A DCT-based local and non-local fuzzy C-means algorithm for segmentation of brain magnetic resonance images
Introduction
The purpose of segmentation of brain MRI is to assign each pixel or voxel to a specific tissue class. The process of tissue classification in MRI plays a crucial role in the treatment of diseases. Brain MRI has several advantages over other medical imaging modalities including a detailed view of the brain in different dimensions, high contrast resolution for various tissues, and multi-spectral characteristics. Normal brain MRI consists of tissues like gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF). Variation in the composition of these tissues within specific regions helps to identify diseases [1]. Several automated algorithms have been developed for the segmentation of brain MRI into these three tissue classes. However, segmentation of brain tissues is still a very challenging task due to the presence of noise and intensity inhomogeneity. The presence of such artifacts can severely affect visual evaluation as well as segmentation based on absolute pixel intensities. Classical segmentation approaches based on edge detection, thresholding, and region growing are not very effective in MRI segmentation. In MRI, segmentation based on supervised and unsupervised classification has been observed to yield excellent results. Supervised classification requires human intelligence in the form of prior knowledge. Atlas-guided approaches [2,3] are widely used in supervised classification. Atlases are the labeled training images that are aligned with the target image using some registration approaches. Supervised techniques that are based on classifier like k-nearest-neighbor [4], artificial neural networks [5], and support vector machine [6] learn from the features of different labeled MRI images to train the classifier for the segmentation purpose. Although supervised techniques improve the segmentation accuracy by incorporating prior knowledge, they may provide highly inaccurate results because of the physiological variability between different subjects. On the other hand, unsupervised classification methods train themselves from the features in the available data by iteratively characterizing the properties of each class and provide excellent segmentation results.
In the unsupervised classification, pixels with similar features are classified into one cluster while the pixels with dissimilar features are classified into different clusters. Unsupervised classification methods include K-means [7], expectation-maximization (EM) [8,9], and fuzzy C-means (FCM) [10] algorithms. FCM is widely used for brain MRI segmentation due to its simplicity and high segmentation accuracy. FCM allows a data point to belong to more than one cluster using its soft classification model. Since the original FCM algorithm does not consider any local spatial information, it is very sensitive to noise. MRI images are often corrupted by Rician noise caused by operator performance, equipment setting, and the environment [11]. The segmentation with the FCM, therefore, becomes problematic. There are some algorithms that introduce the noise clustering concept in the original FCM algorithm to reduce noise sensitivity [[12], [13], [14]]. The main concept in these algorithms is to introduce a new noise cluster that is supposed to contain all the noise data. The prototype of the noise cluster is determined according to a distance threshold. These methods are very effective if all the cluster centers have similar size. However, if the cluster's size varies widely in the dataset then determining a suitable threshold becomes very difficult. Moreover, it is also difficult to separate noise from the outliers or to identify actual outliers, which may represent noise and fine image structures as well. Many researchers have incorporated the local spatial information into the original FCM algorithm to overcome the effect of noise. Ahmed et al. [15] proposed fuzzy C-means with spatial constraints (FCM_S). The algorithm allows the labeling of the pixels to be influenced by the labels in its immediate neighborhood. The neighborhood effect introduces extra computational cost as it is computed in each iteration step. To reduce the computational complexity, Chen and Zhang [16] proposed two variants of FCM_S, called FCM_S1, and FCM_S2. Szilagyi et al. [17] proposed the enhanced fuzzy C-means (EnFCM) in which clustering is performed based on the gray level histogram of a filtered image. Cai et al. [18] proposed the fast generalized fuzzy C-means (FGFCM) algorithm which incorporates both the local spatial and gray-level relationship among pixels, to reduce the effect of noise. All these methods which are based on the extensions of the FCM method use a parameter, called the regularization parameter, which controls the trade-off between the robustness to noise and preservation of the image details which are not required to be lost due to excessive smoothing. The value of this parameter is set low for high signal-to-noise ratio (SNR) and high for low SNR [15]. Wang et al. [19] modified the FCM distance function as weighted sum of distance influenced by local and nonlocal information, and proposed the local and nonlocal fuzzy C-means (LNLFCM) algorithm. Krinidis et al. [20] proposed a fuzzy local information C-means (FLICM) clustering algorithm that modifies the objective function of FCM by introducing a novel fuzzy factor. This fuzzy factor contains the spatial constraints to provide robustness to noise. Gong et al. [21] extended FLICM by replacing the Euclidean distance in the objective function of the FCM by kernel distance-based objective function. To make the local information more effective for reducing the effect of noise, a weighted contribution of the local pixel intensities which depends both on the spatial distance and photometric distance was introduced. Their modified algorithm is called kernel weighted fuzzy local information C-means (KWFLICM) clustering algorithm. The algorithm is reported to provide very high segmentation results. It however, requires proper initialization of the cluster centers and initial values of the membership. For its optimum performance the initial values of the cluster centers and membership are obtained from the classical FCM algorithm [22]. The main advantage of FLICM and KWFLICM algorithms is that they are free from any parameter selection. Recently, some of the authors replace the local information used in the original FCM with the nonlocal information to provide more robustness to noise. Zhao [23] proposed fuzzy C-means clustering algorithm with self-tuning nonlocal spatial information (FCM_SNLS) that replaces the mean and median filtered images used in the FCM_S1 and FCM_S2 algorithms, respectively, with the nonlocal means (NLM) filtered image. The NLM-based noise removal mechanism is made much more effective by using self tuning adaptive filtering parameter. Recently, Zhang et al. [24] proposed nonlocal fuzzy C-means (NLFCM) that extends FLICM algorithm by utilizing the non-local spatial information in place of local information used in FLICM to enhance the robustness to noise. They use weighted value of the Euclidean distance between an intensity level and a cluster center to augment the local information. The weights are computed using the NLM approach used for MRI image denoising. Like FLICM, this algorithm is also free from any parameter selection.
The nonlocal information used in the distance function of LNLFCM to reduce the effect of the noise in the segmentation process to enhance its accuracy has its roots in the use of the NLM approach to reduce Rician noise in the MRI [[25], [26], [27]]. Therefore, it provides a much needed background to find an effective method to reduce Rician noise for the purpose of enhancing MRI segmentation accuracy. The NLM approach denoises a noisy pixel by replacing it with the weighted average of pixel values in its neighborhood. The weights are computed by matching two image patches, one around the pixel being denoised and the other in its neighborhood. The weights are computed as a Gaussian function of the photometric distance between the two image patches. The NLM-based denoising approach provides excellent denoising performance which leads to better segmentation accuracy. However, NLM approach suffers from three problems: rare patch effect, patch jittering blur effect, and false patch detection due to rotation [28,29]. The rare patch effect refers to the inability of the NLM method to find enough similar patches for singular structures, such as edges and corners, thus, performing insufficient denoising of the noisy image in such regions. The patch jittering blur effect causes over-smoothing of the image by averaging several pixels that do not truly belong to the same underlying texture. The presence of noise in the compared patches can lead to false detections. In order to minimize rare patch effect and patch jittering blur effect, local constraints should also be considered. The discrete cosine transform (DCT)-based nonlocal mean approaches have been observed to address some of these issues and they have been observed to be very effective in removing Gaussian and Rician noise. In particular, DCT-based NLM (DCT-NLM) has been used in [[30], [31], [32]] to remove Rician noise in MRI. The transform domain approach using the DCT for representing an image has an advantage over the spatial domain methods as the DCT decorrelates the intensities and represents images using various independent frequency bands. Thus, it decorrelates pixels into various frequency bands. The low frequency bands provide the holistic view of an image and the high frequency bands represent fine image structures and noise. The DCT-NLM approach for MRI denoising uses low and middle level frequency values while the high frequency values are discarded suspecting them to carry noise information. This leads to better values of weights needed for the denoising purpose. The same concept is also used in the proposed DCT-LNLFCM approach, where the low and middle level DCT coefficients are used to represent local and nonlocal information in the form of local and nonlocal weights for the purpose of the weighted distance measure in the DCT-LNLFCM. The LNLFCM performs this task in the spatial domain. Thus, working in the DCT domain reduces the anomalies caused by rare patch effects, patch jittering blur effect, and false detections due to the rotation.
Motivated by these considerations, in this paper, we develop a combined DCT-based local and nonlocal fuzzy C-means (DCT-LNLFCM) algorithm for segmentation of brain MRI and demonstrate its high performance as compared to the existing state-of-the-art approaches including the NLM-based approaches in the spatial domain [23,24]. The main contributions of the proposed approach are:
- i.
The proposed method DCT-LNLFCM works in the transform domain that is better suited to find the similar patterns in the images that suffer from various noise distortions.
- ii.
The proposed method is based on the DCT which has the advantage of decorrelating the image data into various uncorrelated frequency components such as the low, middle, and high frequency components that represent the holistic view of an image, fine structures of the image, and noise components, respectively.
- iii.
A good trade-off between image noise and image details such as edges, corners, and other fine structures is maintained by selecting the low and middle frequency DCT coefficients for the weight computation for the local and nonlocal information. Thus, the effect of image noise is reduced by eliminating the roles of the very high-order DCT coefficients.
- iv.
In the regions of high image details, the proposed method is perceived to be better than other spatial domain methods. This enhances the segmentation accuracy of the MRI segmentation.
Detailed experiments are conducted on both simulated and real MRI for comparing the performance of the proposed method.
The rest of the paper is organized as follows. Section 2 presents an overview of the FCM and the LNLFCM segmentation approaches. Section 3 presents the proposed method. In Section 4, results obtained on simulated brain MRI, and real MRI, are presented, followed by concluding remarks in Section 5.
Section snippets
Fuzzy C-means
Fuzzy C-means, a clustering algorithm, groups image pixels xi, i = 1, …, N into C clusters by minimizing objective function Jm:where uij is the degree of membership of the ith data point in the jth cluster, vj represents the prototype value of the jth cluster, m is the weighting exponent, and is the L2−norm similarity measure between a feature vector xi and cluster center vj, i.e.,
To minimize the objective
The proposed DCT-based local and nonlocal fuzzy C-means (DCT-LNLFCM) MRI segmentation
The discrete cosine transform (DCT) is observed to be very effective in MRI denoising corrupted by Rician noise. The method is based on the nonlocal mean (NLM) approach for image denoising [[25], [26], [27],34]. In the DCT-NLM approach, a pixel is denoised by taking the weighted average of pixel intensities in the neighborhood of the pixel being denoised. The weights are computed in a manner similar to the Gaussian function whose argument is proportional to the L2 − norm (Euclidean distance) of
Experimental results and discussion
In this section, we analyze the performance of various FCM-based clustering approaches and the proposed DCT-LNLFCM approach. We apply these algorithms to the simulated MRI and real MRI. The simulated database provide ground truth images for the three regions CSF, GM, and WM, whereas the real MRI images provide ground truth images only for GM and WM regions. Therefore, experiments on simulated images are useful when the performance of a method is evaluated for all regions. The Simulated Brain
Conclusion
In this paper, we have proposed a transform-based MRI segmentation method DCT-LNLFCM which incorporates both the local and nonlocal information in the segmentation process. The main characteristic of the proposed method is that it computes the distance function as a weighted sum of the local and nonlocal distances. The weights are computed in the transform domain instead of the spatial domain as adopted by the existing methods. Working in the transform domain has an advantage over the spatial
Acknowledgements
The authors appreciate the useful comments and suggestions given by the anonymous reviewers to raise the standard of the paper. Thanks are also due to the University Grants Commission (UGC), New Delhi, India, for providing financial grants to the Major Research Project entitled, “Development of Efficient Techniques for Feature Extraction and Classification for Invariant Pattern Matching and Computer Vision Applications”, vide its File No.: 43-275/2014(SR), and also for providing project
Chandan Singh received an undergraduate degree in science in 1975 and a postgraduate degree in mathematics in 1977 both from Kumaon University, Nainital, India, and a Ph.D. degree in applied mathematics from Indian Institute of Technology, Kanpur, India, in 1982. He joined M/S Jyoti Ltd., Baroda, India, in 1982, and later Thapar Corporate R&D Centre, Patiala, India, in1987. In the year 1994, he joined Department of Computer Science at Punjabi University, Patiala where he served as Professor
References (36)
- et al.
A systematic review of MRI studies examining the relationship between physical fitness and activity and the white matter of the aging brain
Neuroimage
(2016) - et al.
A review of atlas-based segmentation for magnetic resonance brain images
Comput. Methods Programs Biomed.
(2011) - et al.
Multi-atlas segmentation of biomedical images: a survey
Med. Image Anal.
(2015) - et al.
FCM: the fuzzy C-means clustering algorithm
Comput. Geosci.
(1984) - et al.
Effective FCM noise clustering algorithms in medical images
Comput. Biol. Med.
(2013) - et al.
Robust kernelized approach to clustering by incorporating new distance measure
Eng. Appl. Artif. Intell.
(2013) - et al.
Fast and robust fuzzy C-means clustering algorithms incorporating local information for image segmentation
Pattern Recognit.
(2007) - et al.
A modified FCM algorithm for MRI brain image segmentation using both local and non-local spatial constraints
Comput. Med. Imaging Graphics
(2008) Fuzzy clustering algorithms with self-tuning non-local spatial information for image segmentation
Neurocomputing
(2013)- et al.
MRI denoising using non-local means
Med. Image Anal.
(2008)
Invariant moments and transform-based unbiased nonlocal means for denoising of MR images
Biomed. Signal Process. Control
Comparative performance analysis of various wavelet and nonlocal means based approaches for image denoising
Optik
A fully automatic and robust brain MRI tissue classification method
Med. Image Anal.
MRI fuzzy segmentation of brain tissue using neighborhood attraction with neural-network optimization
IEEE Trans. Inf. Technol. Biomed.
Brain MRI slices classification using least squares support vector machine
Int. J. Intell. Comput. Med. Sci. Image Process
Clustering of image data set using K-means and fuzzy k-means algorithms
IEEE International Conference on Computational Intelligence and Communication Networks (CICN)
Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm
IEEE Trans. Med. Imaging
Fast and robust spatially constrained Gaussian mixture model for image segmentation
IEEE Trans. Circuits Syst. Video Technol.
Cited by (28)
Bio-inspired computing algorithms in dementia diagnosis – a application-oriented review
2023, Results in Control and OptimizationSegmentation of white matter, grey matter and cerebrospinal fluid from brain MR images using a modified FCM based on double estimation
2021, Biomedical Signal Processing and ControlCitation Excerpt :First, we evaluate the performance of double estimation compared to conventional FCM on simulated images. Next, we compare our results with four state-of-the-art algorithms including local and nonlocal fuzzy C-means method (LNLFCM) [36], discrete cosine transform-LNLFCM (DCT-LNLFCM) [14], kernel weighted fuzzy local information C-means (KWFLICM) [31], and bias correction embedded fuzzy C-means with spatial constraint (BCEFCM-S) [37]. Our goal is to segment the brain T1-weighted MR images into three different tissues, namely WM, GM, and CSF.
Robust entropy-based symmetric regularized picture fuzzy clustering for image segmentation
2021, Digital Signal Processing: A Review JournalAn unsupervised orthogonal rotation invariant moment based fuzzy C-means approach for the segmentation of brain magnetic resonance images
2021, Expert Systems with ApplicationsAnalysis of brain sub regions using optimization techniques and deep learning method in Alzheimer disease
2020, Applied Soft Computing JournalDomain-independent severely noisy image segmentation via adaptive wavelet shrinkage using particle swarm optimization and fuzzy C-means
2019, Expert Systems with ApplicationsCitation Excerpt :In this paper, we use the T1-weighted images with a slice thickness of 1 mm. To study brain function and treatment of disease, segmentation of MRI images into three main tissues is of great importance (Namburu, Samayamantula, & Edara, 2017; Singh & Bala, 2018). These tissues are white matter (WM), Gray Matter (GM), and Cerebrospinal Fluid (CSF).
Chandan Singh received an undergraduate degree in science in 1975 and a postgraduate degree in mathematics in 1977 both from Kumaon University, Nainital, India, and a Ph.D. degree in applied mathematics from Indian Institute of Technology, Kanpur, India, in 1982. He joined M/S Jyoti Ltd., Baroda, India, in 1982, and later Thapar Corporate R&D Centre, Patiala, India, in1987. In the year 1994, he joined Department of Computer Science at Punjabi University, Patiala where he served as Professor till December 2014. At present, he is serving as Professor(Re-employed) at Punjabi University. In addition, he worked as Dean, Research, from June 2010 to May 2012. Dr. Singh also served as Dean, Faculty of Engineering and Technology, from 1995 to 2000 and Dean, Faculty of Physical Sciences, during 2007–2008. He has worked in many diverse areas such as fluid dynamics, finite element analysis, optimization and numerical analysis. He has more than 40 years of teaching and research experience. For the last over 25 years he has been working in pattern recognition, face recognition, medical image denoising, optical character recognition, and medical image segmentation. He has published more than 80 papers in various International journals and more than 45 papers in various national and international conferences.
Anu Bala received M.Tech degree in computer science and engineering from Guru Nanak Dev University, Amritsar India, in 2014. She is currently pursuing Ph.D. degree in Computer Science at Punjabi University, Patiala, India. Her research interests include Image processing and Image Segmentation.