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Cerebral edema segmentation using textural feature
biocybernetics and biomedical engineering 39 (2019) 599–612
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/bbe
Original Research Article
Cerebral edema segmentation using textural feature Archana Chaudhari, Jayant Kulkarni * Department of Instrumentation Engineering, Vishwakarma Institute of Technology, Pune, India
article info
abstract
Article history:
Diagnostic imaging provides a vital tool in detection and analysis of Brain pathologies.
Received 15 July 2018
Magnetic resonance imaging (MRI) provides an effective means for non-invasive mapping of
Received in revised form
anatomy and pathology in the brain. Pathologies like cerebral edema and tumors can spread
8 February 2019
in different tissues in the brain and can affect cognitive and other functions in the body.
Accepted 4 June 2019
Accurate segmentation is therefore a challenging task. Human Brain consists of different
Available online 11 June 2019
soft tissues. These tissues can be characterized using different textures.
Keywords:
MR image. The texture of MR image is exploited using the gray co-occurrence matrix (GLCM).
MRI
GLCM creates a textural feature map by taking into account the spatial dependence of the
The work presents an automatic method for segmentation using textural feature of the
Local entropy
pixels and its angular relationship between the neighboring cell pairs. Local entropy as
Brain
second order textural feature is used to capture the texture of MR image. Entropy computes
Segmentation
the randomness in pixel intensities and helps in defining a unique texture of edema for
GLCM
segmentation. The marked contrast enhancement obtained in FLAIR sequence of the MR
Cerebral edema
image is captured as textural information by local entropy and GLCM combination. The proposed method obtains a definite textural signature of edema as well as tumor for threshold selection. Experiments on publically available BRATS database yields an average accuracy of 96%, specificity of 97%, sensitivity of 61%, Dice Coefficient as 50% and structural similarity index of 0.88 for edema. The proposed method demonstrates encouraging results in automatic segmentation of edema as well as tumor core. © 2019 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved.
1.
Introduction
Cerebral edema is a condition that develops as a result of an inflammatory reaction. Most frequently, this is the consequence of cerebral trauma, massive cerebral infarction,
hemorrhages, abscess, tumor, allergy, sepsis, hypoxia, and other toxic or metabolic factors [1]. It is a serious disorder that accompanies an extensive array of pathological processes such as tumors and ischemia [2]. As the brain has little space to expand and does not have a lymphatic system to remove excess fluid, cerebral edema is a potentially life-threatening
* Corresponding author at: Department of Instrumentation Engineering, Vishwakarma Institute of Technology, 666 Upper Indira Nagar, Bibwewadi, Pune 411037, India. E-mail addresses: [email protected] (A. Chaudhari), [email protected] (J. Kulkarni). https://doi.org/10.1016/j.bbe.2019.06.002 0208-5216/© 2019 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved.
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biocybernetics and biomedical engineering 39 (2019) 599–612
condition [3]. Timely and effective diagnose and control of cerebral edema could help to reduce the mortality rate. Mechanisms for early detection and diagnosis are poorly understood and reliable markers are lacking [4]. Medical imaging plays an important role in the early detection, diagnosis and treatment of cerebral edema and tumors. Magnetic resonance imaging (MRI) is preferred modality for brain imaging because of its non invasive nature and good differentiation of soft tissues, useful in imaging tumor origin. The different modalities of MR images and ease of acquisition in many planes makes it a popular modality for clinical diagnosis and analysis. More than one MRI modality is often employed for brain pathology detection and analysis such as T1 weighted (T1-w), T2-weighted (T2-w), Proton Density (PD), Fluid attenuation Inversion Recovery (FLAIR), Diffusion MRI, Gadolinium enhanced T1-w images (T1-c). The contrast between these modalities gives almost a unique signature to each tissue type [5]. Diagnosis and treatment of cerebral edema and tumor involves image processing operations. For further analysis and to extract hidden information, segmentation of these images is required for better visualization of different regions [6]. Brain consists of three tissues, white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF). It is important to locate the tumor and the extent of tumor regions namely active tumor tissue, necrotic tissue, and edema (swelling near the tumor) [5]. The goal of image processing is to detect the location and extent of the tumor or edema using segmentation methods. Few pre-processing steps are required for image segmentation. Skull stripping an important pre-processing operation is applied to remove the skull. MR images may contain artifacts like intensity inhomogenity and noise. These artifacts along with noise are removed in the preprocessing stage. Several methods in literature have been proposed for brain tumor segmentation. Segmentation techniques can be broadly divided into supervised or unsupervised. Supervised technique consists of training and testing database. In training labels are assigned to the tumor and segmentation is achieved using a classification technique. In unsupervised segmentation the image data is not labeled and can be performed using an anatomic objective measure or an image-based objective measure [7]. Segmentation can be performed using manual delineation by human expert or by partial intervention in semi automatic method or fully automatic without any human intervention. Segmentation methods can be broadly divided into pixel classification based, region based, and threshold based and model based [7].
1.1.
Related work
Thresholding based methods are simple segmentation methods in which image gray levels are used to threshold the object from the image. The object can be segmented using several individual thresholds or by using a multi-thresholding technique. When only the pixel intensity is considered, the threshold method can be classified as global threshold. A local threshold is determined adaptively in a local region around a pixel [7]. According to Yao the values of thresholds are generally estimated by the prior knowledge [8]. Local threshold values can also be estimated using the local statistical
or textural image properties. Segmentation based on the gray levels of the image may not give desired results; therefore several texture based segmentation methods are proposed in literature [9–12]. The textural properties are derived using the first or second order statistics of the histogram or the cooccurrence matrix. Mean standard deviation and entropy can be defined as texture features derived using first order statistics. Entropy is defined as the measure of randomness in an image. Several methods have been proposed on entropy-based thresholding. Some of these methods use the gray-level histogram, while others use entropy associated with the two-dimensional histogram or the co-occurrence matrix [13]. Shannon defined entropy as a measure of uncertainty in terms of information theory [14]. Shannon entropy is a special case of Renyi's entropy and parametric family of information measures is defined as Renyi's entropy. Entropy based approaches are widely adopted by the researchers to analyze the abnormality in medical images [15–18] as well as signals [19,20]. A new method for gray level picture thresholding using entropy of the histogram, was proposed by Pun in 1980 and a new approach to entropic thresholding in 1981 [21,22]. Kapur et al. proposed to segment the gray scale image using the entropy of the histogram [23] along with some improvements in Pun's method. In the work of Kapur et al. the optimal threshold is obtained which maximizes overall entropy [24,25]. Sahoo et al. further introduced the concept of threshold selection using Renyi's entropy [26]. Chang et al. proposed relative entropy-based approach to image thresholding [27]. Pal et al. proposed a new method on minimum cross-entropy thresholding [28]. Brink et al. proposed a method to determine the optimum threshold using cross entropy as non metric measure [29]. Chen et al. proposed a fast two-dimensional entropic thresholding algorithm [30]. Li et al. proposed an iterative algorithm for minimum cross entropy thresholding [31]. Tsallis entropy [32] is obtained from the two dimensional histogram determined by using gray value of the pixels and is applied as a generalized entropy formalism [33]. The work by Sahoo et al. presents a new thresholding technique based on two-dimensional Renyi's entropy [34]. Albuquerque et al. proposed image thresholding using Tsallis entropy [35]. Yan et al. proposed local entropy-based transition region extraction and thresholding to effectively reduce the affects of noise during image segmentation [36]. Sahoo et al. presented a thresholding technique based on two-dimensional TsallisHavrda-Charvat entropy [37]. Li et al. developed a criterion of maximum fuzzy entropy for selecting the threshold to breast cancer detection [38]. Cheng et al. proposed a novel fuzzy entropy approach to image enhancement and thresholding [39]. Bloch reviewed the applications of fuzzy spatial relationship in image processing and image interpretation area [40]. Tao et al. proposed a 3-level fuzzy entropy based image segmentation technique [41]. Several methods using fuzzy entropy have been proposed in literature for image segmentation [42–46]. The fuzzy c-partition entropy has been widely adopted as a global optimization technique for finding the optimal thresholds when performing multilevel gray image segmentation. Nevertheless, existing fuzzy c-partition entropy approaches
biocybernetics and biomedical engineering 39 (2019) 599–612
generally have two limitations, partition number needs to be manually tuned for different input and the methods can process gray scale images only. To address these two limitations, an unsupervised multilevel segmentation algorithm was proposed by Yin et al. [47]. Recently Xuan et al. proposed integrating fuzzy entropy clustering with an improved PSO for MRI brain image segmentation [48]. Recently Xiao et al. proposed entropic image thresholding based on gray-level and gradient-magnitude (GLGM) histogram. GLGM histogram explicitly captures the gray level occurrence probability and spatial distribution property simultaneously [49]. Che et al. proposed and validated an automatic algorithm to segment cerebral edema using Computed Tomography (CT) images of patient with Spontaneous intra cranial hemorrhage through a new way to cluster edema based on region growing, with seeds derived from EM algorithm local mean derived from adaptive local thresholding with varied window sizes, and growing rules that combine spatial (local mean) and grayscale information in the form of 2D entropy [2]. Sarkar et al. proposed a multilevel color image thresholding scheme based on minimum cross entropy and differential evolution [50]. Rajinikanth et al. proposed Entropy based segmentation of tumor from brain MR images using teaching learning based optimization approach [15]. A new feature selection method based on the joint maximal information entropy between features and class (FS-JMIE) is proposed in the work by Zheng et al. [52]. Recently Muthuvel et al proposed microcalcification cluster detection using multiscale products based Hessian matrix via the Tsallis thresholding scheme [53]. Nguyen et al. proposed superpixel and multi-atlas based fusion entropic model for the segmentation of X-ray images [54]. Sumathi et al. proposed an algorithm based on Kapur's entropy and Cuckoo search optimization. Entropy was used to locate and segment the tumor boundary and morphological reconstruction filters are used to remove unwanted pixels in the slice images [55]. The article is organized as follows: Section 1 presents the introduction and related work on entropy thresholding. Section 2 discusses the proposed method for edema and tumor segmentation. Section 3 presents the experiments and results and Section 4 presents the conclusions of the research work.
1.2.
Our contribution
Texture is an important spatial feature useful for identifying objects or regions of interest. Human brain consists of different tissues. The information in the different tissues can be captured using textures or textural features. The proposed method exploits the texture of edema for segmentation. By definition cerebral edema is the excess accumulation of water in the intra-and/or extracellular spaces of the brain [56]. MRI provides an excellent tool for in vivo examination and analysis. Images of Cerebral edema are viewed using the Fluid Attenuation Inversion Recovery (FLAIR) sequence. FLAIR imaging provides a marked contrast enhancement, while suppressing Cerebro Spinal Fluid (CSF), resulting in the highest tumor-to-background contrast ratio compared with standard imaging techniques. This attribute of the edema in the MR image proves useful for defining a definite texture.
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In the proposed method the textural information of the MR image is captured using the gray co-occurrence matrix. The GLCM derives the textural feature map of the MR image. Local entropy as textural feature exploits the feature map. The local entropy computes the probability of the pixel intensity variation and helps in the classification of the texture. The GLCM and local entropy combination proves useful in defining the texture of edema for segmentation.
2.
Materials and methods
The section discusses the computation of gray level cooccurrence matrix, and the proposed method for edema as well as tumor segmentation in brain MR images using local entropy as textural feature.
2.1.
Gray level co-occurrence matrix
The gray co-occurrence matrix gives an idea about the transition of intensities between pixels in a certain direction and distance. Co-occurrence means the number of times the gray level of pixel j follows the gray level of pixel i in a particular way. In a brain image of size M * N the gray levels L can be denoted by G = 0, 1, . . ., L 1. The co-occurrence matrix of an image is an L * L square matrix and is denoted as P ¼ tij LL . The elements of the matrix specified by the numbers of transitions between all pairs of gray levels in G = 0, 1, . . ., L 1 and computed for different values of u can be represented as Eq. (1):
Pði; j; d; uÞ ¼ ððk; lÞ; ðm; nÞÞ 2 ðLy Lx Þ ðLy Lx Þjkm ¼ 0j; jlnj ¼ d; Iðk; lÞ ¼ i; Iðm; nÞ ¼ j
(1)
where Lx = 1, 2, . . ., Nx is the horizontal spatial domain, Ly = 1, 2, . . ., Ny is the vertical spatial domain, d = 1 and u can take any value as shown in Fig. 1 (a). The texture information in the image is adequately specified by a set of gray tone spatial dependence matrices, computed from various angular relationships and distance between neighboring resolution cell pairs on the image. The GLCM helps to define the probabilities of gray levels at the individual pixel level. This aspect of GLCM helps in defining coarse and fine textures and is employed in the proposed method. Haralick et al. proposed several textural features derived from these angular nearest neighbor gray tone spatial dependence matrices [57]. Eq. (2) defines the textural entropy extracted from the gray tone dependence matrices as:
H¼
XX i
pði; jÞlogðpði; jÞÞ
(2)
j
where p(i, j) represents the (i, j) th entry in a normalized gray tone spatial dependence matrix, P(i, j)/R. From Eq. (2), entropy as textural feature represent the probability of intensity level which an individual pixel can adapt. In the proposed method entropy acts as a tool to classify the texture using the textural feature map captured by the GLCM.
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biocybernetics and biomedical engineering 39 (2019) 599–612
Fig. 1 – Gray Level Co-occurrence Matrix. (a) Four orientations used for defining the co-occurrence matrices. (b) Four Quadrants of the co-occurrence matrix.
2.2. Edema segmentation using local entropy as textural feature Entropy is measure of uncertainty in an image. In image analysis entropy is used to quantify the minimum descriptive complexity of a random variable [14]. Entropy provides a good level of information to describe an image. Pal et al. [13] extended the concept of entropy to gray tone image for defining its global, local and conditional entropy. The local entropy takes into account the spatial distributions of the gray levels. If t be a value used to threshold an image, it partitions the co-occurrence matrix into four quadrants A, B, C and D as shown in Fig. 1(b). The probabilities of the four quadrants are computed using Eq. (3): t X t X PtA ¼ pij ; i¼0 j¼0
PtB
t X L1 X
¼
pij
pij PtA
;
0 < i; jt
t t X X
ptij logptij C
C
pij PtC
;
t þ 1i; jL1
(7)
C
where both HBB(t) and HFF(t) are determined by the threshold t, thus they are function of t. By summing up the local transition entropies of foreground and background, the local entropy (LE) is defined as Eq. (8):
HLE ¼ HBB þ HFF
(8)
Thus, HLE(t) describes the local entropy of the quadrants A and C. The gray level corresponding to the maximum of HLE corresponds to the threshold for segmentation.
(4) t ¼ argfmaxðHLE ðtÞÞg
ptij ¼
(6)
A
i¼tþ1j¼tþ1
i¼tþ1 j¼0 L1 X L1 X
The probabilities of gray-level transition within each particular quadrant obtained by normalizing the probabilities are further computed for different quadrants. Eqs. (4) and (5) represents the 'cell probabilities' for quadrants A and C respectively:
A
A
The second order local entropy of the background is defined using the local quadrant C. It contains the entropy transitions of the background and can be defined using Eqs. (2) and (5) as Eq. (7):
HBB ðtÞ ¼
i¼tþ1 j¼0
ptij ¼
i¼0 j¼0
(3)
pij ;
PtD ¼
t X t X HFF ðtÞ ¼ ptij logptij
pij ;
i¼0 j¼tþ1 L1 X t X
PtC ¼
transition within the background (bright area). The gray level transition between the object and the background or across the objects boundary is placed in quadrant B and quadrant D. These four regions are further grouped into two classes, referred to as local quadrant and joint quadrant. Quadrant A and C are referred to as local quadrant. This is because the gray level transition arising within the object or the background of the image occur in quadrants A and C [13]. The second order local entropy of the object is defined using the local quadrant A. It contains the entropy transitions of the foreground and can be defined using Eqs. (2) and (4) as Eq. (6):
(5)
Quadrant A represents gray level transition within the object (dark area) while quadrant C represents gray level
(9)
Eq. (9) represents the maximum of local entropy that serves as the threshold for segmentation. In case of edema segmentation, FLAIR images from the BRATS database are used. FLAIR imaging provides a marked contrast enhance-
biocybernetics and biomedical engineering 39 (2019) 599–612
ment, while suppressing CSF, resulting in the highest tumorto-background contrast ratio compared with standard imaging techniques [58]. Fig 2 (a) represents the scatter plot of gray level transitions of the FLAIR image containing edema. In the scatter plot the gray level values are grouped along the main diagonal. The distribution of gray level of the pixel is indicative of rich variation in the intensity values [59]. From the scatter plot it is observed that large areas are characterized by low variations in intensity. The high intensity transitions occur at the object boundary. Local entropy as textural feature computed using the GLCM for the object and the background from quadrants A and C respectively act as a classifier for the image texture. Therefore for the threshold selection in case of edema segmentation, the local quadrants A and C are more useful than the joint quadrants B and D. Fig 2(b) and (c) represent the local entropy transitions in quadrant A and C for FLAIR image. Similarly for tumor segmentation, contrast enhanced T1-w images (T1c) are used. When enhancing agent is injected the tumor appears bright, thus changing the signal intensity and enhancing the contrast. Fig 3 (a) represent scatter plot for T1 weighted contrast enhanced images while Fig. 3 (b) and (c) represent the local entropy transitions in quadrant A and C for tumor segmentation.
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Fig. 4 represents the local entropy plot for threshold selection. Fig. 5 represents the flow chart of the proposed method. The algorithm for the proposed method is: 1. Step 1: Compute the GLCM matrix using the angular relation u = 135 and neighboring resolution cells separated by distance d = 1 and gray levels as 256. 2. Step 2: Compute the probabilities of the quadrants A, B, C, D of the MR image having size L * L. 3. Step 3: Compute the cell probabilities of the quadrants A and C using Eqs. (4) and (5). 4. Step 4: Compute the local entropy transitions of quadrants A and C using Eqs. (6) and (7). 5. Step 5: Compute the local entropy (LE) using Eq. (8) by summing up the local entropy transitions of quadrant A and C. 6. Step 6: Compute the threshold for segmentation as the maximum of the local entropy using Eq. (9). The proposed method presents a new threshold based method for edema and tumor segmentation using local entropy as textural feature captured using the spatial
Fig. 2 – For FLAIR image from BRATS database: (a) Scatter plot of GLCM: (b) Local entropy transitions of Quadrant A: (c) Local entropy transitions of Quadrant C.
Fig. 3 – For T1-c image from BRATS database: (a) Scatter plot of GLCM: (b) Local entropy transitions of Quadrant A: (c) Local entropy transitions of Quadrant C.
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biocybernetics and biomedical engineering 39 (2019) 599–612
Fig. 4 – Entropy curve for: (a) T1 weighted contrast enhanced image for tumor core segmentation: (b) FLAIR image for edema segmentation.
dependence and angular relationship of the gray level cooccurrence matrix.
3.
Results and discussion
Experiments are conducted using publically available BRATS database [60–62]. BRATS 2012, BRATS2 and BRATS 2013 database are used for edema and tumor core segmentation experiments. The BRATS 2012 and BRATS2 database consist of High Grade Glioma (HG) and Low Grade Glioma (LG) images of ten subjects respectively. Experiments are conducted on all HG images of the ten subjects and results for four subjects are
presented for visual comparison for BRATS 2012 and BRATS2 database. BRATS 2013 database consist of MR images of more than two hundred subjects. Experiments are conducted on more than 10 subsampled HG images for BRATS 2013 database and results for four images are shown for visual evaluation and comparison. Most of the images from the database consist of approximately 200 slices of the volume for different MR sequences. For example, the Flair sequence of BRATS 2012 database of subject 3540 consist of 230 slices. Out of the 230 slices, edema is visible only in slice numbers from 130 to 187. Slices without edema or tumor are not considered for quantification. Validation of segmentation using proposed method is done with ground truth images provided from the available BRATS database. The proposed method is unsupervised and no training set is required. Evaluation of the segmentation with the ground truth is an important task. In segmentation evaluation the segmented image is compared with the ground truth by measuring the distance or similarity between them. For the proposed method segmentation evaluation is carried out using Accuracy, Sensitivity, Specificity, Precision, Dice Coefficient and Structural Similarity Index. Implementation and testing of the proposed method is done using the computational facility with Windows 7, Matlab 7.10 (R2010a), Intel Core 2 Duo, 2.09 Ghz, 2 GB RAM. The proposed method is compared with basic methods of minimum Cross Entropy (CE) thresholding [31] and Maximum Entropy (ME) thresholding [23].
3.1.
Fig. 5 – Flow Chart of the proposed Segmentation method.
Experiments for edema segmentation
Fig. 7, 9 and 11 represent the results for edema segmentation. Tables 1–7 present the evaluation metrics for edema. Accuracy is used as a statistical measure of how well a binary classification test correctly identifies or excludes a condition. Local entropy depends on the probability of co-occurrence of pixel intensities and takes into account the spatial distributions of the gray levels. This assist
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Table 1 – Comparison of Accuracy for Edema segmentation for BRATS database.
Table 4 – Comparison of Precision for Edema segmentation for BRATS database.
Database
Database
Proposed method
Cross entropy
Maximum entropy
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.9384 0.9659 0.9386 0.9456
0.9023 0.9356 0.9344 0.9458
0.9234 0.9487 0.9354 0.9456
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.5478 0.2552 0.4280 0.4341
0.3998 0.6862 0.5922 0.4324
0.4673 0.1973 0.4127 0.4336
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9612 0.9756 0.9607 0.9806
0.9648 0.9648 0.9379 0.9842
0.9701 0.9744 0.9605 0.9791
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.3057 0.2618 0.5511 0.7034
0.3232 0.2256 0.4162 0.9248
0.3409 0.1727 0.5435 0.6783
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.9572 0.9512 0.9642 0.9578
0.9579 0.9520 0.9653 0.9665
0.9559 0.9514 0.9706 0.9451
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.4277 0.6616 0.0767 0.5298
0.4327 0.6553 0.0533 0.6640
0.4194 0.6755 0.0028 0.4343
Average
0.9581
0.9510
0.9550
Average
0.4319
0.4838
0.3982
Table 2 – Comparison of Sensitivity for Edema segmentation for BRATS database.
Table 5 – Comparison of Dice Coefficient for Edema segmentation for BRATS database.
Database
Database
Proposed method
Cross entropy
Maximum entropy
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.6361 0.7978 0.5143 0.896
0.8184 0.9631 0.5048 0.856
0.7472 0.9161 0.5554 0.888
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.5887 0.3867 0.4672 0.5849
0.5372 0.3161 0.4501 0.5746
0.5750 0.3247 0.4735 0.5827
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9382 0.643 0.6685 0.859
0.9039 0.8748 0.9547 0.6423
0.7373 0.3369 0.7452 0.873
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.4611 0.3721 0.6041 0.7735
0.4761 0.3587 0.5797 0.7581
0.4662 0.2284 0.6286 0.7634
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.7264 0.6548 0.0784 0.6276
0.7256 0.6974 0.0483 0.5321
0.7332 0.6192 0.0015 0.6906
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.5384 0.6582 0.0776 0.5746
0.5421 0.6757 0.0507 0.5908
0.5335 0.6461 0.0020 0.5333
Average
0.67
0.7101
0.6536
Average
0.5073
0.4925
0.4798
Table 3 – Comparison of Specificity for Edema segmentation for BRATS database.
Table 6 – Comparison of Jaccard Index for Edema segmentation for BRATS database.
Database
Database
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.4171 0.2397 0.3048 0.4133
0.3673 0.1877 0.2904 0.4031
0.2214 0.4782 0.3025 0.7243
0.9743 0.9817 0.9706 0.9834
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.2996 0.2286 0.4328 0.6306
0.3124 0.2185 0.4081 0.6104
0.6757 0.4527 0.4845 0.3263
0.9661 0.9717 0.9832 0.9872
0.9639 0.9770 0.9896 0.9572
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.3683 0.4905 0.0403 0.4031
0.3719 0.5102 0.0260 0.4193
0.0963 0.1712 0.3201 0.2165
0.9687
0.9657
Average
0.3557
0.3438
0.3725
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.9609 0.9682 0.9620 0.9478
0.9085 0.9955 0.9957 0.9498
0.9366 0.9492 0.9564 0.9482
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9616 0.9794 0.9744 0.9855
0.9659 0.9659 0.9371 0.9979
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.9654 0.9741 0.9815 0.9735
Average
0.9695
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biocybernetics and biomedical engineering 39 (2019) 599–612
Table 7 – Comparison of Structural Similarity Index for Edema segmentation for BRATS database. Database
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.7129 0.8308 0.7861 0.8913
0.4992 0.7232 0.7586 0.8389
0.5569 0.7232 0.7332 0.837
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.8864 0.9424 0.8917 0.9299
0.875 0.8111 0.7302 0.9156
0.9164 0.9503 0.8537 0.8888
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.8535 0.8604 0.9287 0.8605
0.8202 0.8173 0.9301 0.8522
0.8092 0.8258 0.9303 0.8045
Average
0.8646
0.7976
0.8191
in identification of edema pixels hence the proposed method exhibits an accuracy of 95% for edema segmentation. Minimum Cross Entropy and Maximum Entropy method also exhibit the same accuracy. Sensitivity represents the ability to correctly detect the condition. It is defined using the ratio of true positive to the sum of true positives and false negatives. In case of minimum CE the method implements an information theoretic distance between two probability distributions for threshold selection.
This helps in correct detection of true positive pixels hence minimum CE method exhibit a better sensitivity as compared to the proposed method and ME method. Specificity, a necessary counterpart of the sensitivity is a measure of the portion of negative voxel in the ground truth segmentation that are also identified as negative by the segmentation being evaluated. The average specificity for edema for all the compared methods is observed as 96%. The precision metric is sensitive to over-segmentation or under-segmentation. Over-segmentation leads to low precision scores. The average precision score for proposed method is 43%. For the methods of CE and ME the scores are 48% and 39% respectively. Edema a swelling in the brain can develop in and around any tissue hence in FLAIR images the intensity of the edema can vary and cause over or under segmentation. The Dice Coefficient measures the overlap between the ground truth and segmentation being evaluated. Average Dice Coefficient is observed as 50% for edema using proposed method and 49% and 47% for CE and ME methods. The proposed method demonstrate better results in comparison to CE and ME methods in terms of Dice Coefficient. The Jaccard Index (JI) measures the intersection over the union of the labeled segments for each class and reports the average. The JI is found better for ME method. One of the reasons for a better JI as compared to other methods is the ME method maximizes the inter-class entropy. Structural Similarity index (SSIM) combines the luminance, contrast and the similarity between the ground truth
Fig. 6 – Tumor core segmentation results for High Grade Glioma T1-w contrast enhanced images from BRATS 2012 database. (a)–(d) Images containing Tumor (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
biocybernetics and biomedical engineering 39 (2019) 599–612
607
Fig. 7 – Edema segmentation results for High Grade Glioma Flair images from BRATS 2012 database. (a)–(d) Images containing Edema (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
Fig. 8 – Tumor segmentation results for High Grade Glioma T1-w contrast enhanced images from BRATS 2013 database. (a)–(d) Images containing Tumor (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
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Fig. 9 – Edema segmentation results for High Grade Glioma Flair images from BRATS 2013 database. (a)–(d) Images containing Edema (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
Fig. 10 – Tumor segmentation results for High Grade Glioma T1-w contrast enhanced images from BRATS-2 database. (a)–(d) Images containing Tumor (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
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Fig. 11 – Edema segmentation results for High Grade Glioma Flair images from BRATS-2 database. (a)–(d) Images containing Edema (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
3.2.
Results for tumor core segmentation
and segmented image [63]. SSIM close to 1 specifies exact similarity. Local entropy as textural feature measures the pixel variability, the marked contrast in FLAIR images is captured as a definite texture for edema hence SSIM for the proposed method is 0.8846 and better than CE and ME methods.
Fig. 6, 8 and 10 demonstrate the segmentation results using the proposed method for BRATS 2012, 2013 and BRATS2 database for tumor core. Tables 8–14 present the comparison of evaluation metrics for tumor segmentation.
Table 8 – Comparison of Accuracy for tumor segmentation for BRATS database.
Table 9 – Comparison of Sensitivity for tumor segmentation for BRATS database.
Database
Database
Proposed method
Cross entropy
Maximum entropy
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.9712 0.9973 0.9844 0.9915
0.9732 0.9957 0.9896 0.9916
0.9737 0.9964 0.9894 0.9915
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.3696 0.8324 0.6476 0.8238
0.3180 0.9631 0.5048 0.8228
0.2571 0.9403 0.3738 0.8238
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9961 0.9921 0.9903 0.9844
0.9937 0.9916 0.9757 0.9835
0.9963 0.9920 0.9832 0.9829
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.6949 0.6067 0.7357 0.4175
0.8917 0.6234 0.8978 0.3609
0.8123 0.5342 0.8519 0.3299
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.9797 0.9925 0.9864 0.9666
0.9764 0.9866 0.9863 0.9672
0.9783 0.9797 0.9856 0.9677
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.1230 0.8068 0.4941 0.2998
0.1569 0.4907 0.4676 0.2750
0.1426 0.1745 0.3441 0.2552
Average
0.9860
0.9843
0.9847
Average
0.5710
0.5644
0.4866
610
biocybernetics and biomedical engineering 39 (2019) 599–612
Table 10 – Comparison of Specificity for tumor segmentation for BRATS database.
Table 13 – Comparison of Jaccard Index for tumor segmentation for BRATS database.
Database
Database
Proposed method
Cross entropy
Maximum entropy
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.9892 0.9995 0.9886 0.9962
0.9929 0.9961 0.9957 0.9962
0.9952 0.9937 0.9971 0.9962
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.2720 0.7610 0.3383 0.7243
0.2569 0.6686 0.3746 0.7243
0.2214 0.4782 0.3025 0.7243
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9990 0.9969 0.9951 0.9991
0.9947 0.9963 0.9772 0.9996
0.9980 0.9977 0.9857 0.9997
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.6301 0.4877 0.5832 0.4031
0.5778 0.4812 0.4066 0.3555
0.6757 0.4527 0.4845 0.3263
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.9938 0.9971 0.9963 0.9908
0.9899 0.9988 0.9967 0.9924
0.9921 0.9995 0.9985 0.9935
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.0895 0.7213 0.4174 0.2393
0.0973 0.4676 0.4020 0.2273
0.0963 0.1712 0.3201 0.2165
Average
0.9951
0.9939
0.9956
Average
0.4723
0.4200
0.3725
Table 11 – Comparison of Precision for tumor segmentation for BRATS database. Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.5076 0.6862 0.4146 0.8571
0.5721 0.7164 0.5922 0.8587
0.6145 0.7592 0.3738 0.8571
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.8710 0.7131 0.7378 0.9209
0.6214 0.6783 0.4263 0.9596
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.2473 0.8719 0.7289 0.5426
Average
0.6749
Database
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.8392 0.9691 0.8120 0.8967
0.8176 0.9127 0.8460 0.8030
0.8457 0.8340 0.8802 0.8030
0.8007 0.7480 0.4263 0.9676
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9708 0.9414 0.9373 0.9379
0.8701 0.9007 0.8367 0.9342
0.9251 0.9253 0.8479 0.9351
0.2042 0.9085 0.7413 0.5673
0.2286 0.8983 0.8211 0.5886
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.9165 0.9097 0.8999 0.8736
0.8527 0.8976 0.8672 0.8423
0.8671 0.9202 0.8963 0.8475
0.6539
0.6737
Average
0.9087
0.8651
0.8773
Table 12 – Comparison of Dice Coefficient for tumor segmentation for BRATS database. Database
Table 14 – Comparison of Structural Similarity Index for tumor segmentation for BRATS database.
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.4277 0.8643 0.5056 0.8401
0.4088 0.8014 0.5450 0.8401
0.3626 0.6470 0.4645 0.8401
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.7731 0.6556 0.7367 0.5745
0.7324 0.6497 0.5782 0.5246
0.8065 0.6233 0.6528 0.4920
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.1643 0.8381 0.5890 0.3862
0.1774 0.6372 0.5735 0.3704
0.1756 0.2923 0.4850 0.3560
Average
0.6129
0.5699
0.5165
Database
In case of tumor segmentation the proposed method performs better or equal for most of the evaluation metrics as compared to the CE and ME methods. The proposed method exhibits an accuracy of around 98% and is same as other compared methods. Specificity relates to the ability to correctly detect, healthy tissues and is observed to be around 99% for all the compared methods. The proposed method demonstrate sensitivity of 57% and is better than CE and ME. Sensitivity is defined as the ratio of true positives to the sum of true positives and false negatives. In case of tumor segmentation the textures are well defined by the local entropy transitions therefore an accurate threshold can be obtained which can classify pixels as tumor or non tumor. The precision metrics is almost equal for all the three methods. The proposed method demonstrates a better Dice Coefficient and JI for tumor segmentation. The SSIM reflects the structural similarity between the gold standard and the segmented image. In case of tumor segmentation the SSIM is close to one
biocybernetics and biomedical engineering 39 (2019) 599–612
as compared to CE and ME methods because of defined tumor texture due to good contrast enhancement of tumor pixels in the MR image. The proposed method thus exhibits encouraging results for tumor core segmentation.
[7]
[8]
4.
Conclusions
Cerebral edema is a serious disorder and potentially lifethreatening condition. MR imaging proves as a vital tool right from detection and localization to treatment planning and clinical management. The work proposes an automatic unsupervised method for edema and tumor segmentation using textural feature. In the proposed method the textural feature map of the brain MR image is computed using the gray co-occurrence matrix. The gray co-occurrence matrix computes the probability of gray level at the individual pixel level. This is helpful to define coarse and fine textures. Entropy as second order textural feature measures the randomness in the pixel intensity and proves advantageous to identify the texture of the edema in MR image. Local entropy acts as a classifier for threshold selection. Experiments on publically available BRATS database yields encouraging results in most of the cases. The proposed method is successful in automatic segmentation of edema as well as tumor core as seen by visual perception and evaluation.
[9]
[10] [11]
[12]
[13] [14] [15]
[16]
[17]
Authorship statement [18]
All persons who meet authorship criteria are listed as authors, and all authors certify that they have participated sufficiently in the work to take public responsibility for the content, including participation in the concept, design, analysis, writing, or revision of the manuscript. Furthermore, each author certifies that this material or similar material has not been and will not be submitted to or published in any other publication before its appearance in Biocybernetics and Biomedical Engineering.
[19]
[20]
[21] [22]
references
[23]
[1] Adukauskiene D, Bivainyte A, Radavieiute E. Cerebral edema and its treatment. Medicina (Kaunas) 2017;43(2). [2] Chen M-Y, Hu1 Q-M, Liu Z-C, Zhou1 S-J, Li X-D. Segmentation of cerebral edema around spontaneous intracerebral hemorrhage. Int J Appl Math Inf Sci 2013. Natural Sciences Publishing Cor.. [3] Norton NS. Cerebral edema. Ref Module Biomed Sci 2014. [4] Castro P, Azevedo E, Serrador J, Rocha I, Sorond F. Hemorrhagic transformation and cerebral edema in acute ischemic stroke: link to cerebral autoregulation. J Neurol Sci 2017;372(15):256–61. [5] Havaei M, Davy A, Warde-Farley D, Biard A, Courville A, Bengio Y, et al. Brain Tumor Segmentation with Deep Neural Networks Medical Image Analysis, vol. 35. 2017;p.
[24]
[6] Gilanie G, Attique M, Ullah H, Naweed S, Ahmed E, Ikram M. Object extraction from T2 weighted brain MR image using
[29]
18–31.
[25]
[26] [27]
[28]
611
histogram based gradient calculation. Pattern Recognit Lett 2013;34:1356–63. Gordillo N, Montseny E, Sobrevilla P. State of the art survey on MRI brain tumor segmentation. Magn Resonance Imaging Vol 2013;31(8):1426–38. Yao J. Image processing in tumor imaging. New Tech Oncol Imaging 2006;79–102. Wu CM, Chen YC. Texture features for classification of ultrasonic liver images. IEEE Trans Med Imaging 1992;11:141–52. Miller P, Astley S. Classification of breast tissue by texture analysis. Image Vision Comput 1992;10:277–82. Koss JE, Newman FD, Johnson TK, Krich DL. Abdominal organ segmentation using texture transform and Hopfield neural network. IEEE Trans Med Imaging 1999;18:640–8. Xie J, Jiang Y, Tsui HT. Segmentation of kidney from ultrasound images based on texture and shape priors. IEEE Trans Med Imaging 2005;24:45–57. Pal N, Pal S. Entropic thresholding. Signal Process 1989;16:97–108. Cover T0, Thomas J, Wiley J, InterScience W. Elements of Information Theory. New York: Wiley; 1991. Rajinikanth V, Satapathy SC, Fernandes SL, Nachiappan S. Entropy based segmentation of tumor from brain MR images – a study with teaching learning based optimization. Pattern Recognit Lett 2017;1–9. Chaudhari AK, Kulkarni JV. Local entropy based brain MR image segmentation. IEEE 3rd International Advance Computing Conference (IACC); 2013. http://dx.doi.org/10.1109/IAdCC.2013.6514403 Priya RK, Thangaraj C, Kesavadas C, Kannan S. Fuzzy entropy based MR brain image segmentation using modified particle swarm optimization. Int J Imaging Syst Technol 2013;23(4):281–8. Priya RK, Thangaraj C, Kesavadas C, Kannan S. Application of swarm intelligence in fuzzy entropy based image segmentation. Stud Comput Intell 2014;561:227–45. Acharya UR, Fujita H, Sudarshan VK, Bhat S, Koh JEW. Application of entropies for automated diagnosis of epilepsy using EEG signals. Knowl Based Syst 2015;88(C): 85–96. Kannathal N, Choo ML, Acharya UR, Sadasivan PK. Entropies for detection of epilepsy in EEG. Comput Methods Programs Biomed 2005;80(3):187–94. Pun T. A new method for gray level picture thresholding using entropy of the histogram. Signal Process 1980;223–7. Pun T. Entropic thresholding: a new approach. Comput Graphics Image Process 1981;210–39. Kapur JN, Sahoo PK, Wong AKC. A new method for graylevel picture thresholding using the entropy of the histogram. Comput Vision Graphics Image Process 1985;29:273–85. Bhandari AK, Kumar A, Singh GK. Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur's, Otsu and Tsallis functions. Expert Syst Appl 2015;42(3):1573–601. Sathya PD, Kayalvizhi R. Optimal multilevel thresholding using bacterial for aging algorithm. Expert Syst Appl 2011; 38(12):15549–64. Sahoo P, Wilkins C, Yeager J. Threshold selection using Renyi's entropy. Pattern Recognit 1997;30(1):71–84. Chang C, Chen K, Wang J, Althouse LJ. A relative entropybased approach to image thresholding. Pattern Recognit 1994;27(9):1275–89. Pal NR. On minimum cross-entropy thresholding. Pattern Recognit 1996;29(4):575–80. Brink AD, Pendock NE. Minimum cross-entropy threshold selection. Pattern Recognit 1996;29(1):179–88.
612
biocybernetics and biomedical engineering 39 (2019) 599–612
[30] Chen W-T, Wen C-H, Yang C-W. A fast two-dimensional entropic thresholding algorithm. Pattern Recognit 1994; 27(7):885–93. [31] Li CH, Tam PKS. An iterative algorithm for minimum cross entropy thresholding. Pattern Recognit Lett Vol 1998;19 (8):771–6. [32] Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys 1998;52:479–87. [33] Mohamed A, El-Sayed S, Abdel-Khalek, Abdel-Aziz E. Study of efficient technique based on 2D Tsallis entropy for image thresholding. Int J Comput Sci Eng (IJCSE) 2011;3(9):1325–36. [34] Sahoo PK, Arora G. A thresholding method based on twodimensional Renyi's entropy. Pattern Recognit Vol 2004;37 (6):1149–61. [35] Portes de Albuquerque M, Esquef IA, Gesualdi Mello AR, Portes de Albuquerque M. Image thresholding using Tsallis entropy. Pattern Recognit Lett 2004;25(9):1059–65. [36] Yan C, Sang N, Zhang T. Local entropy-based transition region extraction and thresholding. Pattern Recognit 2003;24(16):2935–41. [37] Sahoo PK, Arora G. Image thresholding using twodimensional Tsallis-Havrda-Charvát entropy. Pattern Recognit Lett 2006;27(6):520–8. [38] Li X, Zhao Z, Cheng HD. Fuzzy entropy threshold approach to breast cancer detection. Inf Sci – Appl 1995;4(1):49–56. [39] Cheng HD, Yen-Hung, Chen Ying Sun A. novel fuzzy entropy approach to image enhancement and thresholding. Signal Process 1999;75(3):277–301. [40] Bloch I. Fuzzy spatial relationships for image processing and interpretation: a review. Image Vis Comput 2005;23 (2):89–110. [41] Tao WB, Tian JW, Liu J. Image segmentation by three-level thresholding based on maximum fuzzy entropy and genetic algorithm. Pattern Recognit Lett 2003;24:3069–78. [42] Linyi L, Deren L. Fuzzy entropy image segmentation based on particle swarm optimization. Prog Nat Sci 2008;18 (9):1167–71. [43] Jinhui L, Yiliang Z. Multi-threshold image segmentation using maximum fuzzy entropy based on a new 2D histogram. Optik 2013;124(18):3756–60. [44] Yin S, Zhao X, Wang W, Gong M. Efficient multilevel image segmentation through fuzzy entropy maximization and graph cut optimization. Pattern Recognit 2014;47 (9):2894–907. [45] Yu H-Y, Zhi X-B, Fan J-L. Image segmentation based on weak fuzzy partition entropy. Neurocomputing 2015;168:994–1010. [46] Ye Z-W, Wang M-W, Liu W, Chen S-B. Fuzzy entropy based optimal thresholding using bat algorithm. Appl Soft Comput 2015;31:381–95.
[47] Yin S, Qian Y, Ming, Gongb L. Unsupervised hierarchical image segmentation through fuzzy entropy maximization. Pattern Recognit 2017;68:245–59. [48] Xuan TP, Siarry P, Oulhad H. Integrating fuzzy entropy clustering with an improved PSO for MRI brain image segmentation. Appl Soft Comput 2018. Available online 31 January. [49] Xiao Y, Cao Z, Cao Z, Yuan J. Entropic image thresholding based on GLGM histogram. Pattern Recognit Lett 2014;40:47–55. [50] Sarkar S, Das S, Chaudhuri S Sinha. A multilevel color image thresholding scheme based on minimum cross entropy and differential evolution. Pattern Recognit Lett 2015;54:27–35. [52] Zheng KF, Wang X. Feature selection method with joint maximal information entropy between features and class. Pattern Recognit 2018;77:20–9. [53] Muthuvel M, Thangaraju f Balakumaran, Chinnasamy G. Microcalcification cluster detection using multiscale products based Hessian matrix via the Tsallis thresholding scheme. Pattern Recognit Lett 2017;94:127–33. [54] Nguyen DC, Benameur S, Mignotte M, Lavoie F. Superpixel and multi-atlas based fusion entropic model for the segmentation of X-ray images. Med Image Anal 2018;58–74. [55] Sumathi R, Venkatesulu M, Arjunan SP. Extracting tumor in MR brain and breast image with Kapur's entropy based Cuckoo Search Optimization and morphological reconstruction filters. Biocybern Biomed Eng 2018;38(4):918–30. [56] Pollay M. Blood-Brain Barrier, Cerebral Edema.. In: Wilkins RH, Rengachary SS, editors. Neurosurgery. 2nd ed. New York: McGraw Hill Book Co.; 1996. p. 335–44. [57] Haralick R, Shanmugan K, Dinstein I. Textural features for image classification. IEEE Trans Syst Man Cybern 1973;610–21. [58] Essig M, Knopp MV, Schoenberg SO, Hawighorst H, Wenz F, Debus J, et al. Cerebral gliomas and metastases: assessment with contrast-enhanced fast fluid-attenuated inversionrecovery MR imaging. Radiology 1999;210(2):551–7. [59] Gonzalez R, Woods R. Digital Image Processing. 2nd ed. Pearson Education; 2005. [60] http://www.imm.dtu.dk/projects/BRATS2012. [61] Menze. et al. The Multimodal Brain Tumor Image Segmentation Benchmark (BRATS). IEEE Trans Med Imaging 2015;34(10):1993–2024. [62] Kistler. et al. The virtual skeleton database: an open access repository for biomedical research and collaboration. J Med Internet Res 2013;15(11). [63] Wang Z, Bovik AC, Sheikh HR, Simoncelli EP. Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 2004;13(4):600–12.
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Original Research Article
Cerebral edema segmentation using textural feature Archana Chaudhari, Jayant Kulkarni * Department of Instrumentation Engineering, Vishwakarma Institute of Technology, Pune, India
article info
abstract
Article history:
Diagnostic imaging provides a vital tool in detection and analysis of Brain pathologies.
Received 15 July 2018
Magnetic resonance imaging (MRI) provides an effective means for non-invasive mapping of
Received in revised form
anatomy and pathology in the brain. Pathologies like cerebral edema and tumors can spread
8 February 2019
in different tissues in the brain and can affect cognitive and other functions in the body.
Accepted 4 June 2019
Accurate segmentation is therefore a challenging task. Human Brain consists of different
Available online 11 June 2019
soft tissues. These tissues can be characterized using different textures.
Keywords:
MR image. The texture of MR image is exploited using the gray co-occurrence matrix (GLCM).
MRI
GLCM creates a textural feature map by taking into account the spatial dependence of the
The work presents an automatic method for segmentation using textural feature of the
Local entropy
pixels and its angular relationship between the neighboring cell pairs. Local entropy as
Brain
second order textural feature is used to capture the texture of MR image. Entropy computes
Segmentation
the randomness in pixel intensities and helps in defining a unique texture of edema for
GLCM
segmentation. The marked contrast enhancement obtained in FLAIR sequence of the MR
Cerebral edema
image is captured as textural information by local entropy and GLCM combination. The proposed method obtains a definite textural signature of edema as well as tumor for threshold selection. Experiments on publically available BRATS database yields an average accuracy of 96%, specificity of 97%, sensitivity of 61%, Dice Coefficient as 50% and structural similarity index of 0.88 for edema. The proposed method demonstrates encouraging results in automatic segmentation of edema as well as tumor core. © 2019 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved.
1.
Introduction
Cerebral edema is a condition that develops as a result of an inflammatory reaction. Most frequently, this is the consequence of cerebral trauma, massive cerebral infarction,
hemorrhages, abscess, tumor, allergy, sepsis, hypoxia, and other toxic or metabolic factors [1]. It is a serious disorder that accompanies an extensive array of pathological processes such as tumors and ischemia [2]. As the brain has little space to expand and does not have a lymphatic system to remove excess fluid, cerebral edema is a potentially life-threatening
* Corresponding author at: Department of Instrumentation Engineering, Vishwakarma Institute of Technology, 666 Upper Indira Nagar, Bibwewadi, Pune 411037, India. E-mail addresses: [email protected] (A. Chaudhari), [email protected] (J. Kulkarni). https://doi.org/10.1016/j.bbe.2019.06.002 0208-5216/© 2019 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved.
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biocybernetics and biomedical engineering 39 (2019) 599–612
condition [3]. Timely and effective diagnose and control of cerebral edema could help to reduce the mortality rate. Mechanisms for early detection and diagnosis are poorly understood and reliable markers are lacking [4]. Medical imaging plays an important role in the early detection, diagnosis and treatment of cerebral edema and tumors. Magnetic resonance imaging (MRI) is preferred modality for brain imaging because of its non invasive nature and good differentiation of soft tissues, useful in imaging tumor origin. The different modalities of MR images and ease of acquisition in many planes makes it a popular modality for clinical diagnosis and analysis. More than one MRI modality is often employed for brain pathology detection and analysis such as T1 weighted (T1-w), T2-weighted (T2-w), Proton Density (PD), Fluid attenuation Inversion Recovery (FLAIR), Diffusion MRI, Gadolinium enhanced T1-w images (T1-c). The contrast between these modalities gives almost a unique signature to each tissue type [5]. Diagnosis and treatment of cerebral edema and tumor involves image processing operations. For further analysis and to extract hidden information, segmentation of these images is required for better visualization of different regions [6]. Brain consists of three tissues, white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF). It is important to locate the tumor and the extent of tumor regions namely active tumor tissue, necrotic tissue, and edema (swelling near the tumor) [5]. The goal of image processing is to detect the location and extent of the tumor or edema using segmentation methods. Few pre-processing steps are required for image segmentation. Skull stripping an important pre-processing operation is applied to remove the skull. MR images may contain artifacts like intensity inhomogenity and noise. These artifacts along with noise are removed in the preprocessing stage. Several methods in literature have been proposed for brain tumor segmentation. Segmentation techniques can be broadly divided into supervised or unsupervised. Supervised technique consists of training and testing database. In training labels are assigned to the tumor and segmentation is achieved using a classification technique. In unsupervised segmentation the image data is not labeled and can be performed using an anatomic objective measure or an image-based objective measure [7]. Segmentation can be performed using manual delineation by human expert or by partial intervention in semi automatic method or fully automatic without any human intervention. Segmentation methods can be broadly divided into pixel classification based, region based, and threshold based and model based [7].
1.1.
Related work
Thresholding based methods are simple segmentation methods in which image gray levels are used to threshold the object from the image. The object can be segmented using several individual thresholds or by using a multi-thresholding technique. When only the pixel intensity is considered, the threshold method can be classified as global threshold. A local threshold is determined adaptively in a local region around a pixel [7]. According to Yao the values of thresholds are generally estimated by the prior knowledge [8]. Local threshold values can also be estimated using the local statistical
or textural image properties. Segmentation based on the gray levels of the image may not give desired results; therefore several texture based segmentation methods are proposed in literature [9–12]. The textural properties are derived using the first or second order statistics of the histogram or the cooccurrence matrix. Mean standard deviation and entropy can be defined as texture features derived using first order statistics. Entropy is defined as the measure of randomness in an image. Several methods have been proposed on entropy-based thresholding. Some of these methods use the gray-level histogram, while others use entropy associated with the two-dimensional histogram or the co-occurrence matrix [13]. Shannon defined entropy as a measure of uncertainty in terms of information theory [14]. Shannon entropy is a special case of Renyi's entropy and parametric family of information measures is defined as Renyi's entropy. Entropy based approaches are widely adopted by the researchers to analyze the abnormality in medical images [15–18] as well as signals [19,20]. A new method for gray level picture thresholding using entropy of the histogram, was proposed by Pun in 1980 and a new approach to entropic thresholding in 1981 [21,22]. Kapur et al. proposed to segment the gray scale image using the entropy of the histogram [23] along with some improvements in Pun's method. In the work of Kapur et al. the optimal threshold is obtained which maximizes overall entropy [24,25]. Sahoo et al. further introduced the concept of threshold selection using Renyi's entropy [26]. Chang et al. proposed relative entropy-based approach to image thresholding [27]. Pal et al. proposed a new method on minimum cross-entropy thresholding [28]. Brink et al. proposed a method to determine the optimum threshold using cross entropy as non metric measure [29]. Chen et al. proposed a fast two-dimensional entropic thresholding algorithm [30]. Li et al. proposed an iterative algorithm for minimum cross entropy thresholding [31]. Tsallis entropy [32] is obtained from the two dimensional histogram determined by using gray value of the pixels and is applied as a generalized entropy formalism [33]. The work by Sahoo et al. presents a new thresholding technique based on two-dimensional Renyi's entropy [34]. Albuquerque et al. proposed image thresholding using Tsallis entropy [35]. Yan et al. proposed local entropy-based transition region extraction and thresholding to effectively reduce the affects of noise during image segmentation [36]. Sahoo et al. presented a thresholding technique based on two-dimensional TsallisHavrda-Charvat entropy [37]. Li et al. developed a criterion of maximum fuzzy entropy for selecting the threshold to breast cancer detection [38]. Cheng et al. proposed a novel fuzzy entropy approach to image enhancement and thresholding [39]. Bloch reviewed the applications of fuzzy spatial relationship in image processing and image interpretation area [40]. Tao et al. proposed a 3-level fuzzy entropy based image segmentation technique [41]. Several methods using fuzzy entropy have been proposed in literature for image segmentation [42–46]. The fuzzy c-partition entropy has been widely adopted as a global optimization technique for finding the optimal thresholds when performing multilevel gray image segmentation. Nevertheless, existing fuzzy c-partition entropy approaches
biocybernetics and biomedical engineering 39 (2019) 599–612
generally have two limitations, partition number needs to be manually tuned for different input and the methods can process gray scale images only. To address these two limitations, an unsupervised multilevel segmentation algorithm was proposed by Yin et al. [47]. Recently Xuan et al. proposed integrating fuzzy entropy clustering with an improved PSO for MRI brain image segmentation [48]. Recently Xiao et al. proposed entropic image thresholding based on gray-level and gradient-magnitude (GLGM) histogram. GLGM histogram explicitly captures the gray level occurrence probability and spatial distribution property simultaneously [49]. Che et al. proposed and validated an automatic algorithm to segment cerebral edema using Computed Tomography (CT) images of patient with Spontaneous intra cranial hemorrhage through a new way to cluster edema based on region growing, with seeds derived from EM algorithm local mean derived from adaptive local thresholding with varied window sizes, and growing rules that combine spatial (local mean) and grayscale information in the form of 2D entropy [2]. Sarkar et al. proposed a multilevel color image thresholding scheme based on minimum cross entropy and differential evolution [50]. Rajinikanth et al. proposed Entropy based segmentation of tumor from brain MR images using teaching learning based optimization approach [15]. A new feature selection method based on the joint maximal information entropy between features and class (FS-JMIE) is proposed in the work by Zheng et al. [52]. Recently Muthuvel et al proposed microcalcification cluster detection using multiscale products based Hessian matrix via the Tsallis thresholding scheme [53]. Nguyen et al. proposed superpixel and multi-atlas based fusion entropic model for the segmentation of X-ray images [54]. Sumathi et al. proposed an algorithm based on Kapur's entropy and Cuckoo search optimization. Entropy was used to locate and segment the tumor boundary and morphological reconstruction filters are used to remove unwanted pixels in the slice images [55]. The article is organized as follows: Section 1 presents the introduction and related work on entropy thresholding. Section 2 discusses the proposed method for edema and tumor segmentation. Section 3 presents the experiments and results and Section 4 presents the conclusions of the research work.
1.2.
Our contribution
Texture is an important spatial feature useful for identifying objects or regions of interest. Human brain consists of different tissues. The information in the different tissues can be captured using textures or textural features. The proposed method exploits the texture of edema for segmentation. By definition cerebral edema is the excess accumulation of water in the intra-and/or extracellular spaces of the brain [56]. MRI provides an excellent tool for in vivo examination and analysis. Images of Cerebral edema are viewed using the Fluid Attenuation Inversion Recovery (FLAIR) sequence. FLAIR imaging provides a marked contrast enhancement, while suppressing Cerebro Spinal Fluid (CSF), resulting in the highest tumor-to-background contrast ratio compared with standard imaging techniques. This attribute of the edema in the MR image proves useful for defining a definite texture.
601
In the proposed method the textural information of the MR image is captured using the gray co-occurrence matrix. The GLCM derives the textural feature map of the MR image. Local entropy as textural feature exploits the feature map. The local entropy computes the probability of the pixel intensity variation and helps in the classification of the texture. The GLCM and local entropy combination proves useful in defining the texture of edema for segmentation.
2.
Materials and methods
The section discusses the computation of gray level cooccurrence matrix, and the proposed method for edema as well as tumor segmentation in brain MR images using local entropy as textural feature.
2.1.
Gray level co-occurrence matrix
The gray co-occurrence matrix gives an idea about the transition of intensities between pixels in a certain direction and distance. Co-occurrence means the number of times the gray level of pixel j follows the gray level of pixel i in a particular way. In a brain image of size M * N the gray levels L can be denoted by G = 0, 1, . . ., L 1. The co-occurrence matrix of an image is an L * L square matrix and is denoted as P ¼ tij LL . The elements of the matrix specified by the numbers of transitions between all pairs of gray levels in G = 0, 1, . . ., L 1 and computed for different values of u can be represented as Eq. (1):
Pði; j; d; uÞ ¼ ððk; lÞ; ðm; nÞÞ 2 ðLy Lx Þ ðLy Lx Þjkm ¼ 0j; jlnj ¼ d; Iðk; lÞ ¼ i; Iðm; nÞ ¼ j
(1)
where Lx = 1, 2, . . ., Nx is the horizontal spatial domain, Ly = 1, 2, . . ., Ny is the vertical spatial domain, d = 1 and u can take any value as shown in Fig. 1 (a). The texture information in the image is adequately specified by a set of gray tone spatial dependence matrices, computed from various angular relationships and distance between neighboring resolution cell pairs on the image. The GLCM helps to define the probabilities of gray levels at the individual pixel level. This aspect of GLCM helps in defining coarse and fine textures and is employed in the proposed method. Haralick et al. proposed several textural features derived from these angular nearest neighbor gray tone spatial dependence matrices [57]. Eq. (2) defines the textural entropy extracted from the gray tone dependence matrices as:
H¼
XX i
pði; jÞlogðpði; jÞÞ
(2)
j
where p(i, j) represents the (i, j) th entry in a normalized gray tone spatial dependence matrix, P(i, j)/R. From Eq. (2), entropy as textural feature represent the probability of intensity level which an individual pixel can adapt. In the proposed method entropy acts as a tool to classify the texture using the textural feature map captured by the GLCM.
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biocybernetics and biomedical engineering 39 (2019) 599–612
Fig. 1 – Gray Level Co-occurrence Matrix. (a) Four orientations used for defining the co-occurrence matrices. (b) Four Quadrants of the co-occurrence matrix.
2.2. Edema segmentation using local entropy as textural feature Entropy is measure of uncertainty in an image. In image analysis entropy is used to quantify the minimum descriptive complexity of a random variable [14]. Entropy provides a good level of information to describe an image. Pal et al. [13] extended the concept of entropy to gray tone image for defining its global, local and conditional entropy. The local entropy takes into account the spatial distributions of the gray levels. If t be a value used to threshold an image, it partitions the co-occurrence matrix into four quadrants A, B, C and D as shown in Fig. 1(b). The probabilities of the four quadrants are computed using Eq. (3): t X t X PtA ¼ pij ; i¼0 j¼0
PtB
t X L1 X
¼
pij
pij PtA
;
0 < i; jt
t t X X
ptij logptij C
C
pij PtC
;
t þ 1i; jL1
(7)
C
where both HBB(t) and HFF(t) are determined by the threshold t, thus they are function of t. By summing up the local transition entropies of foreground and background, the local entropy (LE) is defined as Eq. (8):
HLE ¼ HBB þ HFF
(8)
Thus, HLE(t) describes the local entropy of the quadrants A and C. The gray level corresponding to the maximum of HLE corresponds to the threshold for segmentation.
(4) t ¼ argfmaxðHLE ðtÞÞg
ptij ¼
(6)
A
i¼tþ1j¼tþ1
i¼tþ1 j¼0 L1 X L1 X
The probabilities of gray-level transition within each particular quadrant obtained by normalizing the probabilities are further computed for different quadrants. Eqs. (4) and (5) represents the 'cell probabilities' for quadrants A and C respectively:
A
A
The second order local entropy of the background is defined using the local quadrant C. It contains the entropy transitions of the background and can be defined using Eqs. (2) and (5) as Eq. (7):
HBB ðtÞ ¼
i¼tþ1 j¼0
ptij ¼
i¼0 j¼0
(3)
pij ;
PtD ¼
t X t X HFF ðtÞ ¼ ptij logptij
pij ;
i¼0 j¼tþ1 L1 X t X
PtC ¼
transition within the background (bright area). The gray level transition between the object and the background or across the objects boundary is placed in quadrant B and quadrant D. These four regions are further grouped into two classes, referred to as local quadrant and joint quadrant. Quadrant A and C are referred to as local quadrant. This is because the gray level transition arising within the object or the background of the image occur in quadrants A and C [13]. The second order local entropy of the object is defined using the local quadrant A. It contains the entropy transitions of the foreground and can be defined using Eqs. (2) and (4) as Eq. (6):
(5)
Quadrant A represents gray level transition within the object (dark area) while quadrant C represents gray level
(9)
Eq. (9) represents the maximum of local entropy that serves as the threshold for segmentation. In case of edema segmentation, FLAIR images from the BRATS database are used. FLAIR imaging provides a marked contrast enhance-
biocybernetics and biomedical engineering 39 (2019) 599–612
ment, while suppressing CSF, resulting in the highest tumorto-background contrast ratio compared with standard imaging techniques [58]. Fig 2 (a) represents the scatter plot of gray level transitions of the FLAIR image containing edema. In the scatter plot the gray level values are grouped along the main diagonal. The distribution of gray level of the pixel is indicative of rich variation in the intensity values [59]. From the scatter plot it is observed that large areas are characterized by low variations in intensity. The high intensity transitions occur at the object boundary. Local entropy as textural feature computed using the GLCM for the object and the background from quadrants A and C respectively act as a classifier for the image texture. Therefore for the threshold selection in case of edema segmentation, the local quadrants A and C are more useful than the joint quadrants B and D. Fig 2(b) and (c) represent the local entropy transitions in quadrant A and C for FLAIR image. Similarly for tumor segmentation, contrast enhanced T1-w images (T1c) are used. When enhancing agent is injected the tumor appears bright, thus changing the signal intensity and enhancing the contrast. Fig 3 (a) represent scatter plot for T1 weighted contrast enhanced images while Fig. 3 (b) and (c) represent the local entropy transitions in quadrant A and C for tumor segmentation.
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Fig. 4 represents the local entropy plot for threshold selection. Fig. 5 represents the flow chart of the proposed method. The algorithm for the proposed method is: 1. Step 1: Compute the GLCM matrix using the angular relation u = 135 and neighboring resolution cells separated by distance d = 1 and gray levels as 256. 2. Step 2: Compute the probabilities of the quadrants A, B, C, D of the MR image having size L * L. 3. Step 3: Compute the cell probabilities of the quadrants A and C using Eqs. (4) and (5). 4. Step 4: Compute the local entropy transitions of quadrants A and C using Eqs. (6) and (7). 5. Step 5: Compute the local entropy (LE) using Eq. (8) by summing up the local entropy transitions of quadrant A and C. 6. Step 6: Compute the threshold for segmentation as the maximum of the local entropy using Eq. (9). The proposed method presents a new threshold based method for edema and tumor segmentation using local entropy as textural feature captured using the spatial
Fig. 2 – For FLAIR image from BRATS database: (a) Scatter plot of GLCM: (b) Local entropy transitions of Quadrant A: (c) Local entropy transitions of Quadrant C.
Fig. 3 – For T1-c image from BRATS database: (a) Scatter plot of GLCM: (b) Local entropy transitions of Quadrant A: (c) Local entropy transitions of Quadrant C.
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Fig. 4 – Entropy curve for: (a) T1 weighted contrast enhanced image for tumor core segmentation: (b) FLAIR image for edema segmentation.
dependence and angular relationship of the gray level cooccurrence matrix.
3.
Results and discussion
Experiments are conducted using publically available BRATS database [60–62]. BRATS 2012, BRATS2 and BRATS 2013 database are used for edema and tumor core segmentation experiments. The BRATS 2012 and BRATS2 database consist of High Grade Glioma (HG) and Low Grade Glioma (LG) images of ten subjects respectively. Experiments are conducted on all HG images of the ten subjects and results for four subjects are
presented for visual comparison for BRATS 2012 and BRATS2 database. BRATS 2013 database consist of MR images of more than two hundred subjects. Experiments are conducted on more than 10 subsampled HG images for BRATS 2013 database and results for four images are shown for visual evaluation and comparison. Most of the images from the database consist of approximately 200 slices of the volume for different MR sequences. For example, the Flair sequence of BRATS 2012 database of subject 3540 consist of 230 slices. Out of the 230 slices, edema is visible only in slice numbers from 130 to 187. Slices without edema or tumor are not considered for quantification. Validation of segmentation using proposed method is done with ground truth images provided from the available BRATS database. The proposed method is unsupervised and no training set is required. Evaluation of the segmentation with the ground truth is an important task. In segmentation evaluation the segmented image is compared with the ground truth by measuring the distance or similarity between them. For the proposed method segmentation evaluation is carried out using Accuracy, Sensitivity, Specificity, Precision, Dice Coefficient and Structural Similarity Index. Implementation and testing of the proposed method is done using the computational facility with Windows 7, Matlab 7.10 (R2010a), Intel Core 2 Duo, 2.09 Ghz, 2 GB RAM. The proposed method is compared with basic methods of minimum Cross Entropy (CE) thresholding [31] and Maximum Entropy (ME) thresholding [23].
3.1.
Fig. 5 – Flow Chart of the proposed Segmentation method.
Experiments for edema segmentation
Fig. 7, 9 and 11 represent the results for edema segmentation. Tables 1–7 present the evaluation metrics for edema. Accuracy is used as a statistical measure of how well a binary classification test correctly identifies or excludes a condition. Local entropy depends on the probability of co-occurrence of pixel intensities and takes into account the spatial distributions of the gray levels. This assist
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Table 1 – Comparison of Accuracy for Edema segmentation for BRATS database.
Table 4 – Comparison of Precision for Edema segmentation for BRATS database.
Database
Database
Proposed method
Cross entropy
Maximum entropy
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.9384 0.9659 0.9386 0.9456
0.9023 0.9356 0.9344 0.9458
0.9234 0.9487 0.9354 0.9456
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.5478 0.2552 0.4280 0.4341
0.3998 0.6862 0.5922 0.4324
0.4673 0.1973 0.4127 0.4336
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9612 0.9756 0.9607 0.9806
0.9648 0.9648 0.9379 0.9842
0.9701 0.9744 0.9605 0.9791
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.3057 0.2618 0.5511 0.7034
0.3232 0.2256 0.4162 0.9248
0.3409 0.1727 0.5435 0.6783
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.9572 0.9512 0.9642 0.9578
0.9579 0.9520 0.9653 0.9665
0.9559 0.9514 0.9706 0.9451
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.4277 0.6616 0.0767 0.5298
0.4327 0.6553 0.0533 0.6640
0.4194 0.6755 0.0028 0.4343
Average
0.9581
0.9510
0.9550
Average
0.4319
0.4838
0.3982
Table 2 – Comparison of Sensitivity for Edema segmentation for BRATS database.
Table 5 – Comparison of Dice Coefficient for Edema segmentation for BRATS database.
Database
Database
Proposed method
Cross entropy
Maximum entropy
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.6361 0.7978 0.5143 0.896
0.8184 0.9631 0.5048 0.856
0.7472 0.9161 0.5554 0.888
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.5887 0.3867 0.4672 0.5849
0.5372 0.3161 0.4501 0.5746
0.5750 0.3247 0.4735 0.5827
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9382 0.643 0.6685 0.859
0.9039 0.8748 0.9547 0.6423
0.7373 0.3369 0.7452 0.873
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.4611 0.3721 0.6041 0.7735
0.4761 0.3587 0.5797 0.7581
0.4662 0.2284 0.6286 0.7634
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.7264 0.6548 0.0784 0.6276
0.7256 0.6974 0.0483 0.5321
0.7332 0.6192 0.0015 0.6906
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.5384 0.6582 0.0776 0.5746
0.5421 0.6757 0.0507 0.5908
0.5335 0.6461 0.0020 0.5333
Average
0.67
0.7101
0.6536
Average
0.5073
0.4925
0.4798
Table 3 – Comparison of Specificity for Edema segmentation for BRATS database.
Table 6 – Comparison of Jaccard Index for Edema segmentation for BRATS database.
Database
Database
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.4171 0.2397 0.3048 0.4133
0.3673 0.1877 0.2904 0.4031
0.2214 0.4782 0.3025 0.7243
0.9743 0.9817 0.9706 0.9834
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.2996 0.2286 0.4328 0.6306
0.3124 0.2185 0.4081 0.6104
0.6757 0.4527 0.4845 0.3263
0.9661 0.9717 0.9832 0.9872
0.9639 0.9770 0.9896 0.9572
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.3683 0.4905 0.0403 0.4031
0.3719 0.5102 0.0260 0.4193
0.0963 0.1712 0.3201 0.2165
0.9687
0.9657
Average
0.3557
0.3438
0.3725
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.9609 0.9682 0.9620 0.9478
0.9085 0.9955 0.9957 0.9498
0.9366 0.9492 0.9564 0.9482
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9616 0.9794 0.9744 0.9855
0.9659 0.9659 0.9371 0.9979
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.9654 0.9741 0.9815 0.9735
Average
0.9695
606
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Table 7 – Comparison of Structural Similarity Index for Edema segmentation for BRATS database. Database
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.7129 0.8308 0.7861 0.8913
0.4992 0.7232 0.7586 0.8389
0.5569 0.7232 0.7332 0.837
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.8864 0.9424 0.8917 0.9299
0.875 0.8111 0.7302 0.9156
0.9164 0.9503 0.8537 0.8888
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.8535 0.8604 0.9287 0.8605
0.8202 0.8173 0.9301 0.8522
0.8092 0.8258 0.9303 0.8045
Average
0.8646
0.7976
0.8191
in identification of edema pixels hence the proposed method exhibits an accuracy of 95% for edema segmentation. Minimum Cross Entropy and Maximum Entropy method also exhibit the same accuracy. Sensitivity represents the ability to correctly detect the condition. It is defined using the ratio of true positive to the sum of true positives and false negatives. In case of minimum CE the method implements an information theoretic distance between two probability distributions for threshold selection.
This helps in correct detection of true positive pixels hence minimum CE method exhibit a better sensitivity as compared to the proposed method and ME method. Specificity, a necessary counterpart of the sensitivity is a measure of the portion of negative voxel in the ground truth segmentation that are also identified as negative by the segmentation being evaluated. The average specificity for edema for all the compared methods is observed as 96%. The precision metric is sensitive to over-segmentation or under-segmentation. Over-segmentation leads to low precision scores. The average precision score for proposed method is 43%. For the methods of CE and ME the scores are 48% and 39% respectively. Edema a swelling in the brain can develop in and around any tissue hence in FLAIR images the intensity of the edema can vary and cause over or under segmentation. The Dice Coefficient measures the overlap between the ground truth and segmentation being evaluated. Average Dice Coefficient is observed as 50% for edema using proposed method and 49% and 47% for CE and ME methods. The proposed method demonstrate better results in comparison to CE and ME methods in terms of Dice Coefficient. The Jaccard Index (JI) measures the intersection over the union of the labeled segments for each class and reports the average. The JI is found better for ME method. One of the reasons for a better JI as compared to other methods is the ME method maximizes the inter-class entropy. Structural Similarity index (SSIM) combines the luminance, contrast and the similarity between the ground truth
Fig. 6 – Tumor core segmentation results for High Grade Glioma T1-w contrast enhanced images from BRATS 2012 database. (a)–(d) Images containing Tumor (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
biocybernetics and biomedical engineering 39 (2019) 599–612
607
Fig. 7 – Edema segmentation results for High Grade Glioma Flair images from BRATS 2012 database. (a)–(d) Images containing Edema (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
Fig. 8 – Tumor segmentation results for High Grade Glioma T1-w contrast enhanced images from BRATS 2013 database. (a)–(d) Images containing Tumor (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
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Fig. 9 – Edema segmentation results for High Grade Glioma Flair images from BRATS 2013 database. (a)–(d) Images containing Edema (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
Fig. 10 – Tumor segmentation results for High Grade Glioma T1-w contrast enhanced images from BRATS-2 database. (a)–(d) Images containing Tumor (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
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Fig. 11 – Edema segmentation results for High Grade Glioma Flair images from BRATS-2 database. (a)–(d) Images containing Edema (e)–(h) Ground truth. Segmented images using (i)–(l) Proposed method (m)–(p) Cross Entropy (q)–(t) Maximum Entropy.
3.2.
Results for tumor core segmentation
and segmented image [63]. SSIM close to 1 specifies exact similarity. Local entropy as textural feature measures the pixel variability, the marked contrast in FLAIR images is captured as a definite texture for edema hence SSIM for the proposed method is 0.8846 and better than CE and ME methods.
Fig. 6, 8 and 10 demonstrate the segmentation results using the proposed method for BRATS 2012, 2013 and BRATS2 database for tumor core. Tables 8–14 present the comparison of evaluation metrics for tumor segmentation.
Table 8 – Comparison of Accuracy for tumor segmentation for BRATS database.
Table 9 – Comparison of Sensitivity for tumor segmentation for BRATS database.
Database
Database
Proposed method
Cross entropy
Maximum entropy
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.9712 0.9973 0.9844 0.9915
0.9732 0.9957 0.9896 0.9916
0.9737 0.9964 0.9894 0.9915
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.3696 0.8324 0.6476 0.8238
0.3180 0.9631 0.5048 0.8228
0.2571 0.9403 0.3738 0.8238
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9961 0.9921 0.9903 0.9844
0.9937 0.9916 0.9757 0.9835
0.9963 0.9920 0.9832 0.9829
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.6949 0.6067 0.7357 0.4175
0.8917 0.6234 0.8978 0.3609
0.8123 0.5342 0.8519 0.3299
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.9797 0.9925 0.9864 0.9666
0.9764 0.9866 0.9863 0.9672
0.9783 0.9797 0.9856 0.9677
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.1230 0.8068 0.4941 0.2998
0.1569 0.4907 0.4676 0.2750
0.1426 0.1745 0.3441 0.2552
Average
0.9860
0.9843
0.9847
Average
0.5710
0.5644
0.4866
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Table 10 – Comparison of Specificity for tumor segmentation for BRATS database.
Table 13 – Comparison of Jaccard Index for tumor segmentation for BRATS database.
Database
Database
Proposed method
Cross entropy
Maximum entropy
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.9892 0.9995 0.9886 0.9962
0.9929 0.9961 0.9957 0.9962
0.9952 0.9937 0.9971 0.9962
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.2720 0.7610 0.3383 0.7243
0.2569 0.6686 0.3746 0.7243
0.2214 0.4782 0.3025 0.7243
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9990 0.9969 0.9951 0.9991
0.9947 0.9963 0.9772 0.9996
0.9980 0.9977 0.9857 0.9997
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.6301 0.4877 0.5832 0.4031
0.5778 0.4812 0.4066 0.3555
0.6757 0.4527 0.4845 0.3263
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.9938 0.9971 0.9963 0.9908
0.9899 0.9988 0.9967 0.9924
0.9921 0.9995 0.9985 0.9935
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.0895 0.7213 0.4174 0.2393
0.0973 0.4676 0.4020 0.2273
0.0963 0.1712 0.3201 0.2165
Average
0.9951
0.9939
0.9956
Average
0.4723
0.4200
0.3725
Table 11 – Comparison of Precision for tumor segmentation for BRATS database. Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.5076 0.6862 0.4146 0.8571
0.5721 0.7164 0.5922 0.8587
0.6145 0.7592 0.3738 0.8571
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.8710 0.7131 0.7378 0.9209
0.6214 0.6783 0.4263 0.9596
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.2473 0.8719 0.7289 0.5426
Average
0.6749
Database
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.8392 0.9691 0.8120 0.8967
0.8176 0.9127 0.8460 0.8030
0.8457 0.8340 0.8802 0.8030
0.8007 0.7480 0.4263 0.9676
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.9708 0.9414 0.9373 0.9379
0.8701 0.9007 0.8367 0.9342
0.9251 0.9253 0.8479 0.9351
0.2042 0.9085 0.7413 0.5673
0.2286 0.8983 0.8211 0.5886
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.9165 0.9097 0.8999 0.8736
0.8527 0.8976 0.8672 0.8423
0.8671 0.9202 0.8963 0.8475
0.6539
0.6737
Average
0.9087
0.8651
0.8773
Table 12 – Comparison of Dice Coefficient for tumor segmentation for BRATS database. Database
Table 14 – Comparison of Structural Similarity Index for tumor segmentation for BRATS database.
Proposed method
Cross entropy
Maximum entropy
Brats2012hg536 Brats2012hg520 Brats2012hg524 Brats2012hg516
0.4277 0.8643 0.5056 0.8401
0.4088 0.8014 0.5450 0.8401
0.3626 0.6470 0.4645 0.8401
Brats2013hgg54512 Brats2013hgg54530 Brats2013hgg54554 Brats2013hgg54560
0.7731 0.6556 0.7367 0.5745
0.7324 0.6497 0.5782 0.5246
0.8065 0.6233 0.6528 0.4920
Brats2hg684 Brats2hg697 Brats2hg703 Brats2hg733
0.1643 0.8381 0.5890 0.3862
0.1774 0.6372 0.5735 0.3704
0.1756 0.2923 0.4850 0.3560
Average
0.6129
0.5699
0.5165
Database
In case of tumor segmentation the proposed method performs better or equal for most of the evaluation metrics as compared to the CE and ME methods. The proposed method exhibits an accuracy of around 98% and is same as other compared methods. Specificity relates to the ability to correctly detect, healthy tissues and is observed to be around 99% for all the compared methods. The proposed method demonstrate sensitivity of 57% and is better than CE and ME. Sensitivity is defined as the ratio of true positives to the sum of true positives and false negatives. In case of tumor segmentation the textures are well defined by the local entropy transitions therefore an accurate threshold can be obtained which can classify pixels as tumor or non tumor. The precision metrics is almost equal for all the three methods. The proposed method demonstrates a better Dice Coefficient and JI for tumor segmentation. The SSIM reflects the structural similarity between the gold standard and the segmented image. In case of tumor segmentation the SSIM is close to one
biocybernetics and biomedical engineering 39 (2019) 599–612
as compared to CE and ME methods because of defined tumor texture due to good contrast enhancement of tumor pixels in the MR image. The proposed method thus exhibits encouraging results for tumor core segmentation.
[7]
[8]
4.
Conclusions
Cerebral edema is a serious disorder and potentially lifethreatening condition. MR imaging proves as a vital tool right from detection and localization to treatment planning and clinical management. The work proposes an automatic unsupervised method for edema and tumor segmentation using textural feature. In the proposed method the textural feature map of the brain MR image is computed using the gray co-occurrence matrix. The gray co-occurrence matrix computes the probability of gray level at the individual pixel level. This is helpful to define coarse and fine textures. Entropy as second order textural feature measures the randomness in the pixel intensity and proves advantageous to identify the texture of the edema in MR image. Local entropy acts as a classifier for threshold selection. Experiments on publically available BRATS database yields encouraging results in most of the cases. The proposed method is successful in automatic segmentation of edema as well as tumor core as seen by visual perception and evaluation.
[9]
[10] [11]
[12]
[13] [14] [15]
[16]
[17]
Authorship statement [18]
All persons who meet authorship criteria are listed as authors, and all authors certify that they have participated sufficiently in the work to take public responsibility for the content, including participation in the concept, design, analysis, writing, or revision of the manuscript. Furthermore, each author certifies that this material or similar material has not been and will not be submitted to or published in any other publication before its appearance in Biocybernetics and Biomedical Engineering.
[19]
[20]
[21] [22]
references
[23]
[1] Adukauskiene D, Bivainyte A, Radavieiute E. Cerebral edema and its treatment. Medicina (Kaunas) 2017;43(2). [2] Chen M-Y, Hu1 Q-M, Liu Z-C, Zhou1 S-J, Li X-D. Segmentation of cerebral edema around spontaneous intracerebral hemorrhage. Int J Appl Math Inf Sci 2013. Natural Sciences Publishing Cor.. [3] Norton NS. Cerebral edema. Ref Module Biomed Sci 2014. [4] Castro P, Azevedo E, Serrador J, Rocha I, Sorond F. Hemorrhagic transformation and cerebral edema in acute ischemic stroke: link to cerebral autoregulation. J Neurol Sci 2017;372(15):256–61. [5] Havaei M, Davy A, Warde-Farley D, Biard A, Courville A, Bengio Y, et al. Brain Tumor Segmentation with Deep Neural Networks Medical Image Analysis, vol. 35. 2017;p.
[24]
[6] Gilanie G, Attique M, Ullah H, Naweed S, Ahmed E, Ikram M. Object extraction from T2 weighted brain MR image using
[29]
18–31.
[25]
[26] [27]
[28]
611
histogram based gradient calculation. Pattern Recognit Lett 2013;34:1356–63. Gordillo N, Montseny E, Sobrevilla P. State of the art survey on MRI brain tumor segmentation. Magn Resonance Imaging Vol 2013;31(8):1426–38. Yao J. Image processing in tumor imaging. New Tech Oncol Imaging 2006;79–102. Wu CM, Chen YC. Texture features for classification of ultrasonic liver images. IEEE Trans Med Imaging 1992;11:141–52. Miller P, Astley S. Classification of breast tissue by texture analysis. Image Vision Comput 1992;10:277–82. Koss JE, Newman FD, Johnson TK, Krich DL. Abdominal organ segmentation using texture transform and Hopfield neural network. IEEE Trans Med Imaging 1999;18:640–8. Xie J, Jiang Y, Tsui HT. Segmentation of kidney from ultrasound images based on texture and shape priors. IEEE Trans Med Imaging 2005;24:45–57. Pal N, Pal S. Entropic thresholding. Signal Process 1989;16:97–108. Cover T0, Thomas J, Wiley J, InterScience W. Elements of Information Theory. New York: Wiley; 1991. Rajinikanth V, Satapathy SC, Fernandes SL, Nachiappan S. Entropy based segmentation of tumor from brain MR images – a study with teaching learning based optimization. Pattern Recognit Lett 2017;1–9. Chaudhari AK, Kulkarni JV. Local entropy based brain MR image segmentation. IEEE 3rd International Advance Computing Conference (IACC); 2013. http://dx.doi.org/10.1109/IAdCC.2013.6514403 Priya RK, Thangaraj C, Kesavadas C, Kannan S. Fuzzy entropy based MR brain image segmentation using modified particle swarm optimization. Int J Imaging Syst Technol 2013;23(4):281–8. Priya RK, Thangaraj C, Kesavadas C, Kannan S. Application of swarm intelligence in fuzzy entropy based image segmentation. Stud Comput Intell 2014;561:227–45. Acharya UR, Fujita H, Sudarshan VK, Bhat S, Koh JEW. Application of entropies for automated diagnosis of epilepsy using EEG signals. Knowl Based Syst 2015;88(C): 85–96. Kannathal N, Choo ML, Acharya UR, Sadasivan PK. Entropies for detection of epilepsy in EEG. Comput Methods Programs Biomed 2005;80(3):187–94. Pun T. A new method for gray level picture thresholding using entropy of the histogram. Signal Process 1980;223–7. Pun T. Entropic thresholding: a new approach. Comput Graphics Image Process 1981;210–39. Kapur JN, Sahoo PK, Wong AKC. A new method for graylevel picture thresholding using the entropy of the histogram. Comput Vision Graphics Image Process 1985;29:273–85. Bhandari AK, Kumar A, Singh GK. Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur's, Otsu and Tsallis functions. Expert Syst Appl 2015;42(3):1573–601. Sathya PD, Kayalvizhi R. Optimal multilevel thresholding using bacterial for aging algorithm. Expert Syst Appl 2011; 38(12):15549–64. Sahoo P, Wilkins C, Yeager J. Threshold selection using Renyi's entropy. Pattern Recognit 1997;30(1):71–84. Chang C, Chen K, Wang J, Althouse LJ. A relative entropybased approach to image thresholding. Pattern Recognit 1994;27(9):1275–89. Pal NR. On minimum cross-entropy thresholding. Pattern Recognit 1996;29(4):575–80. Brink AD, Pendock NE. Minimum cross-entropy threshold selection. Pattern Recognit 1996;29(1):179–88.
612
biocybernetics and biomedical engineering 39 (2019) 599–612
[30] Chen W-T, Wen C-H, Yang C-W. A fast two-dimensional entropic thresholding algorithm. Pattern Recognit 1994; 27(7):885–93. [31] Li CH, Tam PKS. An iterative algorithm for minimum cross entropy thresholding. Pattern Recognit Lett Vol 1998;19 (8):771–6. [32] Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys 1998;52:479–87. [33] Mohamed A, El-Sayed S, Abdel-Khalek, Abdel-Aziz E. Study of efficient technique based on 2D Tsallis entropy for image thresholding. Int J Comput Sci Eng (IJCSE) 2011;3(9):1325–36. [34] Sahoo PK, Arora G. A thresholding method based on twodimensional Renyi's entropy. Pattern Recognit Vol 2004;37 (6):1149–61. [35] Portes de Albuquerque M, Esquef IA, Gesualdi Mello AR, Portes de Albuquerque M. Image thresholding using Tsallis entropy. Pattern Recognit Lett 2004;25(9):1059–65. [36] Yan C, Sang N, Zhang T. Local entropy-based transition region extraction and thresholding. Pattern Recognit 2003;24(16):2935–41. [37] Sahoo PK, Arora G. Image thresholding using twodimensional Tsallis-Havrda-Charvát entropy. Pattern Recognit Lett 2006;27(6):520–8. [38] Li X, Zhao Z, Cheng HD. Fuzzy entropy threshold approach to breast cancer detection. Inf Sci – Appl 1995;4(1):49–56. [39] Cheng HD, Yen-Hung, Chen Ying Sun A. novel fuzzy entropy approach to image enhancement and thresholding. Signal Process 1999;75(3):277–301. [40] Bloch I. Fuzzy spatial relationships for image processing and interpretation: a review. Image Vis Comput 2005;23 (2):89–110. [41] Tao WB, Tian JW, Liu J. Image segmentation by three-level thresholding based on maximum fuzzy entropy and genetic algorithm. Pattern Recognit Lett 2003;24:3069–78. [42] Linyi L, Deren L. Fuzzy entropy image segmentation based on particle swarm optimization. Prog Nat Sci 2008;18 (9):1167–71. [43] Jinhui L, Yiliang Z. Multi-threshold image segmentation using maximum fuzzy entropy based on a new 2D histogram. Optik 2013;124(18):3756–60. [44] Yin S, Zhao X, Wang W, Gong M. Efficient multilevel image segmentation through fuzzy entropy maximization and graph cut optimization. Pattern Recognit 2014;47 (9):2894–907. [45] Yu H-Y, Zhi X-B, Fan J-L. Image segmentation based on weak fuzzy partition entropy. Neurocomputing 2015;168:994–1010. [46] Ye Z-W, Wang M-W, Liu W, Chen S-B. Fuzzy entropy based optimal thresholding using bat algorithm. Appl Soft Comput 2015;31:381–95.
[47] Yin S, Qian Y, Ming, Gongb L. Unsupervised hierarchical image segmentation through fuzzy entropy maximization. Pattern Recognit 2017;68:245–59. [48] Xuan TP, Siarry P, Oulhad H. Integrating fuzzy entropy clustering with an improved PSO for MRI brain image segmentation. Appl Soft Comput 2018. Available online 31 January. [49] Xiao Y, Cao Z, Cao Z, Yuan J. Entropic image thresholding based on GLGM histogram. Pattern Recognit Lett 2014;40:47–55. [50] Sarkar S, Das S, Chaudhuri S Sinha. A multilevel color image thresholding scheme based on minimum cross entropy and differential evolution. Pattern Recognit Lett 2015;54:27–35. [52] Zheng KF, Wang X. Feature selection method with joint maximal information entropy between features and class. Pattern Recognit 2018;77:20–9. [53] Muthuvel M, Thangaraju f Balakumaran, Chinnasamy G. Microcalcification cluster detection using multiscale products based Hessian matrix via the Tsallis thresholding scheme. Pattern Recognit Lett 2017;94:127–33. [54] Nguyen DC, Benameur S, Mignotte M, Lavoie F. Superpixel and multi-atlas based fusion entropic model for the segmentation of X-ray images. Med Image Anal 2018;58–74. [55] Sumathi R, Venkatesulu M, Arjunan SP. Extracting tumor in MR brain and breast image with Kapur's entropy based Cuckoo Search Optimization and morphological reconstruction filters. Biocybern Biomed Eng 2018;38(4):918–30. [56] Pollay M. Blood-Brain Barrier, Cerebral Edema.. In: Wilkins RH, Rengachary SS, editors. Neurosurgery. 2nd ed. New York: McGraw Hill Book Co.; 1996. p. 335–44. [57] Haralick R, Shanmugan K, Dinstein I. Textural features for image classification. IEEE Trans Syst Man Cybern 1973;610–21. [58] Essig M, Knopp MV, Schoenberg SO, Hawighorst H, Wenz F, Debus J, et al. Cerebral gliomas and metastases: assessment with contrast-enhanced fast fluid-attenuated inversionrecovery MR imaging. Radiology 1999;210(2):551–7. [59] Gonzalez R, Woods R. Digital Image Processing. 2nd ed. Pearson Education; 2005. [60] http://www.imm.dtu.dk/projects/BRATS2012. [61] Menze. et al. The Multimodal Brain Tumor Image Segmentation Benchmark (BRATS). IEEE Trans Med Imaging 2015;34(10):1993–2024. [62] Kistler. et al. The virtual skeleton database: an open access repository for biomedical research and collaboration. J Med Internet Res 2013;15(11). [63] Wang Z, Bovik AC, Sheikh HR, Simoncelli EP. Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 2004;13(4):600–12.