# Generalized Exponential Fuzzy Entropy Approach for Automatic Segmentation of Chest CT with COVID-19 Infection

Authors: Saud S. Alotaibi; Ahmed Elaraby
Journal: Complexity
 (2022)

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## Abstract

The proposed work describes an approach for the segmentation of abnormal lung CT scans of COVID-19. Lung diseases are the leading killer in both men and women. The pulmonary experts normally make attempts, such as early detection of patients by tomography tests before lung specialists treat patients who are tortured by lung disease. Moreover, lung specialists do their best to detect the presence of lung conditions. X rays or CT scan checks are performed for tomography tests. The finest approach for medical diagnosis and a wide range of uses is computed tomography (CT). This kind of imaging offers elaborate cross-sectional pictures of skinny slices of the organic structure. However, the preprocessing and denoising methods of Lung CT scans may mask some important image features. To address this challenge, we propose a novel framework involving an optimization technique algorithm to solve a multilevel thresholding problem based on information theory to segment abnormal lung CT scans. The proposed framework will evaluate a sample of CT scan images taken from a well-known benchmark database. The evaluation results will assess subjectively and objectively to demonstrate the effectiveness of the proposed framework.


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## Body

## 1. Introduction

The first case of Corona Virus Disease (COVID-19) was reported in Wuhan, China, in December of 2019. It gradually spread across China in different regions, and the World Health Organization (WHO) declared the COVID-19 outbreak a Public Health Emergency of International Concern (PHEIC) by the end of January 2020, which later became a global pandemic [1]. According to the WHO's progress report, there are more than 166 million confirmed cases and more than 3.5 million deaths worldwide by the 3rd week of May 2021 [2]. Every day, the infection spreads, and the healthcare system struggles to care for each infected person, especially in highly infected countries such as India, the United States, Spain, Italy, and the United Kingdom. Although the characteristics of COVID-19 are not well known due to virus mutations, we can conclude its behavior from statistics such as a high rate of spread, a higher risk for people with weakened immune systems, diabetics, and the elderly recovery time periods are highly varying. One of the most effective approaches is the early detection of this disease for minimizing the infection spread [3]. Many countries' healthcare systems are being strained by a huge number of COVID-19 patients. As a result, having a reliable automated method for defining and quantifying the regions of the infected lung would be extremely beneficial. Patients who are suspected of pneumonia or having a respiratory infection are hospitalized under observation for medical screening that includes laboratory and nonlaboratory tests to determine the origin, location, and severity of the infection.COVID-19 diagnosis can be performed using a variety of medical techniques such as clinical characteristics and radiologist's diagnosis. Human temperature monitoring and reverse transcription-polymerase chain reaction (RT-PCR) are kinds of clinical characteristics [4]. RT-PCR is the primary tool for detecting COVID-19 confirmed cases. This method, however, necessitates analysis time and specimen collection [5] Moreover, COVID-19 RT-PCR may be initially negative due to its low sensitivity. As a result, computed tomographic (CT) imaging has become increasingly relevant in evaluating parenchymal abnormalities in lung diseases like COVID-19. CT scans and chest X-ray (CXR) radiographs are used by radiologists to make diagnoses [5]. CT imaging is useful for diagnosing diseases as well as quantifying their severity and development over time. Significant consolidation and paving dominate the CT scan findings as COVID-19 progress, reaching a peak within 9–13 days after the onset of COVID-19 symptoms. Therefore, CT-based disease quantification can be used for patient stratification, management, and prognostication. A CT scan or computed tomography scan is widely used in hospitals as a standard method with high sensitivity for the diagnosis of COVID-19, and it may perform early screening of defected tissue and identify them precisely. The objective quantification and classification of large numbers of CT datasets necessitate the use of automated image analysis. Especially, to quantifying total lung and regional involvement of the disease, reliable lung and lobe segmentation is an important precursor. Widespread availability, high spatial resolution with present multislice scanners, low cost, higher sensitivity, and fast scan time are all advantages of CT imaging.Manual observation is a time consuming, repetitive, and monotonous method for detecting and extracting texture information from the lungs. Various computer vision methodologies, such as segmentation and classification approaches, have been suggested to deal with various aspects of the COVID-19 pandemic. These procedures are standardizable, repeatable, and can help improve diagnostic accuracy in a short period of time. These procedures work by assisting doctors and specialists in completing complex tasks with precision, using a mix of diversity classification methods with a reasonable running time. Moreover, these methodologies can be categorized into main categories: classical machine learning and deep learning approaches [6]. Image segmentation is challenging and a complex process in biomedical engineering that is influenced by a variety of factors, including object irregularity, low contrast, noise, and lighting. Additional diagnostic insights are obtained, such as calculating the area and volume of segmented structures. Due to intensity inhomogeneity, artifact existence, and the closeness in the gray level of different soft tissues, the major problems of segmentation algorithms are exaggerated.For several years, various aspects of segmentation algorithms have been investigated. Automated segmentation of the lung for COVID-19 patients is a demanding process because of the many unspecific characteristics found on CT (i.e., bilateral and peripheral ground-glass opacities and consolidation). Methods of intensity-based segmentation may not involve infected areas, which are essential to any quantitative image analysis. In addition, lung opacity can mask the presence of fissures, making it difficult to distinguish lobes. A few attempts were recently reported for the semantical segmentation of medical images of COVID-19 patients. A major component of a framework that prioritizes patients by severity will be the implementation of such a method. It would detect an infection and find its main spatial features as parameters of scale, distribution, and form [7–10].


## 2. Proposed Methodology

In this section, we present a description of the proposed framework that will be used for the segmentation of abnormal lung CT scans of COVID-19. First, the multilevel thresholding using information theory is exposed. Second, a differential evolution (DE) optimization approach is used. Entropy-based threshold approaches have drawn great attention in the last few years. They have been identified as one of the most powerful image segmentation approaches. For this reason, we propose an approach that combines generalized exponential entropy and fuzzy c partition for the segmentation of lung CT scan infected with COVID-19.The Shannon entropy [11] is defined as(1)Hp=−∑i=1kpilogpi.An image could be interpreted as an information source with the law of probability which is given by its image histogram. Many types of entropy have been proposed and applied in various fields [12]. From previous research, a good result was obtained using various types of entropy applied in different tasks in image processing [13–16]. In [17], Pal and Pal proposed exponential entropy measures and indicated some advantages for considering exponential entropy over Shannon’s entropy, which is widely acclaimed. Exponential entropy is as follows [17]:(2)eHp=∑i=1npie1−piIn [18], Kvalseth proposed a generalized formula of exponential entropy in (1) given by(3)Gep=1/α∑i=0npie1−piα−1∑i=0npi.In terms of generalized exponential entropy, two distributions of probabilities can be derived to object (class A) and background (class B), where (t is a threshold value, as follows:(4)pA:p1PA,p2PA,…..,ptPA,pB:pt+1PB,pt+2PB,…..,pkPB,(5)PA=∑i=1tpi,PB=∑i=t+1kpi.The generalized exponential entropy of object pixels (GαA) and background pixels GαB can be defined as(6)GeAp=1α∑i=1tpie1−piα−1∑i=1tpi,GeBp=1α∑i=t+1kpie1−piα−1∑i=t+1kpi.The generalized exponential entropy is parametrically reliant on the object's and background’s threshold values (t). It is written as the sum of each entropy, allowing statistically independent systems to have a pseudoadditive property. By increasing the information measure between the two classes as much as possible (object and background) so that Get is maximized, the optimum threshold value is the brightness level (t that maximizes the function as follows:(7)topt=ArgmaxGeAt+GeBt+1−αnGeAtnGeBt.A classical setA in the fuzzy domain can be defined as(8)A=x,μAx|x∈X,where 0≤μAx≤1 and μAx is known as the membership function, and it determines how close x is to A. For a n level threshold, the following membership function can be calculated:(9)μ1k=n1k≤a1nk−c1a1−c1a1≤k≤c1n0k>c1n⋮(10)μn−1k=n0k≤an−2nk−an−2cn−2−an−2an−2≤k≤cn−2n1cn−2≤k≤an−2nk−cn−1an−1−cn−1an−1≤k≤cn−1n0k>cn−1(11)μnk=n1k≤an−1nk−ancn−anan−1≤k≤cn−1n1k>cn−1nMaximum fuzzy generalized exponential entropy for each segment of n level is defined as(12)Ge1p=1α∑i=0t1piP1e1−piP1α−1/∑i=0t1piP1,Ge2p=1α∑i=t1+1t2piP2e1−piP2α−1/∑i=t1+1t2piP2,(13)Genp=1α∑i=tn−1+1L−1piPne1−piPnα−1/∑i=tn−1+1L−1piPn,where P1=∑i=0L−1pi∗μ1i,P2=∑i=0L−1pi∗μ2i,⋯,Pn=∑i=0L−1pi∗μni.By maximizing total entropy, the optimal value of the parameters is achieved.(14)φa1,c1,…an−1,cn−1=ArgMaxH1t+H2t+…+HntThen−1 threshold values can be obtained as(15)t1=a1+c12t1=a1+c12,t2=a2+c22,…,tn−1=an−1+cn−12Differential evolution (DE) [19], a population-based global optimization technique, is used in the suggested method. The generalized exponential entropy in (2) is optimized by the “DE” optimization algorithm to acquire an image threshold.


## 3. Experimental Results

In our experimental study, we used a sample of lung CT scan images taken from the benchmark databases. This section is organized as follows: first, we mentioned the information about the utilized dataset of CT images. Next, the programming environment and computer specifications are mentioned. Then, the experimental results are demonstrated followed by comparison algorithms that are identified. Finally, some concluding remarks are provided (Figure1).Figure 1
Gallery of some lung CT scan images with COVID-19 dataset [20].As for the dataset of CT images, we utilized the COVIDx CT-2 dataset [20] including more than 195 thousand CT scan images. Figure 2 shows some CT image samples of utilized datasets arranged as a gallery. As for the comparison methods to verify the efficiency of the proposed method, two similar efficient algorithms applied in this area of such are used which are Tao [21] and Tang [22]. The programming environment utilized to implement the proposed approach and run the experiments and comparisons is MATLAB R2018a running in Windows OS in laptops with an IntelCore i5 processor. Figures 2 to 7 demonstrate the experimental attained outcomes by the proposed approach for various experiments. Figures 813 show the attained results of various companions. Table 1 provides the details of parameters obtained in the experiments of the proposed approach.Figure 2
CT image-1 segmentation results of three threshold levels using the proposed approach. (a) Original CT image, (b) level-2 threshold segmentation, (c) level-3 threshold segmentation, and (d) level-4 threshold segmentation.
(a)(b)(c)(d)Figure 3
CT image-2 segmentation results of three threshold levels using the proposed approach. (a) Original CT image, (b) level-2 threshold segmentation, (c) level-3 threshold segmentation, and (d) level-4 threshold segmentation.
(a)(b)(c)(d)Figure 4
CT image-3 segmentation results of three threshold levels using the proposed approach. (a) Original CT image, (b) level-2 threshold segmentation, (c) level-3 threshold segmentation, and (d) level-4 threshold segmentation.
(a)(b)(c)(d)Figure 5
CT image-4 segmentation results of three threshold levels using the proposed approach. (a) Original CT image, (b) level-2 threshold Segmentation, (c) level-3 threshold segmentation, and (d) level-4 threshold segmentation.
(a)(b)(c)(d)Figure 6
CT image-5 segmentation results of three threshold levels using the proposed approach. (a) Original CT image, (b) level-2 threshold Segmentation, (c) level-3 threshold segmentation, and (d) level-4 threshold segmentation.
(a)(b)(c)(d)Figure 7
CT image-6 segmentation results of three threshold levels using the proposed approach. (a) Original CT image, (b) level-2 threshold Segmentation, (c) level-3 threshold segmentation, and (d) level-4 threshold segmentation.
(a)(b)(c)(d)Figure 8
The comparison outcomes. (a) Original CT image-1; (b–d) segmentation result of threshold levels 2,3, and 4, respectively, of the proposed approach; (e) segmentation results obtained by Tao [21]; (f) segmentation results obtained by Tang [22].
(a)(b)(c)(d)(e)(f)Figure 9
The comparison outcomes. (a) Original CT image-2; (b–d) segmentation result of threshold levels 2,3, and 4, respectively, of the proposed approach; (e) segmentation results obtained by Tao [21]; (f) segmentation results obtained by Tang [22].
(a)(b)(c)(d)(e)(f)Figure 10
The comparison outcomes. (a) Original CT image-3; (b–d) segmentation result of threshold levels 2,3, and 4, respectively, of the proposed approach; (e) segmentation results obtained by Tao [21]; (f) segmentation results obtained by Tang [22].
(a)(b)(c)(d)(e)(f)Figure 11
The comparison outcomes. (a) Original CT image-4; (b–d) segmentation result of threshold levels 2,3, and 4, respectively, of the proposed approach; (e) segmentation results obtained by Tao [21]; (f) segmentation results obtained by Tang [22].
(a)(b)(c)(d)(e)(f)Figure 12
The comparison outcomes, (a) Original CT image-5; (b-d) Segmentation result of threshold level 2,3,4 respectively of proposed approach, (e) Segmentation results obtained by Tao [21], and (f) Segmentation results obtained by Tang [22].
(a)(b)(c)(d)(e)(f)Figure 13
The comparison outcomes. (a) Original CT image-6; (b–d) segmentation result of threshold levels 2,3, and 4, respectively, of the proposed approach; (e) segmentation results obtained by Tao [21]; (f) segmentation results obtained by Tang [22].
(a)(b)(c)(d)(e)(f)Table 1
Parameter values obtained using DE for 2–4 level thresholds of the proposed approach.
ImageLevelParameter valuesFigure220 173 197 255310 91 162 173 193 239477 86 94 125 188 200 206 251Figure3232 170 171 210336 125 129 135 145 237418 170 190 212 213 231 232 251Figure4226 171 228 23437 114 186 205 229 24044 100 103 158 175 189 216 242Figure52211 211 220 230353 83 92 157 179 255434 175 176 213 222 241 250 255Figure622 253 255 25530 104 146 218 243 25140 104 140 177 178 181 189 213Figure7251 123 141 209325 83 187 197 199 225427 86 101 105 118 148 196 203The experimental results of the proposed approach are shown in Figures2 to 7, where an original CT image has been shown in (a), and level-2, level-3, and level-4 threshold-based segmentation results have been shown in figure (b), (c), and (d) in every figure, respectively. The experimental results reveal the performance abilities of the proposed approach with various CT scan images. The results show that the proposed approach has tremendous abilities in segment CT scan infected with COVID-19 and in that most of the edge information is displayed without noisy details noticed on the results. Likewise, the segmentation results have a realistic and rich appearance. This is an achievement because such promising results are obtained with an approach that does not require many calculations yet produces satisfactory segmentation results for abnormal and poor-quality CT scans, as infected with COVID-19.Using the comparison outcomes from Figure8 to Figure 13, it is observed that the method by Tao [21] is almost similar with a slight favor for method introduced by Tang [22] as indicated by subjective evaluation. If we look at the output images of these methods, they seem almost identical. The proposed approach provided best performances due to the produced segmentation strong intensities and clear details among the comparison methods. Since the method segmented CT lung images to support diagnosis for medical doctors, the quality of our segmentation approach also is evaluated by five medical doctors which they indicate that the output results of the proposed segmentation approach have clear details compared with other approaches, as shown in Table 2, where the best average rank is bold. The ranking score range [1 : 5] is 1: bad, 2: poor, 3: decent 4: good, and 5: very good.Table 2
Observer’s assessment of experimental results.
FiguresObserver rankingImage No.Obv.1Obv.2Obv.3Obv.4Obv.5AverageFigure8(b)454454.4(c)545544.6(d)323332.8(e)233232.6(f)232332.6Figure9(b)545454.6(c)555544.8(d)332332.8(e)233232.6(f)323232.6Figure10(b)444454.2(c)445544.4(d)332332.8(e)233232.6(f)232332.6Figure11(b)554454.6(c)544544.4(d)323332.8(e)333232.8(f)232332.6Figure12(b)454454.4(c)545544.6(d)323332.8(e)333232.8(f)232332.6Figure13(b)454454.4(c)444544.2(d)323332.8(e)233322.6(f)322332.6Bold values represent the best results.This is a good achievement as such a low-complexity approach showed significant outcomes. Designing a high dependability segmentation algorithm for Corona virus disease is uneasy as many challenges exist in this task. Still, such a task is accomplished as witnessed by the outcomes of the proposed approach. Finally, the proposed approach can be utilized or integrated in different frameworks of image processing and computer vision systems that require a simple but efficient method to achieve the segmentation task of Corona virus disease mentoring and treatment.


## 4. Conclusion

In this paper, a multithreshold using a generalized exponential entropy-based algorithm is developed for segmentation CT scanning infected with COVID-19 disease. The proposed approach combines generalized exponential entropy and fuzzy c partition. An image is first transformed into a fuzzy domain; subsequently, the fuzzy generalized exponential entropy is defined for foreground and background. After that, the total fuzzy generalized exponential entropy is maximized to compute the accurate threshold. The generalized exponential entropy is then optimized to acquire an image threshold by the differential evolution “DE” optimization algorithm. The reliability of the methodology as a threshold selection mechanism considers the information of object and background as well as interactions between them. The experimental results are explained by subjective evaluations as a realistic measure for this task. The results revealed the superiority of the proposed approach as it produced well-structured segmentation with clear and rich intensities. Such results are important because the outcomes are obtained by a low-intricacy and fully automatic approach.



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