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PERFORMANCE EVALUATION OF HSO AND EMO USING KAPUR’S ENTROPY FOR MRI BRAIN TUMOR SEGMENTATION.
VINAY KUMAR SINGHAL 1, R. B. DUBEY 2 AND ANIL KUMAR 3
1,Al-Falah School of Engineering & Technology, Faridabad, Haryana, India
2SRM University, Delhi-NCR, Sonepat, Haryana, India
3,Al-Falah School of Engineering & Technology, Faridabad, Haryana, India
Abstract:-The segmentation of brain tumors in MR images is a challenging, time - ingesting and tedious assignment. Brain tissue has a complex structure and its segmentation is an important step for deriving the computerized anatomical atlases as well as pre and intra operative guidance for therapeutic intervention. Traditional methods available for segmentation of brain tumor aren’t accurate. In this paper two novel techniques for segmentation of the brain tumor MR images are used. Here we ed on electromagnetism optimization algorithms and harmony search algorithm for figuring out the multilevel threshold of images. The objective functions utilized in aforesaid strategies are famous Kapur’s entropy function. Test results of both subjective and quantitative comparative similar investigations for a few existing methodologies outline the viability and strength of the proposed calculations.
Keywords:-Brain tumor segmentation, multilevel thresholding, Electromagnetism-like optimization, Harmony search optimization, Otsu’s function.
INTRODUCTION
Currently, image segmentation is playing a vital role in medical imaging analysis.
Automated recognition of brain tumors in magnetic resonance images (MRI) is a difficult task owing to the variability and complexity of the location, size, shape, and texture of these lesions. Because of intensity similarities between brain lesions and normal tissues, some approaches make use of multi-spectral anatomical MRI scans.
MRI based brain tumor segmentation studies are attracting more and more attention in recent years due to non- invasive imaging and good soft tissue contrast [1-4]. Automatic segmentation of brain tissues into white matter, gray matter and cerebro-spinal fluid from MRI is of great importance for scientific research and clinical diagnostics [5]. During past two decades, more attentions have been focused on parametric methods, nonparametric approaches and atlas based strategies for the segmentation work. For feature learning, it is not clear which type of MRI feature is useful for the task of tissue segmentation. Among classification-based segmentation method, the fuzzy C-means (FCM) clustering algorithm is slightly more effective than existing methods [6]. FCM is a very popular unsupervised clustering method, it does not account for the image spatial information and is very sensitive to noise and imaging artifacts. To make the FCM robust to noise, many modified fuzzy clustering approaches have been reported
[7–17]. Pedrycz [7] introduced a conditional fuzzy C-means-based clustering method guided by an auxiliary variable. Mohamed et al. [8] modified the FCM algorithm through the introduction of the spatial information. Ahmed et al. [9] introduced the local grey level information by changing the objective function with another similarity measure. Various researchers modified the objective functions to develop several robust FCM variants for image segmentation [8–
15]. These algorithms have shown better performance than the standard FCM algorithm. Chuang et al. [18] introduced a new work with spatial information into the FCM membership function. Adhikari et al.
[19] presented a method with introduction of intensity inhomogeneity and spatial information through probabilistic FCM algorithm. Azadeh et al introduced a new k- means clustering algorithm for the segmentation of background from brain tissue and separates normal brain pixels from the pixels inside the brain [20]. Tsai et al. [21] added a method of histogram and morphological operation for segmenting the various tissues from MRI data. Logeswari et al. [22] implemented the hierarchical self organizing map for segmentation of the tumors. Ben George et al. [23] documented bacteria foraging optimization algorithm to segment the brain tumor. Zhang et al. [24]
invented an improved artificial bee colony algorithm. Segmentation process can be made more accurate by including the best optimization algorithm [25]. Cuckoo search
2 has generalized breeding behavior and now it can be applied to a wide range of optimization problems which surpass the other meta-heuristic algorithms in relevance [26]. Hammouche et al. [27] uses genetic algorithm for multilevel image segmentation. Dirami et al. [28] proposes a multilevel segmentation through level set method. [29-35] shows that the Electromagnetism-like optimization can be used for solving a lot of multidimensional problems. [36-39] uses both the Kapur as an objective function for various optimization techniques. The rest of the paper is organized as follows. Section 2 presents the test image dataset used.
Section 3 outlines the details of methodologies used to perform the discussed task. Section 4 provides results and discussions. Conclusions are drawn in Section 5.
IMAGE DATABASE
The feasibility of the proposed technique is tried on 12 T2 weighted MR brain images collected from internet as shown in Figure 1.
PROPOSED METHODOLOGY
Thresholding is one of the techniques utilized for image segmentation. In bi-level thresholding techniques, a given image is separated into two classes while in multi–
level image segmentation; the image is divided into several classes depending on the requirement of the problem [28]. In optimal multi-level thresholding problem, the calculation of threshold value requires complex computational efforts and an objective function whose value is to be maximized or minimized. Consider a gray image I having L gray levels. Let denotes the number of pixels with k gray levels, thus the total number of pixels will be given by equation (1).
Figure 1 Original Test Images.
(1)
The probability of occurring k’th gray level is given by , which results in equation (2).
(2)
The ideal multilevel thresholding method searches the values in search space so that the segmented class on the histogram fulfills some criteria. This is accomplished by the objective function, which utilizes the calculated threshold values as one of the parameters. Here, we use the Kapur’s entropy function [36,37].
3. Kapur’s Entropy Function
In this method firstly the entropy is calculated for each segmented class so as to have more centralized distribution and then entropy associated with each class is added and the overall function is maximized [38].
Basically this method was deployed for bi- level segmentation problem for which the objective function is given by Eqn. (3):
(3)
Where , entropy of one class and is of another class.
And
The value of t which produces maximum value for Eqn. (3) will be the optimal solution for bi-level thresholding. This function tries to have centralized distribution for every class. Eqn. (4), (5) gives the corresponding entropy values for different class. Later on this kapur’s entropy method was extended for multilevel image thresholding problem and the new objective function for m optimal threshold values looks Eqn. (6):
(6)
Where,
3 .
. .
3.2 ELECTROMAGNETISM-LIKE OPTIMIZATION (EMO)
Electromagnetism algorithm (EM) is an optimization technique proposed by [29].
This technique was devised to optimize the issues related to bounded variables and non-linear stochastic problems. This mechanism mirrors the attraction or repulsion of charged particle. [30] The main objective of this algorithm is to move particles towards the optimal solution by applying forces of repulsion or attraction.
Here, a set of possible solution in search space is represented by a charged particle.
Each particle differs from other particles in their charge quantity, characteristics, and location from other particles. Each particle exerts an electromagnetic force on another particle. The total force exerted on a particle is calculated by adding vectorially the forces on that particle from remaining ones. i.e.
the total force calculation is done on the basis of principle of superposition. This computed force is now used for updating the individual particle’s position and higher the amount of force higher will be the objective function value [31, 32]. Figure 2 shows important steps of the algorithm in the form of flow chart.
Initialization: This is the very first step in EM algorithm and a great care is required to ensure that this scheme generates the best optimal solution within the uniformly distributed bounded condition. Here, a psize
populace with m particles is randomly created from uniformly distributed search
space within the bounding limits [33]. Then the objective functions value is evaluated for each particle in psize. A pairwise comparison of objective function values is carried out and the particle with the best value in terms of objective function’s value is saved as Zbest in equation (6) [34].
Local Search: (6) EM has the ability of diversification, still a local search procedure is required for optimal result. This is done by gathering the information from all sample point in its neighbor. From various search procedures [35], we use a simple random line search algorithm which is one of the least complex, fastest and effective search methods. In this algorithm we use two parameters – LSITER and δ. LSITER denotes the number of local search iteration and δ [0, 1] represents the multiplier for its neighborhood search.
Resultant force Calculation: According to [51], the method for calculating the force on each charged particle is analogous to Coulomb’s Law. The objective function’s value for each particle in Psize represents the corresponding charge on the particle [36]. This charge determines its power of attraction and repulsion. This value of charge can be calculated by equation (7).
(7)
After getting the charge value on each particle of the population, the resultant force on each particle is computed. Let and be two particles chosen randomly from the Psize having and charge respectively. The force exerted on due to
is calculated using the equation (8).
Figure 2 Flowchart for Electromagnetism- like optimization.
4
(8) The resultant force in equation (9) exerted on by the other (Psize −1) particle is computed by adding the individual forces computed earlier by using equation (8).
(9) Where,
is the Euclidean space between the points and
Movement along the resultant force: A movement of particle plays a vital role. This movement is carried out on the basis of resultant force computed in the third step.
The direction of movement is determined by the resultant force and step size (λ) of the movement. The step size is chosen randomly between 0 and 1 in the direction of the resultant force [29]. A movement of the particle is executed according to equation (10).
(10)
The term RNG allows the set of feasible value satisfying the upper bound or lower bound toward the movement. denotes the normalized force so as to maintain the feasibility of movement.
3.3 Harmony Search Optimization (HSO)
Harmony search optimization is a meta- heuristic technique for global optimization developed by [41]. It mimics the musician’s behavior of changing the pitches of their respective instruments together to accomplish a fantastic harmony. It uses the synchronization between newly suggested results (harmony) and the results obtained after exploring the search space. This synchronization shows both intensification and diversification capability of HSO. The implementation of standard HSO consists of three main phases: initialization, improvisation, and updating as shown in figure 3.
Initialization: In this step a harmony
memory matrix U is
defined. D is a dimension of the problem.
is a harmony vector of size HMS, generated randomly from the uniformly distributed search space within the lower and upper bound constraints for each dimension.
Other control parameters like dimension, pitch adjusting rate (PAR), harmony memory considering rate (HMCR), bandwidth factor (BW), and the maximum number of iteration (NI) are also initialized in this step [41]. After initialization the objective function or fitness value is computed using the discussed objective function.
Improvisation: The memory of this algorithm stores the previous optimal results. is a new improved harmony vector
5 constructed by applying the following rules in a defined order i.e. firtsly the memory consideration is applied then the random re-initialization and lastly the pitch adjustment [42]. This process of Generation is known as improvisation.
(11) where,
is upper and lower bounding limits for a dimension respectively.
Components generated from equation (11) are further examined for pitch adjustment. The PAR is defined for assigning the frequency of pitch adjustment and BW, so as to control the local search around the chosen elements of the harmony memory (HM). The pitch adjustment rule is given by equation (12).
(12)
Updation of the harmony memory: After generating new harmony vector , we update the HM. Updating procedure is based on fitness value of i.e. if this value for is better than the worst value in HM, than HM includes the and the worst harmony is removed from HM. The process of improvisation and update are carried out till NI is reached or some stopping criteria are achieved.
Figure 3 Flowchart for Harmony Search Optimization.
Figure 4 Gaussian filtered image.
1
2 RESULTS AND DISCUSSIONS
This section discusses the performance and experimental outcomes of HSO and EMO based segmentation. Here, for multi-level
6 thresholding problem we used Kapur’s entropy as an objective function. The discussed techniques perform the multilevel thresholding on the MRI Brain tumor dataset shown in figure 1. By applying the discussed algorithm we calculated the optimal threshold values within the range [0, L-1] which in turn, maximizes the fitness criterion. The dimension of an optimization problem can be any number of threshold values (m) and in our case we chose m = 4.
Figure1 shows the set of 12 original brain MR images. In the preprocessing step, these images are filtered using Gaussian filter and the result is shown in figure 4.
The best objective values obtained using Kapur’s entropy function on EMO algorithm is shown in figure 5. Figure 6, 7, 8 belongs to EMO on Kapur’s entropy function. Figure 6 shows the set of the segmented images.
From the segmented image only the region of interest is selected which is shown in figure 7. Graphically, the 4 optimal thresholds values are shown in figure 8.
The same set of figure 1 is applied to the HSO algorithm also. The graphical representation of the best objective values obtained from Kapur’sentropy function on HSO algorithms for 4 level thresholding is shown in figure 9. Figure 10, 11, 12 belongs to HSO Otsu’s function. Figure 10 shows the set of segmented image and the selected region of interest is shown in Figure 11.
Figure 12 shows the 4 optimal thresholds graphically.
Figure 5 Plot of best values generated after implementing EMO on Kapur’s entropy function.
Figure 6 Segmented Images from EMO on Kapur’s entropy function.
Figure 7 Region of Interest from EMO on Kapur’s entropy function.
Figure 8 Plot of Optimal Threshold Values generated after implementing EMO on Kapur’s entropy function.
Figure 9 Plot of best values generated after implementing HSO on Kapur’s entropy function.
Figure 10 Segmented Images from HSO on Kapur’s entropy function.
7 Figure 11 Region of Interest from HSO on Kapur’s entropy function.
Figure 12 Plot of Optimal Threshold Values generated after implementing HSO on Kapur’s entropy function.
Table 1 Results of EMO and HSO on Kapur’s entropy function.
Images
EMO on Kapur’s Objective Function HSO on Kapur’s Objective Function Elapse
d time (sec)
Threshold values PSNR Area Elapse d time
(sec)
Threshold values PSNR Area 1st 2n
d 3rd 4th 1st 2nd 3rd 4th
IM 01 169.2
8 44 9
1 138 18
9 22.94 3766 8.00 44 91 138 189 22.94 3910
IM 02 174.5
4 13 5
7 108 18
0 22.78 5823 6.27 13 57 108 180 22.78 4906
IM 03 174.4
1 95 1
3
4 171 20
9 16.23 6354 7.06 96 14
1 190 234 16.15 6139
IM 04 186.22 84 12
8 172 21
6 16.92 98 16.2
8 84 12
6 170 215 16.92 2316
IM 05 186.83 26 10
4 155 20
3 19.83 715 19.9
1 26 10
4 155 203 19.31 815
IM 06 182.18 30 76 125 19
0 25.56 1295 21.4
7 27 75 125 190 25.36 1293
IM 07 182.00 21 71 123 15
5 24.88 557 18.9
7 21 71 123 164 24.89 573
IM 08 184.57 42 88 134 19
8 23.10 290 10.3
4 42 88 134 198 23.10 270
IM 09 187.83 72 12
1 157 20
5 18.89 1740 18.0
6 62 10
6 146 205 20.51 1487
IM 10 920.49 61 11
7 167 21
7 20.68 6289 6.48 27 80 141 215 21.46 7056
IM 11 185.40 23 79 130 19
1 21.74 6163 6.69 23 79 130 191 21.74 5748 IM 12 187.39 85 12
8 178 23
0 15.37 1811 16.3
5 85 12
8 178 230 15.37 1769
Table 2 Results of EMO and HSO on Kapur’s entropy function.
Images EMO on Kapur’s Objective Function HSO on Kapur’s Objective Function
Ext ent Per im ete
r Ec cen tric ityOri ent atiEq onuiv ale nt Dia me ter Obj ecti ve val ue Ext ent Per im ete
r Ec cen tric ity Ori ent ati Eqon uiv ale nt Dia me ter Obj ecti ve val ue
IM 01 0.73 245.87 0.40 41.31 69.25 25.19 0.75 232.45 0.36 20.50 70.56 25.18 IM 02 0.73 293.91 0.68 -25.70 86.11 24.77 0.76 270.55 0.58 -24.83 79.03 23.92 IM 03 0.72 335.76 0.35 65.54 89.95 25.41 0.74 309.76 0.30 82.89 88.41 25.28 IM 04 0.64 49.21 0.95 0.63 11.17 25.07 0.50 292.84 0.88 -78.15 54.30 23.39 IM 05 0.60 125.30 0.75 -81.90 30.17 25.14 0.66 122.57 0.68 -82.30 32.21 25.14 IM 06 0.75 136.81 0.35 35.85 40.61 23.48 0.77 134.23 0.36 32.15 40.57 21.72
8
IM 07 0.64 108.08 0.84 73.08 26.63 23.87 0.65 114.91 0.83 71.79 27.01 23.88 IM 08 0.81 63.21 0.59 -76.98 19.22 25.49 0.76 63.80 0.67 -70.63 18.54 25.44 IM 09 0.80 162.12 0.62 87.61 47.07 25.48 0.73 154.95 0.62 85.40 43.51 24.49 IM 10 0.60 411.71 0.74 61.20 89.48 25.90 0.59 459.16 0.72 64.63 94.78 25.74 IM 11 0.69 327.42 0.76 74.90 88.58 25.97 0.71 320.59 0.67 69.59 85.55 25.97 IM 12 0.74 164.02 0.62 -27.30 48.02 26.18 0.72 175.20 0.65 -26.49 47.46 26.11
Table 1 shows the results obtained from above mentioned schemes on Kapur’s entropy function. For the comparative analysis of the discussed schemes we have considered certain parameters like thresholding values, PSNR, Area of detected tumor in pixels and mm2. While doing the segmentation, our main aim is to maximize the objective function value. Table 2 reveals the result in term of equivalent diameter, perimeter, extent, objective function value etc.
CONCLUSIONS
Segmentation of medical images needs to have accuracy, less computation time, capability of producing results in real-time and requiring minimum user interaction. In this study for the first time, EMO and HSO algorithms are implemented successfully on Otsu’s function for the segmentation of MRI brain tumor. Both the algorithms are exploited to maximize the objective function’s value so as to find optimum multilevel thresholds. The results of segmentation mainly depend on the selection of proper threshold values and number of classes. The proposed methods for image segmentation is efficient and faster when compared with other multilevel thresholding techniques Here, the image segmentation approach based on 4 thresholding level has been developed and it may be used for any number of thresholding level. HSO takes very less computation time to perform segmentation as desired in case of medical images. The algorithm required minimal user interaction. As the number of threshold level increases the segmented image gives more clarity of information. The higher level of thresholds might be very useful in the brain images to distinguish the normal and abnormal.
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