Entropy based segmentation of tumor from brain MR images – a study with teaching learning based optimization

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Entropy based segmentation of tumor from brain MR images – a study with teaching learning based optimization V. Rajinikanth a,∗, Suresh Chandra Satapathy b, Steven Lawrence Fernandes c, S. Nachiappan a a

St. Joseph’s College of Engineering, Old Mahabalipuram Road, Chennai 600 119, Tamil Nadu, India P.V.P. Siddhartha Institute of Technology, Vijayawada 520 007, Andhra Pradesh, India c Sahyadri College of Engineering & Management, Adyar, Mangalore 575007, Karnataka, India b

a r t i c l e

i n f o

a b s t r a c t

Article history: Available online xxx

Image processing plays an important role in various medical applications to support the computerized disease examination. Brain tumor, such as glioma is one of the life threatening cancers in humans and the premature diagnosis will improve the survival rate. Magnetic Resonance Image (MRI) is the widely considered imaging practice to record the glioma for the clinical study. Due to its complexity and varied modality, brain MRI needs the automated assessment technique. In this paper, a novel methodology based on meta-heuristic optimization approach is proposed to assist the brain MRI examination. This approach enhances and extracts the tumor core and edema sector from the brain MRI integrating the Teaching Learning Based Optimization (TLBO), entropy value, and level set / active contour based segmentation. The proposed method is tested on the images acquired using the Flair, T1C and T2 modalities. The experimental work is implemented and is evaluated using the CEREBRIX and BRAINIX dataset. Further, TLBO assisted approach is validated on the MICCAI brain tumor segmentation (BRATS) challenge 2012 dataset and achieved better values of Jaccard index, dice co-efficient, precision, sensitivity, specificity and accuracy. Hence the proposed segmentation approach is clinically significant. © 2017 Elsevier B.V. All rights reserved.

1. Introduction

the clinical study. The recent advancement in MRI technology helps to provide the complete details about the internal brain sections in the form of a three dimensional (3D) picture [7]. After recording the image, 3D or slice based analysis is carried out using a chosen image processing scheme to locate and localize the tumor for superior diagnosis and treatment planning. The brain image processing literature presents a number of methods to examine the abnormality using the MRI. The modern MRI examining procedures includes the neural network based approach [2,18,34], watershed segmentation [47], clustering techniques [1,9,37], fuzzy c-means algorithm [17,22,23,48], edge detection algorithm [6], ANFIS approach [50], Gaussian mixture models [12], cellular automata [49], multi-level thresholding [13], and heuristic approaches [24,32]. Moreover, recent work by Despotovic et al. [16] highlights that, combination of several techniques is essential to achieve better segmentation accuracy. Except the neural network based approaches [18,34], most of the above said tumor segmentation methods are modality based approaches, works well on the brain MRI registered with a particular modality. Hence, it is recommended to develop a unique segmentation and analysis tool for the MRI dataset, registered with a variety of modalities, such as Fluid Attenuation Inversion Recovery (Flair), spin lattice relaxation (T1), T1-contrast enhanced (T1C) and spin-

Brain tumor is one of the life threatening diseases for human community. The mainstream of brain tumor commences in the regions and associated parts of the brain. Bauer et al. [7] reported that, glioma is the most common brain tumor with the maximum morbidity and mortality rates. Based on its severity, brain tumor can be classified as the low and high grade gliomas [18, 34]. The availability of the latest therapeutic technology can help the human community in the early detection and examination of the gliomas during the screening inspection process. When the location and nature of glioma is identified, then the possible treatment procedure can be provided to cure the disease. After detecting the tumor, the oncologist will plan the one of the following treatment procedures; (i) radiation therapy, (ii) chemotherapy and (iii) surgery. In which the radiation and chemotherapy are recommended to slow down the tumor growth and the surgical procedure can be used to completely remove the tumor region [18, 34]. Magnetic Resonance Image (MRI) is the widely adopted procedure to record the brain abnormality using various modalities for

∗

Corresponding author. E-mail address: [email protected] (V. Rajinikanth).

http://dx.doi.org/10.1016/j.patrec.2017.05.028 0167-8655/© 2017 Elsevier B.V. All rights reserved.

Please cite this article as: V. Rajinikanth et al., Entropy based segmentation of tumor from brain MR images – a study with teaching learning based optimization, Pattern Recognition Letters (2017), http://dx.doi.org/10.1016/j.patrec.2017.05.028

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spin relaxation (T2). In this paper, a novel procedure based on meta-heuristic optimization is proposed to segment the tumor core and the edema regions from the brain MRI dataset recorded using Flair, T1C and T2 modalities. The proposed computer aided brain MRI segmentation methodology is grouped as (i) Pre-processing and (ii) Post-processing sections. Pre-processing section includes the skull stripping operation along with the global multi-thresholding scheme based on entropy function. In order to improve the multi-thresholding accuracy, maximal entropy function is integrated with the recent metaheuristic algorithm called the Teaching Learning Based Optimization (TLBO) algorithm introduced by Rao et al. [41]. In this section, an investigation on some well known maximal entropy functions such as Kapur [21], Tsallis [51] and Shannon [19] also presented. Image quality based analysis is carried out between the original brain MRI image and the multi-threshold image in order to identify the best entropy function among the Kapur, Tsallis and Shannon approaches. The post-processing section is used to extract the tumor core and edema based on chosen segmentation procedure. This section presents examination with some well known segmentation procedures such as the level set approach [27], local active contour [26] and global active contour [10]. After the segmentation, a comparative study involving the segmented tumor region and the expert’s ground truth is performed to evaluate the significance of proposed segmentation approaches. During the experimental work, various appearances of brain images such as coronal, sagittal and axial views obtained from Cerebrix and Brainix dataset [56] are initially considered for the analysis. The validation of the proposed procedure is done using the MICCAI brain tumor segmentation (BRATS) challenge 2012 dataset [57]. Further, few abnormal MRI images of brain deviations like, Craniophryngioma (CP), High Grade Glioma (HGG) and Microadenoma (MA) of Radiopaedia [58] is also considered for the analysis. This study, confirms that, the brain tumor segmented using the Shannon’s entropy function and level set approach offers better result compared with the Kapur’s function and Tsallis functions. Finally, the performance of Shannon’s entropy and level set based procedure is validated against the Fuzzy c-means algorithm (FCM) [17], Particle Swarm Optimization with Markov Random Field (PSO-MRF) [32] and Principal Component Analysis (PCA) [55] existing in the literature.

Fig. 1. Structure of the proposed segmentation process.

timization problems [40, 42]. A comprehensive description about the TLBO can be found in [39, 43]. Fig. 1 depicts the pseudo code of the traditional TLBO algorithm adopted in this paper. Pseudo code of the TLBO algorithm START; Initialize the algorithm with number of learners (NT ), search dimension (D), Maximum iteration (Miter ) and the objective value ( Jmax ); Arbitrarily initialize ‘NT ’ learners for xj (j = 1, 2, … n); Assess the routine and choose the finest solution f(xbest ); WHILE iter = 1:Miter ; %TEACHER PHASE% Use f(xbest ) as teacher; Sort based on f(x), chose new teachers based on: f(x)s = f(xbest ) – rand for f(x)s = 2,3, . . ., T; FOR j = 1:n Compute TFj = round[1 + rand (0, 1 ){2 − 1}]; j = x j + rand (0, 1 )[xteacher − (TFj .xmean )]; xnew % Calculate objective value; f(xj new )% If f(xj new ) < f(xj ), then xj = xj new ; End If % End of TEACHER PHASE% %STUDENT PHASE% Randomly chose the learner xj , such that k = j; If f(xj ) < f(xk ), then xj new = xj + rand(0,1)(xj − xk ); Else xj new = xj + rand(0,1)(xk – xj ); End If If xj new is better than xj , then xj = xj new ; End If % End of STUDENT PHASE% End FOR Set m = m+ 1; End WHILE Record the threshold values, Jmax , and performance measures and CPU time; STOP;

2. Methodology

2.1.1. TLBO

2.1.2. Skull stripping Skull stripping is the initial step in the brain MRI segmentation process. It is necessary to eliminate the skull from the background area from MRI for quantitative analysis. Skull stripping is usually performed using an image filter which separated the skull and the rest of the image sections by masking the pixels having similar intensity levels. In MR image, normally the skull/bone section will have a maximum threshold value (threshold > 200) compared to the tumor and other brain regions. Hence, the image filter is used to separate the brain regions based on a chosen threshold value. Then by employing the solidity property, the skull is stripped from the brain MRI. In this paper, the skull stripping procedure discussed by Chaddad and Tanougast [13] is adopted.

Teaching Learning Based Optimization (TLBO) algorithm is a recently developed meta-heuristic procedure based on the mathematical model of the teaching-learning practice existing in the classroom scenario [41]. It is an optimal search procedure among two closed linked set, such as teacher phase and learner phase. The teacher stage starts learning from a most outstanding teacher and the scholar stage authorize the students to learn through interactions. Due to its superiority, TLBO approaches are widely implemented by the researchers to solve a variety of engineering op-

2.1.3. Multi-level thresholding In recent years, traditional and heuristic algorithm assisted multi-level image thresholding is adopted by most of the researchers due to its significance [46, 52]. During this process, a digital image frame is divided into multiple regions by grouping similar pixel values in order to locate and examine all the significant information available in the image. From the image processing literature, it can also be noted that, the implementation of multilevel thresholding is uncomplicated for gray scale image compared

This paper focuses on developing the meta-heuristic algorithm supported tool to extract tumor and edema from the brain MRI irrespective of modalities. The proposed work is segregated as the pre-processing and post-processing section. 2.1. Pre-processing The overall accuracy of the proposed meta-heuristic assisted segmentation approach depends mainly on the pre-processing stage.

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to the RGB images [38]. In this work, all the MRI modality offers a gray scaled brain image; hence the implementation of the TLBO assisted multi-level thresholding is quite easy. From the literature, it can be observed that, entropy based approaches are widely adopted by the researchers to analyze the abnormality in medical images [15,35,36] as well as signals [3,20]. In this paper, TLBO and entropy function based multi-level thresholding process is chosen as the pre-processing stage. A comparative study among the most successful entropy functions, such as Kapur, Tsallis and Shannon’ s entropy are also presented.

2.1.3.3. Tsallis function. The entropy is related to the chaos measure within a system. Shannon initially considered the entropy to measure the ambiguity regarding the information content of the system [51]. Shannon stated that: when a physical system is separated as two statistically free subsystems A and B, then the entropy value can be expressed as:

2.1.3.1. Kapur’s function. Kapur’s image segmentation was initially proposed in 1985 to segment the gray scale image using the entropy of the histogram [21]. This approach finds the optimal T which maximizes overall entropy [8, 45]. Let, T = [t1 , t2 , …, tk-1 ] is a vector of the image thresholds. Then, Kapur’s entropy will be;

Sq =

Jmax = fkapur (T ) =

k 

(1)

Generally, each entropy is computed independently based on the particular t value. For multi-level thresholding problem, it can be expressed as;



t

1  P hCj

j=1

ω

C 0

ln

H2C =

ω

C 1

j=tl+1

ω 

ln

.. . HkC

L  P hCj j=tk+1

ω

C k−1



C 0

t2

 P hCj

P hCj

 ln

(6)

Based on Shannon’s theory, a non-extensive entropy concept was proposed by Tsallis [4,8,54] and which is defined as:

1−

T

i=1

( pi )q

(7)

q−1

Where T is the system potential, q is the entropic index, and pi denotes the probability of each state i. Typically, the Tsallis entropy Sq will meet Shannon’s entropy when q → 1. The entropy value can be expressed using a pseudo additive rule as:

Sq ( A + B ) = Sq ( A ) + Sq ( B ) + ( 1 − q ).Sq ( A ).Sq ( B ) f or C {1, 2, 3}

HCj

j=1

H1C =

S (A + B ) = S (A ) + S (B )

P hCj

ω

f (T ) = [t1 , t2 , . . . , tk−1 ] = argmax



where

(2)



SqA

SqB

(T ) = (T ) =

1−

ωC0 , ωC1 , ...ωCk−1

probability occurrence for k levels. Detailed explanation for the Kapur’s function can be found in Akay [5] and Lakshmi et al. [25]. In the proposed work, the Kapur’s function discussed by Manic et al. [30] is implemented. 2.1.3.2. Shannon’s function. Entropy is usually adopted to compute the ambiguity of a variable [19]. The detailed information regarding Shannon entropy can be found in Paul and Bandyopadhyay’s work [33]. The procedure is as follows: Let us choose an image frame of size M∗ N. Then, the gray value of the pixel with coordinates (x, y) can be expressed as f (x, y), for x ∈ {1, 2, ..., M} and y ∈ {1, 2, ..., N}. Let L be the number of gray levels of image I0 and the set of all gray levels {0,1,2,…, L−1} can be symbolized as G, in such a way that:

f (x, y ) ∈ G∀(x, y ) ∈ image

(3)

The normalized histogram of the image can be represented as H = {h0 , h1 , …, hL-1 }. For multi-thresholding problem, the above equation can be written as;

H (T ) = h0 (t1 ) + h1 (t2 ), . . . , hL−1 (tk−1 )

(4)

T ∗ = max {H(T )}

(5)

T

in which T∗ is the optimal threshold. Shannon’s entropy should satisfy Eq. (5).

SqK

(T ) =

t1 −1  Pi q i=0

PA

, PA =

q−1 1−

i=t1

PB

1−

L−1

i=tk−1

q−1

Pi

(9.1)

Pi

(9.2)

t

, PB =

2 −1 

i=t1

 Pi q PK

t1 −1  i=0

t2 −1  Pi q q−1

ω

where P hCj is the probability distribution of the intensity levels and

 (9)

SqA (T ) + SqB (T ) + . . . + SqK (T ) + (1 − q ).SqA (T ).SqB (T ) . . . SqK (T )

,

C 1

P hCj C K−1

The Tsallis entropy can be considered to find the optimal thresholds of an image. Consider a given image with L gray levels in the range {0,1, …, L−1} with probability distributions pi = p0 , p1 , …, pL -1 . Thus, the Tsallis multi-level thresholding can be obtained using the following objective function:



,

(8)

, PK =

L−1 

Pi

(9.3)

i=tk−1

During the multi-level thresholding process, it is required to determine the optimal threshold value T which maximizes the objective function f(T). In the present work, (f(T)) maximization was carried using the TLBO algorithm. 2.2. Post processing The post-processing stage is implemented to extract the glioma section from the pre-processed brain MRI image. This section presents the details of the well known level set and active contour segmentation approaches considered in this work. 2.2.1. Level set Level Set (LS) approaches have been broadly used in image segmentation applications. This procedure was initially implemented in 1990’s [11, 29]. An added advantage of the LS contrast to the active contour approach is, LS can produce contours of complex topology to handle splitting and merging operation during the image outline search. This paper implements the recent version of LS methodology [27] to segment the tumor region of brain MRI database. The chosen LS approach can be mathematically expressed as follows:

Let the curve evolution is =

∂ C  (s, t ) = FN ∂t

(10)

where, C is the curve vector with the spatial parameter (s) and temporal variable (t), F is the speed function and N is the inmost

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normal vector to the curve C . The curve evolution in Eq. (7) can be converted into the LS by implanting the dynamic contour C (s, t) as the zero LS of a time charged level set function φ (x,y,t). The parameter φ offers negative values inside the zero level contour and positive values outside. The inner most normal vector N can be expressed as;

N=

−∇φ

(11)

∇φ

where ∇ is the gradient operator. The LS evolution equation can be expressed as;

∂φ = F |∇φ| ∂t

(12)

More details regarding the chosen LS function in this work can be found in Vaishnavi et al. [53].

Fig. 2. Brain MRI dataset (a) Test image (Coronal, Sagittal and Axial), (b) Skull stripped image, (c) Kapur’s thresholding, (d) Tsallis thresholding, (e) Shannon’s thresholding.

2.2.2. Active contour Active Contour (AC) is an essential segmentation procedure to extract the suspicious region from pre-processed image. In this paper, deformable snake based AC [10] and localized AC [14] are also considered to extract the tumor from the pre-processed image. This procedure has the following essential steps, such as initialization, boundary detection and extraction based on minimized energy. This approach tracks the similar pixel groups existing in pre-processed image based on energy minimization concept as discussed by Lankton and Tannenbaum [26]. The energy function of the AC can be denoted as;



min EGAC (C ) = C



 L (C )

g(|∇ I0 C(s ))|ds

0

(13)

where ds is the Euclidean component of length and L(C) is the

L (C ) length of the curve C which satisfies L(C ) = 0 ds. The parameter g is an edge indicator, which will disappear based on the object boundary defined as;

g(|∇ I0 | ) =

1 1 + β|∇ I0 |

2

(14)

where I0 represents original image and β is an arbitrary constant. The energy value rapidly decreases based on the edge value, based on gradient descent criterion. This procedure is mathematically represented as;

∂t C = (kg − ∇g , N )N

(15)

where ∂t C = ∂ C/∂ t represents the deformation in the snake model, t is the iteration time, and k, N are the curvature and normal for the snake C. In this procedure, the snake silhouette is continuously corrected till minimal value of the energy; EGAC is achieved. 2.3. Image quality assessment In this paper, two types of MRI datasets, such as brain image with skull and without skull sections are considered. For both the cases, the tri-level thresholding quality is assessed using the image quality measures, such as peak signal-to-noise ratio (PSNR), normalized cross-correlation (NCC), normalized absolute error (NAE) and structural similarity index (SSIM) [44]. Further, the segmented tumor mass is analyzed using a comparative study with the expert’s ground truth image. Firstly, the image similarity measures, such as Jaccard index, Dice coefficient, False Positive Rate (FPR), and False Negative Rate (FNR) are computed [13]. The mathematical expression is presented below;

Fig. 3. Segmentation result of Level set and Active contour approaches: (a) Kapur, (b) Tsallis, (c) Shannon.

F P R(Igt , It ) = (Igt /It )/(Igt ∪ It )

(18)

(19)

JSC (Igt , It ) = Igt ∩ It /Igt ∪ It

(16)

F NR(Igt , It ) = (It /Igt )/(Igt ∪ It )

DSC (Igt , It ) = 2(Igt ∩ It )/|Igt | ∪ |It |

(17)

where, Igt represents the ground truth image and It stands for the segmented tumor image.

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V. Rajinikanth et al. / Pattern Recognition Letters 000 (2017) 1–9 Table 1 Quality measure values of multi-threshold images. Entropy

Slice

PSNR

NCC

NAE

SSIM

Kapur

Coronal Sagittal Axial Average Coronal Sagittal Axial Average Coronal Sagittal Axial Average

16.3173 14.8605 15.8953 15.7186 17.0187 15.0823 16.0176 15.3218 31.0579 27.6764 18.5289 26.3405

0.3923 0.2046 0.1742 0.2780 0.4842 0.2402 0.2279 0.3696 0.9882 0.9600 0.4340 0.8302

0.6852 0.8570 0.8880 0.7692 0.6112 0.8328 0.8693 0.7288 0.1091 0.1465 0.6373 0.2840

0.7955 0.7095 0.6992 0.7539 0.8083 0.7153 0.6983 0.7082 0.9295 0.9205 0.7943 0.8812

Tsallis

Shannon

Table 2 Segmented tumor region with the level set approach.

View

Kapur

Tsallis

Shannon

Sagittal

Axial

Further, the image statistical measures, such as precision (PRE), F-measure (FM), sensitivity (SEN), specificity (SPE), Balanced Classification Rate (BCR), Balanced Error Rate (BER) and accuracy (ACC) are also computed [28,31]. The capability of the level set approach and active contour approaches are then computed using the image similarity and the statistical measures. 3. Results and discussions This section presents the experimental results of the proposed brain MRI segmentation and analysis work. The proposed procedure is initially implemented on 256 × 256 sized various brain MR images, such as coronal, sagittal and axial views obtained from Cerebrix and Brainix dataset. Later, the proposed method is validated using 216 × 160 sized MICCAI brain tumor segmentation

(BRATS) challenge 2012 dataset images (a sum of 72 images of 6 patients recorded with Flair, T1C and T2 modalities). Fig. 1 depicts the proposed approach considered to segment the brain MRI dataset. The brain MRI images are initially recorded in a controller environment with a chosen modality. After choosing a test image, initially the pre-processing procedure is executed to enhance the image regions. This stage involves in the skull stripping procedure and a tri-level thresholding process. The reliability of pre-processing section is then analyzed based on the image quality measures. In the post-processing section a suitable segmentation approach is implemented to mine the tumor region from the pre-processed MRI. Finally the mined tumor section is compared against the ground truth offered by an expert member and the essential information like similarity measures and the statistical measures are computed. Fig. 2 shows the sample images of Cerebrix and Brainix dataset initially considered for the study. During the implementation process, 10 slices of each test images are considered for the analysis. As shown in Figs. 1 and 2(b), initially the skull stripping is applied to remove the skull section from the rest image. The image pixels of the skull stripped image are then grouped using the TLBO algorithm assisted tri-level thresholding process with the maximization of entropy value. Each image is separately analyzed using the well known entropy approaches, such as Kapur (Fig. 2(c)), Tsallis (Fig. 2(d)) and Shannon (Fig. 2(e)). In order to assess the superiority among the considered entropy based analysis, well known image quality measures, like PSNR, NCC, NAE and SSIM are computed as presented in Table 1. From this table, it can be observed that, average of image quality measures obtained with the Shannon’s entropy is better than the alternatives considered in this work. This confirms that, Shannon entropy function can be considered during the preprocessing work in order to have the better segmentation of the tumor region from the brain MRI dataset. Fig. 3 shows the experimental result of the post-processing section of Coronal test image. From this result, it can be noted that, the brain MRI extracted using the Shannon entropy and level set offers better result compared with the localized AC (LAC) and global AC (GAC) considered in this work. Similar procedure is repeated for the other test images considered in this work and the results for the sagittal and axial test images are presented in Table 2. This confirms that, level set approach is superior to the active contour for the proposed segmentation work.

Table 3 BRATS image dataset registered with Flair, T1C, and T2 modality.

T1C

T2

Ground truth

Tumor core

Slice130

Slice120

Slice110

Slice100

Flair

5

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Table 4 Multi-thresholding of Flair images with different entropy approaches.

Kapur

Tsallis

Test image

Shannon

Kapur

Tsallis

Shannon

Slice110

Slice110

Slice120

Slice120

Slice130

Slice130

Slice100

Slice100

Test image

Table 7 Multi-thresholding of T1C image with different entropy approaches.

Table 8 Image similarity measures for T1C brain MRI images.

Table 5 Segmented tumor core and edema region using the level set.

Modality

Slice100

Slice110

Slice120

Slice130

T1C

Slice

Jaccard

Dice

FPR

FNR

Kapur

100 110 120 130 Average 100 110 120 130 Average 100 110 120 130 Average

0.8972 0.7743 0.7147 0.6536 0.7599 0.8583 0.7581 0.7120 0.5486 0.7192 0.8816 0.8397 0.7485 0.6650 0.7837

0.9458 0.8728 0.8336 0.7905 0.8607 0.9238 0.8624 0.8317 0.7085 0.8316 0.9371 0.9128 0.8562 0.7988 0.8762

0.0546 0.1134 0.2356 0.1973 0.1502 0.0725 0.1056 0.1373 0.0852 0.1002 0.0794 0.1098 0.1654 0.1446 0.1248

0.0539 0.1379 0.1169 0.2175 0.1316 0.0794 0.1618 0.1903 0.4047 0.2090 0.0483 0.0682 0.1277 0.2388 0.1208

Flair

T1C

Tsallis

T2 Shannon

Table 6 Image similarity measures for Flair MRI images. FPR

FNR

0.8995 0.8668 0.8715 0.8162 0.8635 0.8942 0.8906 0.8272 0.7920 0.8510 0.9078 0.9564 0.9401 0.9057 0.9275

0.0644 0.0177 0.0570 0.1014 0.0601 0.1839 0.0881 0.0542 0.0770 0.1008 0.0558 0.0493 0.0691 0.1021 0.0691

0.1301 0.2216 0.1838 0.2406 0.1940 0.0427 0.1264 0.2564 0.2939 0.1799 0.1225 0.0383 0.0518 0.0878 0.0751

Tsallis

Shannon

Similar approach is then tested on the MICCAI brain tumor segmentation (BRATS) challenge 2012 dataset. During this study, brain MR images of fifteen patients are considered. The sample images of a patient considered for the analysis is presented in Table 3. During this study, the MR images registered using the Flair, T1C and T2 are considered. This table also shows the ground truth region and the tumor core of the considered MRI slices. The considered dataset does not require the skull stripping section. The tumor extraction procedure is initially implemented for the Flair modality images and the outcome of the pre-processing section is depicted in Table 4. This table clearly shows the tri-level threshold images of various entropy values like Kapur, Tsallis and Shannon. During the post-processing operation, the tumor region is extracted from the pre-processed image using the level set approach as discussed earlier and its results are presented in Table 5.

Table 9 Multi-thresholding of T2 image with various entropy approaches.

Test image

Kapur

Tsallis

Shannon

Slice100

Dice

0.8173 0.7649 0.7722 0.6895 0.7610 0.8086 0.8029 0.7054 0.6556 0.7431 0.8311 0.9165 0.8869 0.8277 0.8655

Slice110

Jaccard

100 110 120 130 Average 100 110 120 130 Average 100 110 120 130 Average

Slice120

Slice

Kapur

Slice130

Entropy

The vital image metrics, such as the similarity measures and the statistical measures are then computed by comparing the extracted tumor with the ground truth image and the corresponding results are presented in Table 6. Similar procedure is then adopted for the modalities T1C and T2 and its results are depicted in Tables 7–10. From Tables 5 and 7, it can be observable that, T1C modality offers only the tumor core and the rest of the modalities are efficient in offering the tumor core and edema sections.

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Table 12 Average similarity measures obtained for BRATS dataset.

Table 10 Image similarity measures for T2 brain MRI images. T2

Slice

Jaccard

Dice

FPR

FNR

Method

Jaccard

Dice

FPR

FNR

Kapur

100 110 120 130 Average 100 110 120 130 Average 100 110 120 130 Average

0.7853 0.8701 0.8451 0.5873 0.7719 0.7938 0.7976 0.6674 0.7108 0.7424 0.7925 0.8857 0.8459 0.8247 0.8372

0.8797 0.9305 0.9161 0.7400 0.8666 0.8850 0.8874 0.8006 0.8310 0.8510 0.8842 0.9394 0.9165 0.9039 0.9110

0.0965 0.0409 0.0619 0.0623 0.0654 0.0631 0.0674 0.0599 0.0878 0.0696 0.0919 0.0510 0.0708 0.1051 0.0797

0.1389 0.0943 0.1026 0.3761 0.1780 0.1561 0.1486 0.2925 0.2267 0.2060 0.1346 0.0691 0.0941 0.0886 0.0966

SE-LS FCM PSO-MRF PCA

0.8377 0.8301 0.8294 0.8274

0.9408 0.9381 0.9316 0.9316

0.0395 0.0417 0.0491 0.0501

0.0814 0.0903 0.0960 0.0917

Tsallis

Shannon

Table 13 Average statistical measures achieved for BRATS dataset.

Table 11 shows the image statistical measures obtained for the BRATS 2012 dataset registered with Flair, T1C and T2 modalities. Each image is independently pre-processed with the Kapur, Tsallis and Shannon entropy approaches and the corresponding tumor section is extracted using the level set segmentation approach. The average values of the PRE, FM, SEN, SPE, BCR, BER and ACC confirms that, the Shannon Entropy and Level Set (SE-LS) approach offers superior result compared with the alternatives Further, the potential of SE-LS is tested against the FCM, PSO-MRF and PCA approaches using the BRATS dataset and the average values of simi-

Method

SEN

SPE

ACC

SE-LS FCM PSO-MRF PCA

0.9815 0.9802 0.9796 0.9807

0.8277 0.8251 0.8268 0.8271

0.9413 0.9388 0.9397 0.9374

larity measures and statistical measures are presented in Tables 12 and 13 respectively. The results of these tables confirm that SE-LS approach offers better Jaccard index of 83.77%, Dice co-efficient of 94.08%, FPR of 3.95%, FNR of 8.14%, sensitivity of 98.15%, specificity of 82.77% and accuracy of 94.13% values on the BRATS dataset. Finally, the efficacy of the SE-LS method is tested by considering the images of well known brain tumor cases, such as Craniophryngioma (CP), High Grade Glioma (HGG) and Microadenoma (MA) available in Radiopaedia [58]. During this study, 10 separate image slices of Flair, T1C and T2 modalities are chosen for the anal-

Table 11 Image statistical measures for the BRATS 2012 dataset. Entropy

Modality

Slice

PRE

FM

SEN

SPE

BCR

BER

ACC

Kapur

Flair

100 110 120 130 100 110 120 130 100 110 120 130

0.9833 0.9667 0.9761 0.9801 0.9976 0.9919 0.9944 0.9942 0.9821 0.9855 0.9865 0.9694 0.9840 0.9944 0.9805 0.9669 0.9759 0.9965 0.9905 0.9910 0.9894 0.9800 0.9772 0.9625 0.9813 0.9822 0.9843 0.9940 0.9931 0.9926 0.9979 0.9960 0.9939 0.9937 0.9827 0.9893 0.9876 0.9926 0.9915

0.9874 0.9817 0.9842 0.9858 0.9976 0.9926 0.9916 0.9945 0.9848 0.9895 0.9891 0.9819 0.9884 0.9852 0.9834 0.9797 0.9846 0.9967 0.9921 0.9922 0.9935 0.9859 0.9833 0.9770 0.9869 0.9867 0.9885 0.9932 0.9920 0.9921 0.9972 0.9947 0.9930 0.9949 0.9854 0.9907 0.9891 0.9919 0.9919

0.9917 0.9973 0.9925 0.9915 0.9976 0.9933 0.9888 0.9948 0.9875 0.9936 0.9918 0.9948 0.9929 0.9762 0.9863 0.9928 0.9936 0.9968 0.9938 0.9935 0.9977 0.9918 0.9895 0.9921 0.9927 0.9914 0.9928 0.9923 0.9909 0.9915 0.9965 0.9935 0.9921 0.9962 0.9881 0.9921 0.9906 0.9912 0.9923

0.8699 0.7784 0.8162 0.7594 0.9461 0.8621 0.8831 0.7825 0.8611 0.9057 0.8974 0.6239 0.8321 0.9573 0.8736 0.7436 0.7061 0.9206 0.8382 0.8097 0.5953 0.8439 0.8514 0.7075 0.7733 0.8017 0.8775 0.9617 0.9482 0.9122 0.9517 0.9318 0.8723 0.7612 0.8654 0.9309 0.9059 0.9114 0.9025

0.9308 0.8878 0.9043 0.8755 0.9718 0.9277 0.9359 0.8886 0.9243 0.9497 0.9446 0.8093 0.9125 0.9667 0.9299 0.8682 0.8498 0.9587 0.9160 0.9016 0.7965 0.9179 0.9205 0.8498 0.8829 0.8965 0.9351 0.9770 0.9695 0.9518 0.9741 0.9627 0.9322 0.8787 0.9267 0.9615 0.9482 0.9513 0.9474

6.9208 11.2182 9.5668 12.4540 2.8127 7.2278 6.4021 11.1358 7.5704 5.0343 5.5371 19.0665 8,.7455 3.3239 7.0049 13.1777 15.0173 4.1295 8.4015 9.8405 20.3482 8.2135 7.9536 15.0236 11.7031 10.3448 6.4864 2.2996 3.0456 4.8183 2.5908 3.7311 6.7782 12.1310 7.3262 3.8529 5.1749 4.8683 5.2586

0.9288 0.8810 0.90 0 0 0.8677 0.9715 0.9254 0.9345 0.8823 0.9221 0.9486 0.9434 0.7878 0.9078 0.9667 0.9282 0.8592 0.8376 0.9579 0.9127 0.8969 0.7707 0.9149 0.9179 0.8378 0.8761 0.8897 0.9334 0.9769 0.9693 0.9510 0.9738 0.9622 0.9303 0.8708 0.9247 0.9610 0.9473 0.9505 0.9459

T1C

T2

Tsallis

Average Flair

T1C

T2

Shannon

Average Flair

T1C

T2

Average

100 110 120 130 100 110 120 130 100 110 120 130 100 110 120 130 100 110 120 130 100 110 120 130

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Fig. 4. Results obtained for the Radiopaedia dataset (a) Test image, (b) Skull stripped image, (c) SE-LS, (d) FCM, (e) PSO-MRF, (f) PCA.

ysis and the results obtained for the sample image is depicted in Fig. 4. From this result, it can be noted that, the SE-LS approach offers considerable result compared with the alternatives. In this study, a novel two stage approach by integrating the meta heuristic multi-thresholding and the segmentation approach is presented to extract the tumor region from the well known brain MRI dataset. This work also presented a detailed comparative study between the well known entropy approaches such as Kapur, Tsallis and Shannon. This study confirmed that, Shannon’s approach is efficient in providing better image quality measures for the considered dataset. Further, a detailed comparative study among the level set, localized active contour and global active contour also presented. Finally, integration of Shannon entropy with level set segmentation (SE-LS) is validated against the FCM, PSOMRF and PSC using the BRATS dataset and using the images collected from Radiopaedia. From this work, it is confirmed that, the SE-LS offers the superior result compared with the other methods considered in this paper. 4. Conclusion In this paper, Teaching Learning Based Optimization (TLBO) algorithm assisted segmentation and analysis of brain tumor is demonstrated by considering well known brain MR images. Proposed approach is an automated procedure and effectively extracts the tumor mass from the MRI dataset obtained using various modalities, such as T1, T2 and Flair. The proposed approach is grouped in to two sections, namely the pre-processing region and the post-processing region. The experimental result shows that, combination of Shannon’s entropy based thresholding and level set segmentation offers better result for the considered dataset. The competence of the proposed segmentation procedure is validated using the BRATS 2012 dataset. Results of this study also exhibit that, the segmented tumor mass is approximately similar to the ground truth image and offers better values of Jaccard, Dice, FPR and FNR for the T1, T2 and Flair MRI dataset. The accuracy measure values, such as precision, F-measure, sensitivity, specificity, BCR, BER and accuracy are also better. Hence the proposed segmentation approach is clinically significant. References [1] E. Abdel-Maksoud, M. Elmogy, R. Al-Awadi, Brain tumor segmentation based on a hybrid clustering technique, Egypt. Inform. J. 16 (1) (2015) 71–81, doi:10. 1016/j.eij.2015.01.003. [2] A.A. Abdullah, B.S. Chize, Z. Zakaria, Design of cellular neural network (CNN) simulator based on matlab for brain tumor detection, J. Med. Imaging Health Inform. 2 (3) (2012) 296–306, doi:10.1166/jmihi.2012.1095. [3] U.R. Acharya, H. Fujita, V.K. Sudarshan, S. Bhat, J.E.W. Koh, Application of entropies for automated diagnosis of epilepsy using EEG signals, Knowl.-Based Syst. 88 (C) (2015) 85–96, doi:10.1016/j.knosys.2015.08.004.

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Please cite this article as: V. Rajinikanth et al., Entropy based segmentation of tumor from brain MR images – a study with teaching learning based optimization, Pattern Recognition Letters (2017), http://dx.doi.org/10.1016/j.patrec.2017.05.028