the edges and reducing the image noise introduced during image acquisition process. Noise free image is very important for correct diagnosis of the brain and other diseases as well as many post processing techniques and analysis.

For analyzing the brain’s anatomical structures from image, the computer-based algorithms have been developed. These algorithms called image segmentation algorithms [7]. The automated segmentation of brain images plays a significant role in neurological research [8, 9]. In a nutshell there are problems which plague automatic segmentation of modern times. According to researchers and scholars, there are two reasons for that. Firstly, the vastly unique and varied nature of brain tissues which differ from each other in their feature characteristics such as shape, size location. This makes it difficult to have one automatic segmentation method which covers several different image types [10]. Secondly, partial volume effect where a pixel occurs due to improper MRI acquisition causing it to become not distinguishable among many tissue types and as such difficult for interpretation by automated segmentation [11]. Another significant problem with precise segmentation of brain MR images into different classes of brain tissues. These classes can be varied as white matters, grey matters and cerebrospinal fluid is a crucial task [9]. The diagnosis can be made such quicker if this information is at hand. The precise evaluation can be very critical for disease diagnosis. As literature shows, problems have been persisting with automated segmentation. In this research work, we are segmenting the brain MRI image into different brain tissue classes such as white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF) in an automated manner using 2D MRI image data. First and foremost, number of classes has been set down and then randomly initialized the classes centers. In third step, a membership matrix for each point is initialized and calculated the class center. At the end, the algorithm updates the membership matrix and sets the number of classes.

2 Background study

Image segmentation shows a fundamental role in the image processing and computer vision. Image segmentation is the process of partitioning a digital image into multiple distinct and non-overlapping regions. General segmentation approaches are Thresholding approaches, Region based approaches, Morkov Random Filed approaches, Artificial Neural Network Approaches, Clustering methods, Histogram methods, Deformable methods, Atlas-guided methods and Level set methods [6]. There are lots of applications of image segmentation. In the many recent works have been done to solve these issues and among them very little or no single segmentation method has been proposed that considered several types of brain MRI images [12]. For example, some methods performed better on T1-weighted images, some on T2-weighted images; however, they still faced some limitations such as inadequate results and performance because of varying structures of different MRI images. Moreover, some methods did not reproduce the precise segmentation of anatomical areas. Commonly, most of the segmentation techniques are affected by noise due to which the performances of the methods suffer. Thresholding method proposed in [1] used the histograms of the intensities and tries to find values of intensities. Thresholding methods are computationally efficient and simple, but these are noise sensitive and intensity in homogeneities and do not consider the spatial context in the image. Another disadvantage of Thresholding method is that, only two classes are generated in the segmentation result. A hybrid segmentation technique proposed for brain MRI images by combining the Region growing and Thresholding techniques [13]. Image noise is suppressed with median and wavelet filters and then segmentation is performed by Region growing and Thresholding methods. The drawback of this technique is that some brain tissues information is lost in the final segmented images. Accuracy of segmentation achieved by this method is 93.96%. An information fusion-based Thresholding segmentation technique proposed for brain MRI images [14].

A fusion scheme is then established by using spatial and intensity information of the pixels. This fusion scheme is then used for calculating Thresholding values. This Thresholding value is then used in Otsu method to segment the images. Though the method performs better but its computation cost is high and achieves average accuracy of segmentation as 98.42%. A multi-level Thresholding segmentation technique was proposed for brain MRI in [15]. The proposed technique used intensity and edge magnitude information and finds out the multiple Thresholding values with the help of grey-level co-occurrence matrix. Then these Thresholding values along with mutation-based particle swarm optimization (MPSO) have been used later for the segmentation of different tissues. The limitation of this technique is the optimization of parameters for MPSO algorithm which is not an easy task. The average accuracy achieved by this method is 85.9%. A Thresholding method for segmentation was proposed for brain MR images where mean, variance, standard deviation and entropies have used to determine the Thresholding values [16]. This Thresholding value is then used to segment the brain tissues. However, this method performs better on noise free images and is sensitive to noise. The average accuracy of segmentation on noise free images achieved is 98.16%.

Recently, many brain MRI segmentation techniques have been proposed by using region growing method. A brain MR images segmentation technique based on Region growing introduced by [17]. In this method, first image is preprocessed by Histogram equalization method and median filter and Thresholding is applied by using global Thresholding. After the features are extracted by wavelet technique. In the last, Region growing method is applied to segment the image. The drawback of this method is that the segmented image contains noise and disjoints regions. The average segmentation accuracy achieved by this method is 97.5%. A brain MRI segmentation technique by using Region growing and k nearest neighbors (kNN) methods was proposed in this method, preprocessing is performed by applying smoothing filter and then region growing method is used for segmentation [18]. After segmentation, co-occurrence and wavelet-based features have been extracted and classified by kNN classifier to classify the region of interest. The limitations of this method include that it works only on T2-weighted image and there are holes in the output image. A brain MRI segmentation method by using Region growing techniques was proposed by [19]. In this method, first, image is mothed by an edge-aware filter, secondly, Otsu based multilevel Thresholding has been performed on original and smoothed images. Then segmentation maps obtained in first and second step have been combined by K Nearest Neighbors rule and obtained the refined segmentation. In the last, a bi-directional region growing method is employed on refined segmentation to segment the brain. Averaged segmentation accuracy achieved by this technique is 92.95%.

To improve the computational cost, several techniques have been proposed. A brain MRI segmentation method by using Anisotropic diffusion filter and random forests algorithm proposed in [20]. The proposed method works better at normal noise level but is sensitive to noise as the level of noise increases. The average accuracy of this method in classifying brain tissues is 64.38%. Similarly, another technique naming a Discrete Markov Random Field framework for segmentation of brain MR images was proposed in [21]. In this method, registration and segmentation nodes are coupled towards simultaneously recovering all atlas deformations and labeling the query image. The coupling is achieved by promoting the consistency between selected deformed atlas segmentations and the estimated query segmentation. Additional membership fields are estimated, determining the participation of each atlas in labeling each voxel. Inference is performed by using a sequential relaxation scheme. There is no mechanism adopted to handle the noise. The accuracy of segmentation achieved is 79%. A brain MR image segmentation method by combining Dynamic Classifier Selection (DCS) and Markov Random Field (MRF) techniques) was proposed by [22]. In this method, in order to ensemble Dynamic Classifier System-Weighted Local Accuracy is used which is combination of multiple classifier (CMC) algorithm. Later, the spatial context of the image is incorporated in MRF algorithm to segment the image into brain classes. The computational cost of this method is reduced as compared to original MRF algorithm however; the method is sensitive to noise. The average accuracy of segmentation achieved is 69.90%.

In the last few decades, several segmentation and classifications methods have been proposed. A brain tumor and brain tissues segmentation technique of brain MRI images using Neural Network approach was proposed in [23]. A Neural Network based segmentation technique for the tissues and abnormalities classification from brain MR images was proposed in [24]. The input image is preprocessed by using the intensity normalization method. After that the texture-based features such as mean and variance have been extracted and classified, a convolution neural network approach is used to segment the image. Performance of the method is better in terms of computational cost and achieved the average accuracy of segmentation as 72.67%. Table 1 represents summary of the segmentation methods.

Table 1
Summary of Segmentation Techniques

Segmentation Method Merits Demerits Applications

Thresholding Computationally efficient, simple Sensitive to noise, do not consider spatial information of image, only two classes generate in segmented image, not suitable for textured images, intensity in homogeneities Medical imaging. Locate tumors and other pathologies

Region Growing Simple, less computation intensive, to extract a connected region of similar pixels from image Sensitive to noise, disconnected segmented regions, sensitivity to the initialization of seed point D Shape Reconstruction, pixel Aggregation, tumor segmentation

Markov Random Field (MRF) Graphical Method High computational cost, need prior knowledge Image restoration, edge detection, enhancement, segmentation, classification

Artificial Neural Network Computational Mathematical Models, powerful technique Needs long time for training Image segmentation, enhancement, classification

Clustering Fast, simple, homogeneity inside clusters, heterogeneity between the clusters Sensitive to noise, needs no. of classes in advance to initialize, does not consider spatial-context, unsatisfactory results in noisy images Image segmentation, medical image segmentation, classification, pattern recognition

Segmentation Method	Merits	Demerits	Applications
Thresholding	Computationally efficient, simple	Sensitive to noise, do not consider spatial information of image, only two classes generate in segmented image, not suitable for textured images, intensity in homogeneities	Medical imaging. Locate tumors and other pathologies
Region Growing	Simple, less computation intensive, to extract a connected region of similar pixels from image	Sensitive to noise, disconnected segmented regions, sensitivity to the initialization of seed point	D Shape Reconstruction, pixel Aggregation, tumor segmentation
Markov Random Field (MRF)	Graphical Method	High computational cost, need prior knowledge	Image restoration, edge detection, enhancement, segmentation, classification
Artificial Neural Network	Computational Mathematical Models, powerful technique	Needs long time for training	Image segmentation, enhancement, classification
Clustering	Fast, simple, homogeneity inside clusters, heterogeneity between the clusters	Sensitive to noise, needs no. of classes in advance to initialize, does not consider spatial-context, unsatisfactory results in noisy images	Image segmentation, medical image segmentation, classification, pattern recognition

3 Proposed method

Magnetic resonance imaging (MRI) segmentation is a procedure from which the medical practitioners attempt to find information from features of images like lines and curved which may provide useful information about ailment. Brain MRI segmentation process consists of separating the different tissues, such as solid tumor, edema, and necrosis from the normal brain tissues. The current segmentation approaches which are either manual or lack intelligent approach have several limitations. Manual segmentation and analysis of brain magnetic resonance (MR) images by radiologists and experts, though reliable, yet involves a hectic exercise of time-consuming nature towards medical imaging diagnosis in which a radiologist routinely analyzes a large number of images for every single patient. However, the time-consuming nature makes it impossible to perform several screenings to analyze the scans of all patients. Manual segmentation is also highly subject to variations of interpretation between various observers or even within single observer. In order to tackle these problems, a directional weighted optimized Fuzzy C-Means (dwsFCM) algorithm is introduced for the segmentation of brain MRI images. The proposed method considers the spatial context by establishing the local neighborhood of a pixel in all possible directions of a pixel under consideration and assigns the weights to the neighboring pixels based on the distance from central pixel. The fuzzy membership function which provides the probability to a pixel to be in true cluster is modified and incorporated in the original Fuzzy C-Means membership function. The modified membership function provides the better solution of uncertainty handling of a misclassified pixel and the modified Fuzzy C-Means algorithm performs better than the standard Fuzzy C-Means algorithm. A new objective function has been proposed as: $J_{dwsFCM} = \sum_{j = 1}^{n} \sum_{i = 1}^{c} {(\frac{U_{ij}^{P} h_{ij}^{q}}{\sum_{k = 1}^{c} U_{jk}^{P} h_{ij}^{q}})}^{m} {∥ x_{j - V_{i}} ∥}^{2}, 1 \leq m < \infty$ (1) where xj is the data point, centre of ith cluster denoted by vi, ∥… ∥ Euclidean distance, and m denotes a constant >1. m is partition of weight fuzziness.

To assign the points to each cluster based on the modified membership or partition, following function is used: $Vi = \frac{\sum_{j = 1}^{n} {dU}_{ij}^{im} Xj}{\sum_{j - 1}^{n} {dU}_{ij}^{im}}$ (2) Where Vi are the clusters centers, U^′ is the modified membership matrix and xj are the points of image. And “U ^′i j^″ signifies the ith cluster membership degree of pixel xj.

The modified membership function to introduce the spatial information is given as: $U_{ij}^{'} = \frac{U_{ij}^{p} h_{ij}^{q}}{\sum_{k = 1}^{c} U_{ik}^{p}} h_{ij}^{q}$ (3) where p and q are factors to control the comparative rank of both functions and i, j are data points, and h_ij is the spatial function that has been incorporated in the modified membership function.

To develop spatial function, directional weighted window has been incorporated. In other words, neighboring pixels possess similar features, and the probability belonging to the same cluster becomes large. By utilizing this spatial context of the image, the spatial function h_ij is given as: $h_{ij} = \sum_{k ɛ NBH (xj)} W_{IJ} 1 pt U_{ik}$ (4)

Here squared window denoted by NBH (xj). W_ij are the directional weights that has been incorporated in the spatial neighborhood in such a way that:

A 5×5 window was used throughout this work as given in Fig. 1. A spatial function h_ij for probability similar to the membership function shows a pixel xj belongs to ith cluster.

Fig.1

Directions of the Neighborhood Window.

Directional weighted optimized spatial FCM (dwsFCM) algorithm process is summarized in the following steps (as shown in Fig 2):

Fig.2

A flow diagram of the directional weighted optimized spatial FCM (dwsFCM) algorithm.

Step 1: Set the number of classes c.

Step 2: Initialize randomly the centers of classes.

Step 3: Initialize the partition or membership matrix for each point with randomly generated values between 0 and 1 such that $U_{ij} = \sum_{j = 1}^{c} U_{ik} = 1, \forall i$ .

Step 4: Calculate the class centers V_i by Equation (2).

Step 5: Update the Membership matrix U^′ij by Equation (3).

Step 6: If $max | V_{C}^{I} V_{C}^{I - 1} | < 0.01$ , then terminate, otherwise go to step 4.

It is worth of note that in the above algorithm, the membership values are randomly initialized so that the constraint on the sum of memberships for each point should be satisfied. In contrast, other criteria for initialization also exist. For instance, the memberships of a point in all classes can be initialized with identical values. However, when implemented, it is followed with random initialization criteria in order to make the algorithm consistent with the standard FCM.

In this Section, a fuzzy based segmentation method is presented in which the membership function of the standard FCM algorithm which plays an important role in partitioning the given data is modified by incorporating the spatial information of the image data. The proposed algorithm (dwsFCM) performs better than the standard FCM and other state of the art methods in handling intensity in homogeneities. The proposed algorithm also generates the better results for overlapped data set, preserves the edges detail and comparatively better than the standard Fuzzy C-Means algorithm and spatial FCM approaches.

4 Results and discussion

In the previous section the formation of this framework was described with all its composite details. In this section, the experimentation is performed to evaluate and validate the performance of the proposed segmentation framework. In order to evaluate and validate the proposed framework for segmentation, experimentation is performed on simulated dataset and real dataset which were downloaded from publically available datasets. The simulated dataset was downloaded from BrainWeb (http://brainweb.bic.mni.mcgill.ca/brainweb/) provided by McConnell Brain Imaging Centre at Montreal Neurological Institute and Hospital, McGill University, Canada. The real images dataset was downloaded from Internet Brain Segmentation Repository (IBSR). These real MR brain data sets and their manual segmentations were provided by the Center for Morphometric Analysis at Massachusetts General Hospital (http://www.cma.mgh.harvard.edu/ibsr/). The details of these both datasets are described as following.

The downloaded simulated dataset consists of 181 normal brains MRI images having volume size 181×217×181 pixels’ axial view acquired at intensity non-uniformity (“RF”) 20%, varying noise levels as 1%–18%, relaxation time (TR) 18 ms, echo time (TE) 10 ms and slice thickness 1 mm. The modalities used to generate these simulated magnitude MRI images databases are T1-weighted and T2-weighted. In order to evaluate and validate the results quantitatively, anatomical models (ground truth) are also available on this publically available database, which were downloaded for results validation purpose. The downloaded database has file format Medical Image NetCDF (MINC) which is a Medical Imaging file format. This file format is not directly readable by the windows-based computer. Thus, the MINC format was converted to computer readable format Joint Photographic Experts Group (jpeg) with the help of tool/ application like Medical Image Processing Analysis and Visualization (MIPAV) version 7.3.0 which is available on internet to get downloading free of cost. MIPAV is developed by the Centre for Information Technology (CIT), National Institute of Health (NIH), USA (http://mipav.cit.nih.gov/index.php). A sample as example of some of the images from this database is shown in Figs. 3 and 4.

Fig.3

BrainWeb dataset images, first two rows are T1-weighted and last two rows are T2-weighted.

Fig.4

Real IBSR dataset images.

The real IBSR brain MRI images dataset “IBSR_V2.0_nifti_stripped” of a normal subject consists of 256 axial view T1-weighted positionally normalized rotation only are the images of a 35 years old female having image dimensions 256×128 with slice thickness 1.5 mm. In order to validate the results, manually drawn anatomical models or ground truths of gray matters, white matters and cerebrospinal fluids by experts are also available for this dataset. A sample example of some of the images from this database is shown in Figs. 3 and 4.

The results achieved from proposed segmentation method with those of existing techniques and showed those in Table 2 and Fig. 5. These results are achieved on brain MR images with 9% of noise and 20% intensity inhomogeneity on 51 simulated dataset T1-weighted images (slices 50–100).

Table 2

Results comparison with existing methods over 51 simulated T1-weighted images using Segmentation Accuracy (SA) measure

S. No	Methods	Average accuracy of tissues segmentation %			Average (SA)
		GM	WM	CSF	Complete
1	sFCM [25]	87.20	89%	83.10%	86.43%
2	FGFCM [26]	78.30	89.40	77.90	81.87%
3	ASIFC [27]	88.50	92.60	85.60	88.90%
4	csFCM [28]	89.00	94.70	88.40	90.70%
5	Proposed framework with brain	96.45	96.62	94.15	95.74%

Fig.5

Comparative values of Segmentation Accuracy (SA) of sFCM, FGFCM, ASIFC, csFCM and proposed segmentation framework over 51 T1-weighted images with 9% noise and 20% intensity inhomogeneity.

The segmentation method given in Table 2 at serial 1 is the modification of standard FCM algorithm. The work is done to overcome the sensitivity issue of noise. It is good technique with decent results but is not efficient in presence of high noise. It performs well to some extent but still lacks enough robustness to noise and outliers in image and does not generate very satisfactory segmentation results on images corrupted with heavily noise. Moreover, this technique includes those points in the clusters which are not nearer to clusters center. The weighted average segmentation accuracy of 51 images achieved by this method is 86.43%. The method given in Table 2 at serial 2 is the effort to make the standard FCM algorithm as robust against noise. The method performs fast but is not robust against high noise and produces blurring effect in the final segmented images. Moreover, it needs careful parameters selection for noise and robustness for preserving the detail which is not an easy task. The weighted average segmentation accuracy of this method is 81.87%. The method presented in Table 2 at serial 3 is another effort to make the standard FCM as robust to noise and bias field caused by intensity inhomogeneity. The method performs better on the images corrupted with low or normal noise, however, the performance of the method decreases at high noise levels and inhomogeneity in the image. The weighted average segmentation accuracy of this method is 88.90%. In Table 2, serial 4 shows the results of using a modified FCM in the form of conditional spatial FCM (csFCM). Despite giving good results, this method loses useful information about tissues in some cases and author also mentioned the drawback that the performance of the algorithm decreases as the noise level increases. The average accuracy of segmentation of this approach is 90.70 percent. As results show, the proposed framework outperforms above mentioned state-of-the-art techniques with better accuracy of segmentation as 95.74 percent on average. The results show that overall performance of proposed framework is always better even though performance suffers if brain and non-brain parts are not separated properly. The qualitative evaluation provides very useful knowledge on the target application, the types and quality of the images, the limitations of the segmentation algorithms, and the results of the individual steps of a method. This evaluation is based on results of segmentation of different classes of tissues such as grey matter (GM), white matter (WM), and cerebrospinal fluid (CSF).

Figure 6 shows the qualitative comparison of proposed segmentation framework with previous techniques. It can be clearly observed that with other techniques there is always risk of some tissues being wrongly classified. The above referred methods, hence, do not concentrate on removing the non-brain parts from brain parts due to which overlapping of intensities occur and accuracy of segmentation is affected. Out of benchmark techniques csFCM performs better than other methods. Proposed framework though shows its superiority over both of existing techniques. Through GP based effective noise removal method, isolation of brain and non-brain tissues, edge preservation, proper intensity inhomogeneity handling mechanism and dynamic Thresholding, the proposed segmentation framework ensures delivering much better results than any of existing techniques.

Fig.6

Qualitative segmented results of the CSF, GM, WM (from left to right) by the different existing algorithms on a T1-weighted MRI BrainWeb dataset image (slice#95) with 9% noise and 20% inhomogeneity, (a): Original noisy image; (b)–(d): Ground Truths; (e)–(h): sFCM; (i)–(l): FGFCM; (m)–(p): ASIFC; (q)–(t): csFCM; (u)–(x): proposed framework without brain skull removal; (y)–(z”): proposed framework with brain skull stripped.

5 Conclusion

The real challenge at hand for researchers is to perform precise segmentation while overcoming the effects of noise and other imaging artifacts like intensity inhomogeneity introduced in medical images during image acquisition process. In this research work, a directional weighted optimized Fuzzy C-Means (dwsFCM) method was applied for segmentation of brain MR images. This method worked by incorporating the spatial information of the pixels of the images and assigning the directional weights to the neighborhood. The experimental results showed that the performance of the proposed segmentation framework is much improved, the framework suppressed the sufficient amount of noise especially rician noise and reproduces good segmentation by overcoming the effect of intensity inhomogeneity.

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