BioMed Research International

Volume 2017, Article ID 6783209, 17 pages

https://doi.org/10.1155/2017/6783209

## Multilevel Thresholding Method Based on Electromagnetism for Accurate Brain MRI Segmentation to Detect White Matter, Gray Matter, and CSF

^{1}Department of ECE, VNITSW, Guntur, Andhra Pradesh, India^{2}Department of ECE, VVIT, Guntur, Andhra Pradesh, India^{3}Department of ECE, JNTUCE, Hyderabad, Telangana, India

Correspondence should be addressed to G. Sandhya; moc.liamg@604gayhdnas

Received 12 July 2017; Revised 5 September 2017; Accepted 10 October 2017; Published 9 November 2017

Academic Editor: Nasimul Noman

Copyright © 2017 G. Sandhya et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This work explains an advanced and accurate brain MRI segmentation method. MR brain image segmentation is to know the anatomical structure, to identify the abnormalities, and to detect various tissues which help in treatment planning prior to radiation therapy. This proposed technique is a Multilevel Thresholding (MT) method based on the phenomenon of Electromagnetism and it segments the image into three tissues such as White Matter (WM), Gray Matter (GM), and CSF. The approach incorporates skull stripping and filtering using anisotropic diffusion filter in the preprocessing stage. This thresholding method uses the force of attraction-repulsion between the charged particles to increase the population. It is the combination of Electromagnetism-Like optimization algorithm with the Otsu and Kapur objective functions. The results obtained by using the proposed method are compared with the ground-truth images and have given best values for the measures sensitivity, specificity, and segmentation accuracy. The results using 10 MR brain images proved that the proposed method has accurately segmented the three brain tissues compared to the existing segmentation methods such as* K*-means, fuzzy* C*-means, OTSU MT, Particle Swarm Optimization (PSO), Bacterial Foraging Algorithm (BFA), Genetic Algorithm (GA), and Fuzzy Local Gaussian Mixture Model (FLGMM).

#### 1. Introduction

The present use of neuroimaging procedures allows the scientists and specialists to detect and distinguish various activities and the complications inside the human brain without using any intrusive neurosurgery. Though there are many medical imaging techniques, Magnetic Resonance Imaging is the best imaging technique due to no radiation exposure hence no side effects and it is highly accurate in detecting abnormalities in the internal structures of human organs. The structure of the brain is complex and its tissue segmentation is very crucial to visualize and quantify various brain disorders.

Noise is the main parameter that affects the medical image segmentation. Images can be denoised by using various spatial filters like the low-pass, median, adaptive filter, and so forth. But these filters blur the sharp lines or edges, may respect the edges but the resolution gets decreased by abolishing fine details, and may generate artifacts [1–3]. To overcome the drawbacks of spatial filters Perona and Malik proposed anisotropic diffusion filter [4, 5] which has the properties of (a) sharpening the discontinuities, (b) preserving detailed structures and object boundaries so loss information is minimized, and (c) removing noise in homogeneous regions.

##### 1.1. State-of-the-Art Review

A wide range of algorithms has been proposed for the automatic segmentation MR images [6–9]. Image segmentation is a fundamental task in the process of image analysis. Segmentation divides the total image into small regions based on the intensity distribution of the pixels. Thresholding [10–12] is a simple technique for the image segmentation. It separates the object in an image from its background by using an appropriate gray-level value called the threshold. Choosing threshold is very difficult in brain image as the intensity distribution in it is complex. Region-growing [13–15],* K*-means clustering [16, 17], Expectation Maximization (EM) [18, 19], and fuzzy* C*-means (FCM) [20, 21] are the widely used techniques for the medical image segmentation and are the extensions to thresholding. The main drawbacks of these methods are long computational time, sensitivity to noise and sensitivity to the initial guess, very slow convergence, and having no global solution.

Otsu and Kapur proposed two methods for thresholding [22–25]. The first approach maximizes the between-class variance and the other maximizes the entropy between the classes to find the homogeneity. These are reliable for bilevel thresholding [26]. When these algorithms proposed by Otsu and Kapur are used to segment the images of complex intensity distributions which can be effectively segmented by Multilevel Thresholding (MT), the algorithms will extensively search for multiple thresholds which is computationally tedious and the computation time depends on the complexity of the image. Many techniques were developed to reduce the computation time such as [27–29] that are specifically designed to accelerate the computation of objective function, [30–32] that involve Sequential Dichotomization, [33] that is based on an iterative process, and [34] that consists of some Metaheuristic Optimization Techniques. There are methods to solve the problem of determining threshold number in MT process. In [27, 30] multiphase level set method and a new criterion for Multilevel Thresholding are specified in which the optimal threshold number is found by optimizing a cost function. Genetic Algorithm (GA) is combined with wavelet transform [35, 36] to reduce the time.

Evolutionary optimized MT methods are best in terms of speed, accuracy, and robustness compared to classical MT techniques. In [37], various evolutionary approaches such as Differential Evolution (DE), Tabu Search (TS), and Simulated Annealing (SA) are discussed to solve the limitations of Otsu’s and Kapur’s approaches for MT. In [37, 38], Genetic Algorithms (GAs) based methodologies are utilized for the segmentation of multiclasses. Particle Swarm Optimization (PSO) [39] has been considered for MT, to maximize Otsu’s objective function. Other methods [26, 39–43] such as Artificial Bee Colony (ABC), Bacterial Foraging Algorithm (BFA), and Fuzzy Local Gaussian Mixture Model (FLGMM) were developed for the brain image segmentation.

As the proposed method performance is compared with some of the state-of-the-art methods such as -Means, FCM, Otsu MT, PSO, BFA, GA, and FLGMM these are summarized in the following section.

##### 1.2. *K*-Means Clustering

-means clustering [16, 17] is an extensively used technique for the image segmentation. This is an iterative method that classifies the pixels of a given image into distinct clusters by converging to a local minimum. Hence the clusters generated are independent and compact. The algorithm comprises two phases. In the first phase, centers are selected randomly, by choosing the value of in advance. The other phase is to bring every pixel to the closest center. Euclidean distance is the generally used metric to measure the distance between each pixel and the centers of clusters. Early grouping is being done when all the pixels are included in different clusters. Now new centroids are refigured for every cluster. In the wake of having these new centroids, another binding must be done between the same group of pixels and the closest new center. This is an iterative process during which the location of centers will change repeatedly until no more changes are done or, in another way, this iterative procedure continues until the criterion function converges to the minimum.

-means is fast, robust, relatively efficient, and easier to understand, and it gives excellent result when data is well separated. The main drawbacks of the -means are as follows: it requires prior specification of the cluster center number, it is unable to divide highly overlapping data, the same data with different representations gives different results, it is sensitive to noise, and the algorithm does not work for the nonlinear type of data.

##### 1.3. Fuzzy* C*-Means Clustering

The fuzzy -means algorithm [20, 21] is widely preferred for the medical image segmentation due to its flexibility of allowing pixels to have a place in multiple classes with different degrees of membership and, compared to other clustering methods, it retains more pixel information in the given image. FCM method partitions the pixels of a given image into “” fuzzy clusters regarding some criteria. Different similarity measures such as connectivity, distance, and intensity are used to separate the pixels. In this work, brain images are segmented into three clusters specifically White Matter, Gray Matter, and CSF based on the feature values.

The algorithm is based on the minimization of the objective function: is the membership value and it is in the range , is the centroid of the th cluster, is the Euclidian Distance between th cluster centroid and th data point, and is a weighting exponent in the range .

Fuzzy clustering of the data samples is carried out through an iterative optimization of the above objective function by updating the membership value and the cluster centers by

The major operational drawbacks of FCM are as follows: it is time-consuming and hence it achieve the stabilization condition after a long time, and it does not consider any local or spatial information of the image, and hence it is easily affected by noise and other imaging artifacts.

##### 1.4. Otsu Thresholding

Bilevel thresholding can be used to segment the simple images whose object has clear boundaries. But, for the segmentation of complicated images, Multilevel Thresholding (MT) is required. Otsu bilevel thresholding is a well-known nonparametric technique for the segmentation of medical images and it deals with discriminate analysis [22–24]. The value of gray-level at which between-class variance is maximum or within-class variance is minimum is selected as the threshold. This bilevel thresholding divides the pixels of a given image into two separate classes and , and it belongs to objects and background at the gray-level th; that is, and . Let , , and be the within-class variance, between-class variance, and the total variance, respectively. By minimizing one of the below criterion functions with respect to th an optimal value for the threshold can be found. The criterion functions are and here is the number of pixels with th gray-level, is the total number of pixels in the given image, and is the probability of occurrence of gray-level. are the areas occupied by the two classes and , respectively, and , are the mean values of the classes and , respectively.

Among the criterion functions, is minimum. Hence, the optimal threshold . The maximum estimate of *η*, designated as , is used to evaluate the amount of separability of classes and It is very significant as it does not vary under affine transformations of the gray-level scale.

Otsu bilevel thresholding can be extended to MT and is direct by virtue of the discriminant criterion. For instance, on account of three-level thresholding, two thresholds are defined as for separating three classes, for , for , and for . The between-class variance is a function of and , and the optimal thresholds and can be found by maximizing the function , where .

The main drawback of the Otsu is the following: as the number of segments to be divided increases, the selected thresholds become less accurate. This is simple and effective for two-level and three-level thresholding, which can be applied to almost all applications.

##### 1.5. Particle Swarm Optimization (PSO)

PSO [39] is a population-based stochastic optimization process. The method searches for a solution by altering the directions of individual vectors, termed as “particles.” The initial location of the particles is chosen randomly from the search area Ω. For every iteration, a velocity is assigned to every particle in Ω and it gets updated by the best value that the particle has visited. Then, using the updated velocity in iteration the position of every particle is updated. The performance of the particle is assessed by its fitness function value. At every iteration, the values of the best positions visited by the particle and their companions are saved as personal and population observations by which every particle will converge to the optimal solution. Thus, PSO has quick convergence compared to the other population-based methods such as DE or GA.

In the -dimensional search space, the position vector of the th particle is defined as and its velocity vector as . According to a predefined fitness function, if and are assumed as the best position of each particle and the fittest particle for an iteration , respectively, then, the new position and velocities of the particles for the next fitness function are calculated as where and are positive constants and and are two random functions uniformly distributed in the interval (0, 1). The variable representing the inertia weight causes the convergence of the algorithm. The PSO algorithm can be surely converged if each particle must converge to its local attractor

According to (4), all the particles are greatly influenced by and . If the best particle reaches a local optimum, then all the remaining particles will fast converge to the location of the final best particle. Hence, in the PSO global optimum of the fitness function is not guaranteed which is called premature.

A globally optimal solution is considered as a feasible solution whose objective value is better than other feasible solutions. For locally optimal solution no better feasible solutions can be found in the immediate neighborhood of the given solution. Subsequently, if the algorithm loses the diversity at early iterations it may get trapped into local optima, and it implies that the population turns out to be exceptionally uniform too soon. Despite the fact that PSO finds good solutions faster than other evolutionary algorithms it generally can not enhance the quality of the solution as the number of iterations is improved. The solution of the global best is improved when the swarm is iterated. It could happen that all particles being influenced by the global best eventually approach the global best and from there on the fitness never improves despite however many runs the PSO is iterated thereafter. The particles also move in the search space in close proximity to the global best and not exploring the rest of the search space. This is called premature convergence.

##### 1.6. Bacterial Foraging Algorithm (BFA)

BFA optimization strategies are methods for locating, handling, and ingesting food. Natural selection eliminates the animals with poor foraging methodologies. This encourages the propagation of qualities of the best foraging methods. After so many generations, the poor foraging strategies are either wiped out or upgraded into better ones. A foraging animal tries to maximize the energy intake per unit time spent on foraging within its environmental and physiological constraints. The* E. coli* bacteria, present in human intestine, follow foraging behavior, which consists of processes of chemotaxis, swarming, reproduction, and elimination or dispersal. In [42, 44] this evolutionary technique was modeled as an effective optimization tool.

*Chemotaxis*. The bacterial movement of swimming and tumbling in presence of attractant and repellent chemicals from other bacteria is called chemotaxis. A chemotactic step is a tumble followed by a tumble or run. After defining a unit length random direction the chemotaxis can be modeled as where is the th bacterium at th chemotactic, th reproductive, and th elimination or dispersal event. is the step size in the direction of movement specified by tumble called the run length unit.

*Swarming*. Bacterium which reaches a good food source produces chemical attractant to invite other bacteria to swarm together. While swarming, they maintain a minimum distance between any two bacteria by secreting chemical repellent. Swarming is represented mathematically as and here is the value of the cost function to be added to the optimized actual cost function to simulate the swarming behavior, is the total number of bacteria, is the number of parameters to be optimized, and , , , and are the coefficients to be chosen properly.

*Reproduction*. After completion of chemotactic steps, a reproductive step follows. Health of th bacterium is determined as Then, in the descending order of their health, the bacteria are sorted. The least healthy bacteria die and the other healthier bacteria take part in reproduction. In reproduction, each healthy bacterium splits into two bacteria each containing identical parameters as that of the parent keeping the population of the bacteria constant.

*Elimination and Dispersal*. The bacterial population in a habitat may change gradually due to the constraint of food or, suddenly, due to environmental or any other factor. Every bacterium in a region might be killed or some might be scattered into a new location. It may have the possibility of annihilating chemotactic progress, but it also has the ability to help chemotaxis, since dispersal event may put the bacteria to near-good food sources.

##### 1.7. Genetic Algorithm (GA)

GAs [45, 46] are effective, flexible, and powerful optimization procedures governed by the standards of evolution and natural genetics. GAs have implied parallelism. This algorithm begins with the chromosomal modeling of a set of parameters that will be coded as a limited size string over letters in order of limited length. An arrangement of the chromosomes in a generation is known as population, the measure of which might be consistent or may change starting with one generation and then onto another. In the initially defined population, the chromosomes are either produced randomly or utilizing domain-specific data information. The fitness function is designed, such that the strings or possible solutions that have high fitness values are characterized as best points in the feasible search region. This is known as the payoff information that is used by the GAs to search for probable solutions. During reproduction individual strings are replicated into a temporary new population called the mating pool, to convey genetic operations. The sum of copies received by an individual corresponds to the fitness value and these are used for the next generation. In general, the chromosome which is retained in the population till the final generation is treated as the best chromosome. Exchange of data between arbitrarily chosen parent chromosomes by combining details of their genetic information is treated as crossover. The efficiency of GAs mainly depends on the coding-crossover strategy. Chromosome’s genetic structure can be altered by the process of mutation which is used to bring the genetic diversity into the population.

There are many difficulties and issues in using GAs for image segmentation. The strategy of encoding should be confirmed to the Building Block Hypothesis; otherwise GA gives the poor result. The performance of GAs depends on the design of fitness function in such a way to reduce the computation time, choice of various genetic operators, termination criteria, and methods of keeping off premature convergence.

##### 1.8. Fuzzy Local Gaussian Mixture Model (FLGMM)

In the case of ordinary GMM, it has been assumed that intensities of a region are sampled individually from an identical Gaussian distribution function. This stochastic assumption is not suitable for MR brain images because of the presence of bias field. However, in the recently proposed FLGMM [43] algorithm for MR brain image segmentation, the bias field is expressed as a slowly varying quantity and it can be overlooked inside a small window. The objective function of FLGMM is obtained by integrating the Gaussian Mixture Model (GMM) weighted energy function over the image. The function consists of a truncated Gaussian kernel to establish the spatial constraints and fuzzy memberships to balance the contribution of GMM for segmentation.

In the process of FLGMM, based on the fuzzy* C*-means model of the images with intensity inhomogeneity the local intensity clustering property or the image partitions are derived from the input image. A local objective function is formulated for the given image. Minimization of the energy function is performed by defining individual membership functions locally for each cluster by assuming that it satisfies the Gaussian Mixture Model. A bias-field equivalent to the intensity inhomogeneity is generated. Thus energy minimization generates a homogenous image which is termed as the intensity inhomogeneity corrected image.

The remaining part of the paper is methodized as follows. Section 2 describes the materials and methods utilized in this work. Section 3 consists of experimental results and discussion. Section 4 is the brief concluding section.

#### 2. Materials and Methods

The present section describes the materials and methods used in this work. The overall algorithm is presented like a flow diagram in Figure 1. The stages involved in the implementation of the algorithm are explained in the subsections. The proposed method is implemented in MATLAB.