https://doi.org/10.20965/jaciii.2020.p0963

Cell via Improved Markov

Paper: Robust Cell Image Segmentation via Improved Markov Random Field Based on a Chinese Restaurant Process Model Dongming Li∗1,∗2, Changming Sun∗3,SuWei∗4,YueYu∗2,∗5, and Jinhua Yang∗1,†

∗1College of Opto-Electronic Engineering, Changchun University of Science and Technology No.7089 Weixin Road, Chaoyang District, Changchun, Jilin 130022, China E-mail: [email protected] ∗2School of Information Technology, Jilin Agricultural University No.2888 Xincheng Road, Jingyue District, Changchun, Jilin 130118, China ∗3CSIRO Data61 P.O. Box 76, Epping, New South Wales 1710, Australia ∗4Modern Educational Technology Center, Changchun University of Chinese Medicine No.1035 Boshuo Road, Jingyue District, Changchun, Jilin 130117, China ∗5College of Artificial Intelligence, Tourism College of Changchun University Sheling Town, University Campus District, Changchun, Jilin 130607, China †Corresponding author [Received October 5, 2020; accepted November 18, 2020]

In this paper, a segmentation method for cell images common approaches for cell segmentation is image inten- using Markov random field (MRF) based on a Chi- sity thresholding which suffers from the issue of inten- nese restaurant process model (CRPM) is proposed. sity inhomogeneity. Watershed based methods are com- Firstly, we carry out the preprocessing on the cell im- monly utilized for clustered nuclei segmentation. Dunn ages, and then we focus on cell image segmentation proposed the fuzzy C-means (FCM) method for image using MRF based on a CRPM under a maximum a segmentation [2]. The FCM method is an unsupervised posteriori (MAP) criterion. The CRPM can be used clustering algorithm, which has been widely used in the to estimate the number of clusters in advance, adjust- field of image segmentation. However, its high compu- ing the number of clusters automatically according to tational complexity and the fact that its performance de- the size of the data. Finally, the conditional iteration grades significantly with increased noise. Ng et al. pro- mode (CIM) method is used to implement the MRF posed a methodology that incorporates K-means and im- based cell image segmentation process. To validate our proved watershed segmentation algorithms for medical proposed method, segmentation experiments are per- image segmentation [3]. Zong and Tian proposed seg- formed on oral mucosal cell images. The segmentation mentation and feature extraction of brain tumors based on results were compared with other methods, using pre- magnetic resonance images using a K-means method [4]. cision, Dice, and mean square error (MSE) as the ob- K-means clustering is a simple clustering method with jective evaluation criteria. The experimental results low computational complexity compared to FCM. An show that our method produces accurate cell image image threshold segmentation algorithm based on maxi- segmentation results, and our method can effectively mum and a genetic algorithm is presented in [5]. improve segmentation for the nucleus, binuclear cell, Meng et al. proposed an image segmentation method us- and micronucleus cell. This work will play an impor- ing multi-resolution Markov random field (MRF) [6]. The tant role in cell image recognition and analysis. MRF probabilistic framework is a powerful tool for image segmentation. It introduces spatial dependencies between labels, providing a robust-to-noise segmentation. How- Keywords: cell image segmentation, Markov ran- ever, MRF needs to set the initial classification number in dom field, dual-tree complex wavelet transform, Chinese advance, which is greatly influenced by subjective factors restaurant process model, morphology top-hat transform and is time-consuming. Our work focuses on cell image segmentation using an MRF model based on a Chinese restaurant process model (CRPM) under the maximum 1. Introduction a posteriori (MAP) criterion. The quality of segmenta- tion is evaluated on cell images using the , Dice, Accurate segmentation of cells in fluorescence mi- and mean square error (MSE) criteria. We have used cell croscopy images plays a key role in high-throughput ap- image datasets to evaluate several segmentation methods. plications such as the study of cell function and quantifi- The results show that our proposed method is better than cation of protein expression [1]. Recently, several meth- threshold based techniques. ods have been proposed for the segmentation of cell nu- The remainder of this paper is organized as follows. In clei in fluorescence microscopy images. One of the most Section 2, the related works on cell image segmentation

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© Fuji Technology Press Ltd. Creative Commons CC BY-ND: This is an Open Access article distributed under the terms of the Creative Commons Attribution-NoDerivatives 4.0 International License (http://creativecommons.org/licenses/by-nd/4.0/). Li,D.etal.

are briefly reviewed. Section 3 introduces and explains is that it can segment complex-shaped objects, and the proposed improved MRF-based cell image segmenta- it can deal with topological changes such as image tion method. The cell image segmentation algorithm is splitting and merging. Li et al. [15] proposed a new applied to real cell images and the results are presented in variational formulation for geometric active contour, Section 4. Finally in Section 5, we conclude. which makes the level-set function close to the signed distance function. Therefore, it completely eliminates the cost of reinitialization and improves the perfor- 2. Related Work mance of cell image segmentation. (c) Localized region-based active contour model meth- In the following section, we review existing methods ods [16–17] are region-based methods that use local for cell image segmentation. A wide range of cell im- region parameters for segmentation. They show su- age segmentation methods have been proposed in recent periority in the location of regional information, and years, and they can be categorized into three groups: man- they have the ability to deal with heterogeneous tex- ual segmentation, semi-automatic segmentation, and fully tures. Lankton and Tannenbaum [16] proposed a nat- automatic segmentation. ural framework that allows any region-based segmen- tation energy to be re-formulated locally. Kaur and (1) Manual segmentation (MS) method requires do- Jindal [17] proposed the thyroid segmentation algo- main experts to first determine the region of interest rithm for ultrasound and scintigraphy images by us- (ROI), and then draw precise boundaries around the ROI ing active contour without edges, localized region- to annotate each image pixel correctly. An MS method based active contour, and distance regularized level- is necessary because it provides a ground-truth image set methods. for further development of semi-automatic and automatic (d) Clustering-based method transforms image seg- segmentation methods. However, the disadvantage of mentation into clustering analysis in pattern recogni- manual segmentation is that it is subjective. Because the tion. There are two clustering-based methods for cell manual segmentation method depends on the knowledge image segmentation: K-means clustering [18] and and experience of domain experts, there will be signifi- FCM [2, 19]. The FCM clustering method has the ad- cant differences among experts and even for one expert vantage of obtaining accurate results because it can but at different times [7]. provide a global optimal value when initialization er- (2) Semi-automatic segmentation method uses auto- ror occurs. Therefore, the FCM clustering method is matic algorithms for small-scale user interaction, and gen- suitable for cell image segmentation with uncertainty erates accurate segmentation results of microscopic cell and complexity. images [8]. In microscopic cell image segmentation, the common methods of semi-automatic segmentation are as (3) Fully automatic segmentation method does not follows: require any user interaction, and the typical representa- tive is deep learning-based methods that are widely used in cell image segmentation. Long et al. [20] proposed (a) Seeded region growing methods [9–13] are based fully convolutional networks (FCN) for semantic segmen- on initial seed points provided by users and it- tation, and realized end-to-end pixel-level semantic seg- eratively fuse neighborhood pixels with similarity. mentation. Ronneberger et al. [21] presented a network In [9], Stewart et al. proposed a novel region grow- (U-Net) and a training strategy on biomedical images, ing method with pulse-coupled neural networks. This which greatly improved the segmentation performance. method introduces a new idea for automatic segmen- Jia et al. [22] developed a new weakly supervised learn- tation. Zhou et al. [10] proposed a region segmen- ing algorithm to learn to segment cancerous regions in tation method based on the Otsu method [11] and histopathology images, which was easy to implement and the Chan–Vese method [12] for cytoskeleton images. could be trained efficiently. In recent years, scholars have The method achieves an ideal processing effect, but made full use of the advantages of deep learning methods has high time and space complexities. In [13], a re- for cell image segmentation, and they continue to propose gion growing method with a multi-seed voting mech- new image segmentation methods to provide a reliable ba- anism was proposed by Jiang et al. to realize auto- sis for medical diagnosis. matic cell image segmentation. The results show that this method is effective for cell image segmentation with fuzzy edges, but the calculation process is com- plex. 3. Proposed Algorithm (b) Level-setbased active contour model methods [14– 15] have been widely used in medical image seg- 3.1. Algorithm Framework mentation. Its main advantage is that it does not re- The basic idea of our algorithm is to segment the nu- quire prior shape knowledge and the initial position cleus, binuclear cell, and micronucleus cell from the im- of the region of interest. Sethian [14] proposed a proved MRF based on a CRPM. To segment cell image fast marching level-set method for monotonically ad- pixels into the nucleus and background, an MRF method vancing fronts. The main advantage of this method is adopted.

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3.2. Image Preprocessing ,QSXWFHOOLPDJH In the preprocessing phase, the DTCWT and morphology-based methods [23] were used here to enhance the input cell images for 300 oral mucosal cells 3UHSURFHVVLQJ &RPSXWLQJSULRU SUREDELOLW\E\05) database. For the obtained color cell image, we extracted its green channel and then applied histogram stretching &RQVWUXFWLQJ'3 &RPSXWLQJWKH to the grey cell image. Secondly, the DTCWT was PRGHOIRUREWDLQLQJ SRVWHULRUSUREDELOLW\ applied. The gray cell image (based on the DTCWT WKH&KLQHVHUHVWDXUDQW RILPDJHSL[HOV method) was decomposed into six high-pass and two PRGHO low-pass subbands. For the high-pass subbands, we 2EWDLQLQJWKH used the wavelet-based contourlet transform method for &RPSXWLQJ PD[LPL]HSRVWHULRU denoising and then obtained the enhanced high-pass SUREDELOLW\IRUWKHiWK SUREDELOLW\ subimages. For the low-pass subbands, we used the FXVWRPHUVLWWLQJLQ improved morphology top-hat transform method for 2XWSXWWKH WDEOHK K enhancement and then obtained the low-pass subimages. VHJPHQWHGFHOO Finally, the inverse DTCWT method was applied to the LPDJH obtained subimages, and the final enhanced cell image 8SGDWLQJWKHWDEOH was obtained. K++ QXPEHU The DTCWT was obtained based on the complex wavelet, which is defined as $FFRUGLQJ(T   ψ(t)=ψh(t)+ jψg(t), ...... (1) DGMXVWLQJVDPHRU √ VLPLODUSL[HOV where j = −1, ψh(t) and ψg(t) represent the wavelet’s real part and imaginary part, respectively, and they are wavelet basis functions. 1R :KHWKHUFRXQWLQJ Associated with the row-column implementation of the DOOWKHSL[HOV" wavelet transform, we can obtain the expression for 2D DTCWT, ψ(x,y), which is defined as [23]

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(a)

(a)

(b)

(b)

(c)

(c)

(d)

Fig. 3. Cell image preprocessing results; (a) and (c) are original input cell images; (c) and (d) are the enhanced re- sults obtained by using our proposed method [23]. (d)

Fig. 2. Cell image enhanced results and corresponding brightness of the main cells inside and around the cell is histograms; (a) original oral mucosal cell image, (b) his- togram of (a), (c) enhanced cell image by using our proposed greatly improved. The histogram distribution of the en- method [23], and (d) histogram of (c). hanced cell image is more uniform, the guidance range is enlarged, and the image contrast is enhanced. These are conducive to cell image segmentation, binuclear extrac- tion, and cell image contour preservation. selected for visually acceptable results. Fig. 2 shows the Some enhancement results are shown in Fig. 3. Fig. 3 enhanced cell images and their histograms. From Fig. 2, clearly shows that our enhanced method can effectively we can see that the visual effect of the main features in- enhance the contrast between the cell and the background side the cell was significantly improved. In particular, the and can make the cell image more naturally enhanced

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with better visibility, clearer details, and higher definition. is a discrete distribution) [26]. A distribution over dis- tributions is a DP when its marginal distributions have a Dirichlet distribution. One of the well-known variations 3.3. MRF Model of DP is the Chinese restaurant process (CRP). It is a dis- The MRF is a random process, and the value of the cur- tribution over partitions representing the assumed prior rent state is only related to the value of the previous state, distribution over the cluster structures [26]. The CRP can which can be understood as the value of the adjacent state. be used to estimate the number of clusters in advance, ad- The MRF is {Xn, n ∈ T}, ∀n ∈ T ,andi0,i1,...,in+1 ∈ I justing the number of clusters automatically according to that satisfies the size of the data and eventually, the number of clus- = | = ,..., = ters will lead to a fixed value. In data analysis and clas- P Xn+1 in+1 X0 i0 Xn in sification, the number of potential clusters can be quickly determined. The CRP can be described by a sequence of = P X + = i + | X = i . (4) n 1 n 1 n n customers sitting down at the tables of a Chinese restau- Therefore, conditional probability decides whether it is rant with an infinite number of tables. a MRF. For a 2-D image, it can be observed as a 2-D ran- The CRP process is as follows: the first customer sits dom field, i.e., a 2-D MRF. MRF simulates the image as a at the first table, and the n-th customer (n = 1,2,3,...) grid composed of random variables, and each of them de- sits (1) at an occupied table with the probability propor- pends on the adjacent groups of random variables outside tional to the number of customers already sitting at the itself. table or (2) at a new table with a probability proportional Equivalency between MRF and Gibbs fields is estab- to the concentration parameter [26]. The specific proba- lished by the theorem of Hammersley Clifford’s theo- bility distribution is as follows: ⎧ rem [25]. The following equations characterize the Gibbs n ⎨⎪ k , ≤ , distribution: − + α if k K = | α = n 1 P Zn k Z−n α (7) ⎩⎪ exp − ∑ V (x | x ) , if k = K + 1, c s r n − 1 + α c∈C p(xs | xr,r ∈ δ(s)) = , (5) L where Zn is the cluster (table) assignment for the n-th cus- ∑ exp − ∑ Vc(xs | xr) tomer, α is a DP parameter, K is the number of occupied = ∈ xs 1 c C tables (clusters), nk is the number of customers sitting at where δ(s) is the domain system set in 2-D random table k,andZn is the table assignment for all customers fields, which is defined in the pixel position s = {(i, j) | except the n-th customer. In the cell image segmentation process, the customer 1 ≤ i ≤ N, 1 ≤ i ≤ M}. xs is a in ran- dom field for the space domain, r ∈ δ(s) is the adjacent presents the image pixels, and the table is seen as the num- point of s, c ⊂ s is a potential group, C is the collection ber of segmentations; therefore, the number of tables is of potential groups c ∈ C,andLis the phase space of the equal to the number of the segmented pixel regions. Sim- random field, which represents the number of different re- ilar or identical pixels in the image are assigned to the gions for image segmentation. Phase space L is also di- same table until the pixels are allocated, and the number rectly related to the key for accurately dividing an image of tables corresponds to the number of clusters. Assuming the existence of observed data region. −(∑c∈C Vc(xs | xr)) is an energy function. {y ,y ,...,y }, the following distribution is established: The image segmentation problem can be transformed 1 2 n into an image labeling problem, and the key of image yi | θi ∼ F(θi)...... (8) segmentation is to obtain the classification label for each pixel satisfying the MAP criterion, which is called the la- Each table also has a distribution, i.e., F(θ),andthe beling field, denoted by X. According to the Bayesian distribution here refers to the distribution of parameter θ criterion, the optimal segmentation criterion is: constructed by the CRP, so the image dataset obeys the parameter distribution θ ∼ F(θ). To solve the proba- p(Y | X)p(X) Xˆ = argmaxp X | Y = argmax , (6) bilistic problem of this type of non-analytic expression, X p(Y) there is usually no specific analytic expression for calcu- where Y denotes the gray value of the cell image, p(Y) is lation. It is an iterative convergence or limit process, so a constant. X is the conditional probability determined by the Gibbs algorithm based on the Monte MRF through energy function. Considering the computa- Carlo (MCMC) method is used. tional efficiency, the conditional iteration mode method is used to realize the MRF application in image segmenta- 3.5. Automatic Segmentation of Cell Images tion. To segment a cell image, we first need to describe the position, phase space, and the number of positions and phase space. From Eq. (5), we can know that parame- 3.4. Chinese Restaurant Process Model ter L denotes the number of different regions wherein an The DP is a that can be considered image is segmented. The accuracy of the given initial pa- as a distribution over distributions (each sample of a DP rameter L directly affects the segmentation. In the MRF

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image segmentation method, the initial parameter L is set original cell images. Fig. 5(b) is the cell image seg- manually. In this study, we will employ CRPM for au- mentation based on Dunn’s method [2], and this seg- tomatically adjusting the number of clusters based on the mentation method is based on FCM which is an unsu- data size. Therefore, the parameter W obtained by CRPM pervised clustering segmentation. In this experiment, will replace the parameter L inEq.(5),i.e., Dunn’s method can accurately identify cells and then segment them, but it is difficult to identify the cell nu-

exp − ∑ Vc(xs | xr) cleus. Fig. 5(c) is the cell image segmentation based on c∈C Ng et al.’s method [3], which is a cluster segmentation p xs | xr,r ∈ δ(s) = . (9) W method based on K-means. Here, we selected the cluster ∑ exp − ∑ Vc(xs | xr) number K as 3 (according to the experiment). However, = ∈ xs 1 c C this method cannot achieve better accuracy. Fig. 5(d) Our proposed method can automatically generate the is the cell image segmentation based on our proposed number of regions without the need to provide the ini- method. The clustering number W is obtained by auto- tial segmentation regions. It can effectively solve the matic clustering based on CRPM. Then W is taken as a re- problem of human error segmentation and can save time. gion number parameter of the MRF segmentation method. Compared with traditional MRF cell image segmentation Finally, we used the conditional iteration mode to update methods, our method does not need to set the number of the pixels through the maximum conditional probability regions. of each element in this study.

4. Experimental Results and Discussion 4.2. Results Evaluation To evaluate the cell image segmentation results, we In this section, the performance of our cell image seg- adopted the objective evaluation criteria with the preci- mentation strategies proposed herein is evaluated by com- sion, Dice, and MSE. The precision (precision) is based paring it with current state-of-the-art algorithms using cell on the following equation: images. We take human oral mucosal cells as the research object. Cell images were obtained by extraction and stain- precision × ing for cells, and the image size was 1600 1200 pix- ( ) ∩ ( ) relevant documents retrieved documents els. We selected 300 cell images of human oral mucosal = , (10) cells in the experiment. To verify the cell image segmen- (retrieved documents) tation effect and the reliability of our algorithm, we imple- where {relevant documents} is a documents collection re- mented our algorithm using MATLAB 7.0 and tested it on lated to a query, {retrieved documents} is a documents a 2.7 GHz Intel i7-7500U CPU with 8 GB RAM running collection retrieved by a system, and {relevant docu- on a Windows 10 operating system. ments}∩{retrieved documents} is the actual documents collection that is both relevant and retrieved. 4.1. Experimental Results The statistical method of Dice (Dice) is defined as [27]: We used the same size and format on all cell im- 2V k Dice = Mk = ae , ...... (11) k + k ages. Three methods, i.e., Dunn’s method [2], Ng et al.’s Va Va method [3], and our proposed method, were applied to k the cell image data. Fig. 4 shows the comparison results where Vae denotes the number of overlapping pixels in the of the different cluster numbers. Fig. 4(a) is the origi- results of the k-class organization segmentation algorithm k nal cell image, Fig. 4(b) is based on the traditional MRF and the results of expert manual segmentation. Va and k method, and the cluster number is 2. Fig. 4(c) is based on Ve represent the numbers of the k-class organization pix- the traditional MRF method, and the cluster number is 4. els obtained via the proposed segmentation method and Fig. 4(d) shows the result using our proposed method, and manually segmented by experts, respectively. In this ex- the cluster number is 3. In our method, the cluster num- periment, M is the segmented accuracy. A larger M value ber is automatically obtained. From Fig. 4, we can see indicates that better segmented accuracy is obtained. that our method can achieve better results and gives more The MSE is defined as accurate estimates than the traditional MRF method. The 1 N MSE = ∑(observed − predicted )2, ...(12) traditional MRF method has subjective factors in cell im- N t t age segmentation. Compared with the traditional MRF t=1 method, our method can automatically generate the clus- where observedt is the parameter estimation value, pre- tering number, which can reduce the human factor and the dictedt is the true value, and N is the total number of effect is significant. samples with t = 1,2,...,N.AlowerMSE indicates that Experimental results on Dunn’s method [2], Ng et al.’s the image segmentation result is closer to the groundtruth, method [3], and our algorithm are compared. The com- while a higher MSE means that the segmentation effect is parisons of the cell image segmentation results based on unsatisfactory. Therefore, a smaller MSE demonstrates a the three methods are shown in Fig. 5. Fig. 5(a) is the better result.

968 Journal of Advanced Computational Intelligence Vol.24 No.7, 2020 and Intelligent Informatics Cell Image Segmentation via Improved Markov Random Field

(a) Original input cell images (b) Traditional MRF method: (c) Traditional MRF method: (d) Our proposed method: cluster number = 2 cluster number = 4 cluster number = 3

Fig. 4. Comparison results with the different cluster numbers.

(a) Original input cell images (b) Dunn’s method (c) Ng et al.’s method (d) Our proposed method

Fig. 5. Original cell images and the comparison results of the segmented cell images based on three methods.

Table 1. Comparison results on precision, Dice,andMSE of different segmentation methods.

Cell image names Evaluation criterions Dunn’s method Ng et al.’s method Our method precision 0.8985 0.9136 0.9899 Img01 Dice 0.9466 0.9201 0.9949 MSE 0.0956 0.1055 0.0167 precision 0.8024 0.9594 0.9989 Img02 Dice 0.7042 0.7920 0.8647 MSE 0.4064 0.3073 0.1726 precision 0.7981 0.8576 0.9994 Img03 Dice 0.7127 0.6741 0.8493 MSE 0.3925 0.4042 0.2280

To prevent the uncertainty of single-cell image mea- cell images. Our method can identify the nuclei, binu- surement, we randomly selected 30 oral mucosal cell clear cells, and micronuclei cells, and it can accurately images after preprocessing. To verify our method, we segment them. compare our method with two other methods (Dunn’s method [2] and Ng et al.’s method [3]) for cell images. The objective evaluation criteria for the experimental re- 5. Conclusion sults are measured by precision, Dice,andMSE,asshown in Table 1 (only 3 images are shown). It can be seen As the most important step in cell image processing, that our method exhibits good performance for different segmentation methods have become a hot research topic.

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970 Journal of Advanced Computational Intelligence Vol.24 No.7, 2020 and Intelligent Informatics Cell Image Segmentation via Improved Markov Random Field

Name: Name: Changming Sun Yue Yu

Affiliation: Affiliation: CSIRO Data61 School of Information Technology, Jilin Agricul- tural University College of Artificial Intelligence, Tourism Col- lege of Changchun University

Address: Address: P.O. Box 76, Epping, New South Wales 1710, Australia No.2888 Xincheng Road, Jingyue District, Changchun, Jilin 130118, Brief Biographical History: China 1986 Received B.Sc. degree from Beijing University of Aeronautics and Sheling Town, University Campus District, Changchun, Jilin 130607, Astronautics China 1992 Received Ph.D. degree from Imperial College Brief Biographical History: 2001- Principal Research Scientist, CSIRO Data61 2019 Received M.S. degree from Jilin Agricultural University Main Works: Membership in Academic Societies: • Stereo vision, digital photogrammetry, 3D reconstruction, image • China Artificial Intelligence Education Alliance (CAIEA) matching/registration, and image motion/optical flow Membership in Academic Societies: • EURASIP Journal on Image and Video Processing, a Springer Open Journal, Editor Name: Jinhua Yang

Affiliation: Name: College of Opto-Electronic Engineering, Su Wei Changchun University of Science and Technol- ogy Affiliation: Professor, College of Medicine Information, Changchun University of Chinese Medicine Address: No.7089 Weixin Road, Chaoyang District, Changchun, Jilin 130022, China Brief Biographical History: Address: 1994 Received B.E. degree from Xian University No.1035 Boshuo Road, Jingyue District, Changchun, Jilin 130117, China 1997 Received M.E. degree from Beijing Institute of Technology Brief Biographical History: University 2003 Received Ph.D. degree from Changchun University of Science and 2001 Received Ph.D. degree from Changchun University of Science and Technology Technology Main Works: 2001- Postdoctoral Researcher, The University of Tokyo • Computer vision, pattern recognition, and intelligent computing 2007- Professor and Doctoral Supervisor, Changchun University of Membership in Academic Societies: Science and Technology • China Computer Federation (CCF) Main Works: • China Information Association of Traditional Chinese Medicine • Photoelectric detection technology and quality control, artificial (CIATCM) intelligence, computer vision, and image processing theory • China Higher Education Information Academy (CHEIA)

Vol.24 No.7, 2020 Journal of Advanced Computational Intelligence 971 and Intelligent Informatics

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