Chaotic firefly algorithm-based fuzzy C-means algorithm for segmentation of brain tissues in magnetic resonance images

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Highlights

Abstract

Image segmentation with clustering approach is widely used in biomedical application. Accurate brain Magnetic Resonance (MR) image segmentation is a challenging task due to the complex anatomical structure of brain tissues in addition to the existence of intensity inhomogeneity, partial volume effects and noise. In this study, a spatial modified bias corrected FCM algorithm is applied to brain MRI for the purpose of segmentation into White Matter (WM), Gray Matter (GM) and Cerebrospinal fluid (CSF) in MR images. So to overcome the uncertainty caused by the above effects, a modified Fuzzy C-Means (m-FCM) algorithm for MR brain image segmentation is presented in this paper. Also FCM suffers from initialization sensitivity, to overcome this we have used chaos theory based firefly algorithm. This paper presents a novel application of FCM clustering by using Firefly algorithm with a chaotic map to initialize the population of fireflies and tune the absorption coefficient (λ), for increasing the global search mobility. This algorithm is called chaotic firefly integrated Fuzzy C-means (C-FAFCM) algorithm, which embeds chaos map in the Firefly Algorithm. The proposed technique is applied to several simulated and real T1-weighted for normal magnetic resonance brain images, taken from IBSR and BrainWeb database. The algorithm is realized by incorporating the spatial neighborhood information into the standard FCM algorithm and modifying the membership weighting of each cluster by regularizing it by Total Variation (TV) denoising. The experimental results on both simulated and real brain MRI datasets demonstrate that our proposed method (C-FAFCM) has satisfactory outputs in comparison with some other state of the art, based on FCM and non FCM based algorithms.

Introduction

Image segmentation is essential to study any brain related disorders like seizures, multiple scleroses, stroke, brain tumors, lesions, brain cancers and structural changes. There are three main brain tissues, white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF). To extract these brain tissues, Magnetic Resonances (MR) image segmentation is used. These tissues help in many medical image segmentation applications such as clinical diagnosis, radiotherapy planning, treatment planning, Alzheimer disease and patient follow-up. Manual segmentation of these three brain regions by a professional is time consuming, inconsistent and affected by technician as the data involved in MRI studies is generally large. Hence, an automatic segmentation of brain regions is needed for a physician to speed up their diagnostic process. In Semi-automatic Supervised methods, user interaction is required but in unsupervised techniques no user intervention is necessary it is automatic. Clustering as proposed by Jain and Dubes [1], Fayyad et al. [2], Murty et al. [3] can be used as unsupervised techniques for image segmentation. In clustering an image is partitioned into groups of pixels which are homogeneous with respect to some criterion. Fuzzy C-Means (FCM) [4] is one of the popular clustering methods. When dealing with MRI brain images, there are potential sources of artifacts affecting the image during the imaging process. The main artifacts in MRI are noise, partial volume effect (PVE) and intensity inhomogeneity. The main sources of noise are categorized as biological, and scanner noises introduced in [5]. PVE is recognized as a mixture of intensities due to the presence of more than one tissue type in the same voxel. Increasing the image resolution results in lower PVE, but it may lead to a higher level of system noise and a reduced signal-to-noise ratio [6]. Intensity inhomogeneity, also known as bias field is a low frequency smoothed artifact induced by the radio-frequency coil in magnetic resonance imaging (MRI) during the scanning process [7], [8]. Intensity inhomogeneity causes the intensities of the same tissue vary with voxel locations and can cause segmentation inaccuracies. Therefore, intensity inhomogeneity correction and segmentation can be viewed as an intertwined procedure to enhance the performance of MRI segmentation [9]. Segmentation based methods are the most popular types of methods for bias field correction [10].

Again, if the initialization of cluster centroids is random, then FCM does not assure that it converges on an optimal solution to an optimal time. Initial centroids of required clusters play an important role in deciding the performance of FCM. Hence, the selection of a centroid is crucial to FCM.

To overcome these problems when standard firefly algorithm (FA) [11], [12] is used to optimize the multi-peak function, it can be easily trapped in the local minima, which leads to slow convergence speed. Moreover, it is difficult to obtain an accurate result without the use of a good searching method. To deal with the problems of low accuracy and local convergence in standard FA, we introduce the chaos theory. Chaos is a general nonlinear phenomenon in nature which has characteristics of randomness, ergodicity and regularity because of its fine internal structure. So chaos became an available strategy to avoid being trapped in local optima and improve the searching quality of global optimum. To utilize these advantages, we initialize the population of fireflies and replace the constant value of absorption coefficient (λ) with chaotic map.

Next in Section 2 we highlight some of related works in this field. Chaos theory is discussed in Section 3. The design and implementation of the proposed method is given in Section 4. The result and comparison of our approach to competing methods are presented in Section 5. Performance evaluation are evaluated in Section 6 followed by the conclusions.

Section snippets

Image segmentation by clustering methods: related work

Fuzzy C-Means algorithm (FCM) proposed by Bezdek [4], has been widely and successfully employed in several applications to tackle image segmentation problems. Some of the other important works in this area are done by Kang and Zhang [13]. Segmentation techniques in the field of brain MRI data can be categorized into two groups: parametric and nonparametric algorithms.

Most of the parametric algorithms make the assumption that the intensity of three brain tissue types follows a Gaussian

Chaos

Chaos is a category of unique deterministic random-like process found in nonlinear, dynamical system, which is non-periodic, non-converging and confined and it has been applied extensively in communication, robotics, pattern recognition and other fields including operations research, physics, engineering, economics, biology, philosophy and computer science as proposed by Tavazoei and Haeri [58], Coelho and Mariani [59]. Recently chaos is expanded to various optimization areas since it can

Proposed chaotic firefly integrated Fuzzy C-means (C-FAFCM) algorithm

We have developed a novel image segmentation technique based on clustering; called chaotic Firefly Algorithm incorporated Fuzzy C-means (C-FAFCM), for MR images. To overcome the limitations and get benefits of them, we integrated Chaotic-Firefly Algorithm with the modified Fuzzy C-means (m-FCM) clustering algorithm. FA is introduced to develop an optimized fuzzy segmentation technique which will optimize the performance of pure FCM. Various works have applied FA to data mining and image

Experimental results and discussion

In order to solve the optimization problem in segmentation methods, the stochastic gradient descent (SGD) method is very often used. Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. We have compared the effectiveness of our proposed stochastic meta-heuristic algorithm (C-FAFCM) with stochastic gradient descent based fuzzy clustering (SGFC) method as mentioned in [67]. We have evaluated the C-FAFCM clustering algorithm on synthetically

Segmentation evaluation on simulated T1-weighted MR images

The results are generated by using the MATLAB simulation. The methodology is examined with MR Brain Images. The MR brain images are first converted to gray scale images and then clustered the soft tissues by FCM [4], BCFCM [7], FAFCM [56], En-FAOFCM [52] and proposed Chaotic-FAFCM (i.e., C-FAFCM) techniques. In order to evaluate the segmentation performance quantitatively, some definitions are required. The evaluation metrics is defined by Shen et al. [71] as follows:

Conclusion

A novel efficient and reliable clustering algorithm has been presented by us in this work, which is called C-FAFCM, based on the hybridization of the chaotic firefly algorithm with modified fuzzy c-mean (m-FCM) clustering algorithm for automatic segmentation of MRI volumetric datasets. These datasets are classified to three main classes (WM, GM, CSF). Here we have presented a new energy minimization framework for simultaneous bias field estimation and segmentation. The proposed methodology can

Conflict of interest

None.

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