- Email: [email protected]
Novel image segmentation method based on PCNN
Optik - International Journal for Light and Electron Optics 187 (2019) 193–197
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Novel image segmentation method based on PCNN B. Wanga,b, L.L. Chena, M. Wanga, a b
⁎
T
School of Electrical and Information Engineering, Xihua University, Chengdu, 610036, PR China School of Applied Mathematics, University Electronic Science and Technology of China, Chengdu 610054, PR China
A R T IC LE I N F O
ABS TRA CT
Keywords: Pulse-coupled neural network Image Optimization Membrane computing
In this paper, the problem about image segmentation on the basis of pulse-coupled neural network (PCNN) is studied. Simulated annealing particle swarm optimization (SAPSO) is introduced into membrane computing to design algorithm to achieve image segmentation with better performance. Corresponding typical numerical experiment results illuminate the effectiveness and superiority of the proposed method.
1. Introduction In 1990, Pulse Coupled Neural Network (PCNN) is firstly presented based on the synchronous pulse phenomenon in the brain cortex of mammals [1], and can be applied in image processing. Up to now, many researches on image processing based on PCNN are carried out [2–23]. For instance, in Ref [2] the adaptive PCNN algorithm is applied to extract high-frequency information in high frequency directional sub-band; in Ref [3] an improved PCNN model is proposed to improve the accuracy of crack recognition; in Ref [4] a simplified PCNN is proposed for image segmentation; in Ref [5] a algorithm based on PCNN was designed to realize the detection of breast specificity; in Ref [6] image segmentation method based on SOM-PCNN in frequency domain is given; in Ref [7] a recognition method of landing vehicle based on PCNN model and affine moment invariant is proposed, and has good ability to resist geometrical distortion. In addition, some researches on adaptive PCNN are carried out. In Ref [8] a PCNN which can adaptively adjust parameters is proposed for image segmentation; in Ref [9] an adaptive PCNN is proposed for the fusion of multimodal medical images. Although PCNN algorithm can realize the image segmentation with strong robust ability against many kinds of attacks, but the premature problem is its big concern, and will decrease its image segmentation performance. SA algorithm originates from the cooling thermodynamic process of high-temperature metal, can converge to the global optimum under the condition that the initial temperature is high enough and the temperature drop slowly enough, and can accept the poor solution with the jump probability to jump out the local optimum. Bigger jump probability can deal with the premature problem well, but will bring about the precision problem and convergence problem. As a novel computational model, membrane computing possesses the characteristics of parallelism computing, and has achieved much success in optimization field. In this paper, combined with SA algorithm, membrane computing will be introduced into PCNN to achieve the image segmentation with better property. To our best knowledge, corresponding research has never been carried out up to now, and this motivates this paper. 2. Preliminary In this paper, a PCNN model is presented as Fig. 1.
⁎
Corresponding author. E-mail address: [email protected] (M. Wang).
https://doi.org/10.1016/j.ijleo.2019.05.007 Received 3 March 2019; Accepted 5 May 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 187 (2019) 193–197
B. Wang, et al.
Fig. 1. PCNN model.
The mathematic model of PCNN is described as:
Fij [n] = Iij
∑
L ij [n] =
Wijkl Ykl [n−1]
(k,l) ∈ N(i,j)
Uij [n] = Fij [n](1 + βL ij [n])
1, Uij [n] > θij [n−1] Yij [n] = ⎧ ⎨ 0, Uij [n] ≤ θij [n−1] ⎩ θij [n] = exp(−α θ)θij [n−1] + VθYij [n] where: (i,j) represents the position of a neuron in PCNN. Iij is an external excitation signal input. Fij is the feedback input of neuron (i,j). L ij is the linear connection input term. Ykl is the pulse output of neuron (k,l). Wijkl is the weighted coefficient between Yij and Ykl . β is the connection strength coefficient. Uij is the internal activity term. Yij is the pulse output. α θ is the decay time constant of the θij. Vθ is the intrinsic electric potential of θij. PSO is a kind of optimization algorithm inspired by the collaborative behavior and swarming of bird flocking. The position and velocity of ith particle at iteration t+1 are updated on the basis of the following rules:
vid (t+1) =ωvid (t) +c1∙r1 (Pid -xid (t))
+c2 ∙r2 (Pgd -xid (t)) xid (t+1)=xid (t) + vid (t+1) where t is iteration number, ω is inertia weight, c1 and c2 are learning parameters, r1 and r2 are positive scalars, vid is ith particle’s velocity, xid is of ith particle’s position, Pid is historical individual optimum, Pgd is historical group optimum. 3. Main results The updating rules of the particle are defined as:
vid (t+1) =γ{ωvid (t) + c1∙r1 (Pid − xid (t))
+ c2 ∙r2 (Pgd − xid(t))} xid (t+1)=xid (t) + vid (t+1) where: γ is the compression factor, such that
γ=
2 |2-C- C2-4C |
where C=c1 + c2 . The jump probability of ith particle for simulated annealing (SA) algorithm is defined as：
Pi=
e− N
fpi − fpg T
∑ j=1 e−
fpj− fpg T
where: fpi is the fitness of individual optimum of the ith particle, fpg is the fitness of global optimum, N is the population size and T is the temperature. When one iteration is performed, a random number will be produced. If the random number is bigger than the current jump 194
Optik - International Journal for Light and Electron Optics 187 (2019) 193–197
B. Wang, et al.
Fig. 2. Framework of membrane computing.
probability Pi , the global optimum Pgd will be replaced by the individual historical optimum Pid . For SAPSO, when a particle finds an optimal solution, other particles will move to it quickly. When the jump probability is set bigger to jump out of the local optimal value more easily, the precision of ultimate solution will be influenced. In this paper, membrane computing will be introduced in SAPSO to solve the premature problem with good optimization ability. The framework of membrane computing is constructed as Fig. 2. Memb. 0 is surface membrane with smaller inertia weight, Membs. 1–4 are basic membrane with bigger inertia weight, SAPSO is used as the optimization operator in each membrane. Particles with best solution in Membs. 1 and 3 replace the particles with worst solution in Membs. 2 and 4. Particles with best solution in Membs. 2 and 4 replace two particles with worst solution in Memb. 0; two particles with best solution in Memb. 0 replace the particles with worst solution in Membs. 1 and 3 respectively. When the iteration finishes, the best solution in Memb. 0 will be the final obtained value. The entropy of image can reflect the information of image, and is chosen as fitness in this paper:
H= −P1log 2 (P1) − P0 log 2 (P0) where: H is information entropy of image. P1 is probability when binary pixel is 1. P0 is probability when binary pixel is 0. Bigger entropy means better fitness. 4. Experiment In this paper, the infrared image of high-voltage joint between insulator and cable is included as Fig. 3. For infrared image, the pixel with bigger value represents higher temperature. From Fig. 3 it can be seen that the temperature at the second joint between insulator and cable is higher than others obviously. High temperature at joint will lead to the potential spark. When the temperature at joint exceeds the danger line, alert should be issued. Hence it is important to identify the high temperature area of joint as clearly as possible. Based on PSO-PCNN, one can get α θ=0.021, β=0.03, Vθ=0.4 , and experimental result is shown in Fig. 4. Based on MSAPSO-PCNN, one can get α θ=0.030, β=0.67,Vθ=0.2, and experimental result is shown in Fig. 5. From Fig. 4 it can be seen that high temperature area is marked effectively to identify the potential safety hazard, however is too obscured. From Fig. 5 it can be seen that the given method can more clearly identify the high temperature part, which will be in favor of the fault diagnosis of high-voltage joint. Next, the comparison of two image segmentation method is carried out, and results are displayed in Table 1. Table 1 shows the relationship between fitness and iterations based on MSAPSO-PCNN and PSO-PCNN. One can see that PSO-
Fig. 3. Original infrared image of high-voltage joint between insulator and cable. 195
Optik - International Journal for Light and Electron Optics 187 (2019) 193–197
B. Wang, et al.
Fig. 4. Segmented image of high-voltage joint based on PSO-PCNN.
Fig. 5. Segmented image of high-voltage joint based on MSAPSO-PCNN.
PCNN needs 19 iterations to finish the search of optimum parameters, and MSAPSO-PCNN just requires 15 iterations to obtain the optimum parameters. In addition, it can be noted that the final fitness based on MSAPSO-PCNN is 0.9930, which is bigger than 0.9914 based on PSO-PCNN, and STDEV based on MSAPSO-PCNN is 0.01014, which is smaller than 0.05243 based on PSO-PCNN. These mean that our method can search for optimum with better convergence property. 5. Conclusion The paper has studied the image segmentation issue based on PCNN. As the optimization operator of membrane computing, a simulated annealing particle swarm optimization has been proposed, and applied in image segmentation successfully. At last some typical numerical examples have been included to show the effectiveness of the method given. Acknowledgments This work is partially supported by the Key Laboratory of Fluid and Power Machinery of the Ministry of Education, and the Graduate Innovation Fund of Xihua University (ycjj2018015). 196
Optik - International Journal for Light and Electron Optics 187 (2019) 193–197
B. Wang, et al.
Table 1 Fitness based on PSO-PCNN and MSAPSO-PCNN. Iterations
MSAPSO-PCNN
PSO-PCNN
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Final optimum STDEV
0.9412 0.9589 0.9593 0.9605 0.9902 0.9909 0.9910 0.9915 0.9916 0.9927 0.9930 0.9930 0.9930 0.9930 0.9930 0.9930 0.9930 0.01014
0.8513 0.8779 0.8787 0.8859 0.9063 0.9261 0.933 0.9413 0.9538 0.9551 0.9602 0.9901 0.9904 0.9906 0.9914 0.9914 0.9914 0.05243
References [1] R. Eckhorn, H.J. Reitboeck, M. Arndt, Feature linking via synchronization among distributed assemblies: simulation of results from cat cortex, Neural Comput. 2 (1990) 293–307. [2] C.H. Zhao, G.F. Shao, L.J. Ma, X. Zhang, Image fusion algorithm based on redundant-lifting NSWMDA and adaptive, PCNN Optik 125 (2014) 6247–6255. [3] Y. Cheng, L. Tian, C. Yin, Research on crack detection applications of improved PCNN algorithm in MOI nondestructive test method, Neurocomputing 277 (2017) 249–259. [4] Y. Guo, Z. Yang, Y. Ma, Saliency motivated improved simplified PCNN model for object segmentation, Neurocomputing 275 (2017) 2179–2190. [5] X.Z. Xu, Multimodal medical image fusion using PCNN optimized by the QPSO algorithm, Appl. Soft Comput. 46 (2016) 588–595. [6] A.K. Helmy, G.S. El-Tawee, Image segmentation scheme based on SOM–PCNN in frequency domain, Appl. Soft Comput. 40 (2016) 405–415. [7] H. Li, X. Jin, N. Yang, The recognition of landed aircrafts based on PCNN model and affine moment invariants, Pattern Recognit. Lett. 51 (2015) 23–29. [8] S. Wei, Q. Hong, M. Hou, Automatic image segmentation based on PCNN with adaptive threshold time constant, Neurocomputing 74 (2011) 1485–1491. [9] W. Xie, Y. Li, Y. Ma, PCNN-based level set method of automatic mammographic image segmentation, Opt. Int. J. Light Electron. Opt. 127 (2016) 1644–1650. [10] J. Garcia, C. Pope, F. Altimiras, A Distributed K-Means Segmentation Algorithm Applied to Lobesia botrana Recognition, Complexity (2017) 5137317. [11] B. Wang, L.L. Chen, Y.Z. Liu, New results on contrast enhancement for infrared images, Optik 178 (2019) 1264–1269. [12] B. Wang, J. Cheng, S. Zhong, Bounded input bounded output stability for Lurie system with time-varying delay, Adv. Difference Equations 57 (2018) 1–13. [13] B. Wang, L.L. Chen, New results on the control for a kind of Uncertain chaotic systems based on fuzzy logic, Complexity (2019) 8789438. [14] B. Wang, L.L. Chen, J. Cheng, New result on maximum entropy threshold image segmentation based on P system, Optik 163 (2018) 81–85. [15] P. Viet-Thanh, S. Jafari, C. Volos, Simulation and experimental implementation of a line-equilibrium system without linear term, Chaos Solitons Fractals 120 (2019) 213–221. [16] B. Wang, New results on fuzzy synchronization for a kind of disturbed memristive chaotic system, Complexity (2018) 3079108. [17] B. Wang, L.L. Chen, Z.Y. Zhang, A novel method on the edge detection of infrared image, Optik 180 (2019) 610–614. [18] B. Wang, D. Zhang, J. Cheng, et al., Fuzzy model-based nonfragile control of switched discrete-time systems, Nonlinear Dyn. 93 (2018) 2461–2471. [19] P. Viet-Thanh, Christos Volos, S. Jafari, A novel cubic-equilibrium chaotic system with coexisting hidden attractors: analysis, and circuit implementation, J. Circuits Syst. Comput. 27 (2018) 1850066. [20] B. Wang, J. Cheng, F. Zou, Stochastic finite time H∞ filtering for nonlinear Markovian jump systems with partly known transition probabilities, Proc. Inst. Mech. Eng. Part I 33 (2019) 31–43. [21] B. Wang, Y. Liu, X. Zhang, A New Memristive Chaotic System and the Generated Random Sequence, IEICE transactions on fundamentals of electronics, Commun. Comp. Sci. E102A (2019) 665–667. [22] B. Wang, X.H. Zhang, X.C. Dong, Novel secure communication based on chaos synchronization, IEICE transactions on fundamentals of electronics, Commun. Comp. Sci. E101-A (2018) 1132–1135. [23] B. Wang, Results on a Novel Piecewise-Linear Memristor-Based Chaotic System, Complexity (2019) 8948656.
197
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Novel image segmentation method based on PCNN B. Wanga,b, L.L. Chena, M. Wanga, a b
⁎
T
School of Electrical and Information Engineering, Xihua University, Chengdu, 610036, PR China School of Applied Mathematics, University Electronic Science and Technology of China, Chengdu 610054, PR China
A R T IC LE I N F O
ABS TRA CT
Keywords: Pulse-coupled neural network Image Optimization Membrane computing
In this paper, the problem about image segmentation on the basis of pulse-coupled neural network (PCNN) is studied. Simulated annealing particle swarm optimization (SAPSO) is introduced into membrane computing to design algorithm to achieve image segmentation with better performance. Corresponding typical numerical experiment results illuminate the effectiveness and superiority of the proposed method.
1. Introduction In 1990, Pulse Coupled Neural Network (PCNN) is firstly presented based on the synchronous pulse phenomenon in the brain cortex of mammals [1], and can be applied in image processing. Up to now, many researches on image processing based on PCNN are carried out [2–23]. For instance, in Ref [2] the adaptive PCNN algorithm is applied to extract high-frequency information in high frequency directional sub-band; in Ref [3] an improved PCNN model is proposed to improve the accuracy of crack recognition; in Ref [4] a simplified PCNN is proposed for image segmentation; in Ref [5] a algorithm based on PCNN was designed to realize the detection of breast specificity; in Ref [6] image segmentation method based on SOM-PCNN in frequency domain is given; in Ref [7] a recognition method of landing vehicle based on PCNN model and affine moment invariant is proposed, and has good ability to resist geometrical distortion. In addition, some researches on adaptive PCNN are carried out. In Ref [8] a PCNN which can adaptively adjust parameters is proposed for image segmentation; in Ref [9] an adaptive PCNN is proposed for the fusion of multimodal medical images. Although PCNN algorithm can realize the image segmentation with strong robust ability against many kinds of attacks, but the premature problem is its big concern, and will decrease its image segmentation performance. SA algorithm originates from the cooling thermodynamic process of high-temperature metal, can converge to the global optimum under the condition that the initial temperature is high enough and the temperature drop slowly enough, and can accept the poor solution with the jump probability to jump out the local optimum. Bigger jump probability can deal with the premature problem well, but will bring about the precision problem and convergence problem. As a novel computational model, membrane computing possesses the characteristics of parallelism computing, and has achieved much success in optimization field. In this paper, combined with SA algorithm, membrane computing will be introduced into PCNN to achieve the image segmentation with better property. To our best knowledge, corresponding research has never been carried out up to now, and this motivates this paper. 2. Preliminary In this paper, a PCNN model is presented as Fig. 1.
⁎
Corresponding author. E-mail address: [email protected] (M. Wang).
https://doi.org/10.1016/j.ijleo.2019.05.007 Received 3 March 2019; Accepted 5 May 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 187 (2019) 193–197
B. Wang, et al.
Fig. 1. PCNN model.
The mathematic model of PCNN is described as:
Fij [n] = Iij
∑
L ij [n] =
Wijkl Ykl [n−1]
(k,l) ∈ N(i,j)
Uij [n] = Fij [n](1 + βL ij [n])
1, Uij [n] > θij [n−1] Yij [n] = ⎧ ⎨ 0, Uij [n] ≤ θij [n−1] ⎩ θij [n] = exp(−α θ)θij [n−1] + VθYij [n] where: (i,j) represents the position of a neuron in PCNN. Iij is an external excitation signal input. Fij is the feedback input of neuron (i,j). L ij is the linear connection input term. Ykl is the pulse output of neuron (k,l). Wijkl is the weighted coefficient between Yij and Ykl . β is the connection strength coefficient. Uij is the internal activity term. Yij is the pulse output. α θ is the decay time constant of the θij. Vθ is the intrinsic electric potential of θij. PSO is a kind of optimization algorithm inspired by the collaborative behavior and swarming of bird flocking. The position and velocity of ith particle at iteration t+1 are updated on the basis of the following rules:
vid (t+1) =ωvid (t) +c1∙r1 (Pid -xid (t))
+c2 ∙r2 (Pgd -xid (t)) xid (t+1)=xid (t) + vid (t+1) where t is iteration number, ω is inertia weight, c1 and c2 are learning parameters, r1 and r2 are positive scalars, vid is ith particle’s velocity, xid is of ith particle’s position, Pid is historical individual optimum, Pgd is historical group optimum. 3. Main results The updating rules of the particle are defined as:
vid (t+1) =γ{ωvid (t) + c1∙r1 (Pid − xid (t))
+ c2 ∙r2 (Pgd − xid(t))} xid (t+1)=xid (t) + vid (t+1) where: γ is the compression factor, such that
γ=
2 |2-C- C2-4C |
where C=c1 + c2 . The jump probability of ith particle for simulated annealing (SA) algorithm is defined as：
Pi=
e− N
fpi − fpg T
∑ j=1 e−
fpj− fpg T
where: fpi is the fitness of individual optimum of the ith particle, fpg is the fitness of global optimum, N is the population size and T is the temperature. When one iteration is performed, a random number will be produced. If the random number is bigger than the current jump 194
Optik - International Journal for Light and Electron Optics 187 (2019) 193–197
B. Wang, et al.
Fig. 2. Framework of membrane computing.
probability Pi , the global optimum Pgd will be replaced by the individual historical optimum Pid . For SAPSO, when a particle finds an optimal solution, other particles will move to it quickly. When the jump probability is set bigger to jump out of the local optimal value more easily, the precision of ultimate solution will be influenced. In this paper, membrane computing will be introduced in SAPSO to solve the premature problem with good optimization ability. The framework of membrane computing is constructed as Fig. 2. Memb. 0 is surface membrane with smaller inertia weight, Membs. 1–4 are basic membrane with bigger inertia weight, SAPSO is used as the optimization operator in each membrane. Particles with best solution in Membs. 1 and 3 replace the particles with worst solution in Membs. 2 and 4. Particles with best solution in Membs. 2 and 4 replace two particles with worst solution in Memb. 0; two particles with best solution in Memb. 0 replace the particles with worst solution in Membs. 1 and 3 respectively. When the iteration finishes, the best solution in Memb. 0 will be the final obtained value. The entropy of image can reflect the information of image, and is chosen as fitness in this paper:
H= −P1log 2 (P1) − P0 log 2 (P0) where: H is information entropy of image. P1 is probability when binary pixel is 1. P0 is probability when binary pixel is 0. Bigger entropy means better fitness. 4. Experiment In this paper, the infrared image of high-voltage joint between insulator and cable is included as Fig. 3. For infrared image, the pixel with bigger value represents higher temperature. From Fig. 3 it can be seen that the temperature at the second joint between insulator and cable is higher than others obviously. High temperature at joint will lead to the potential spark. When the temperature at joint exceeds the danger line, alert should be issued. Hence it is important to identify the high temperature area of joint as clearly as possible. Based on PSO-PCNN, one can get α θ=0.021, β=0.03, Vθ=0.4 , and experimental result is shown in Fig. 4. Based on MSAPSO-PCNN, one can get α θ=0.030, β=0.67,Vθ=0.2, and experimental result is shown in Fig. 5. From Fig. 4 it can be seen that high temperature area is marked effectively to identify the potential safety hazard, however is too obscured. From Fig. 5 it can be seen that the given method can more clearly identify the high temperature part, which will be in favor of the fault diagnosis of high-voltage joint. Next, the comparison of two image segmentation method is carried out, and results are displayed in Table 1. Table 1 shows the relationship between fitness and iterations based on MSAPSO-PCNN and PSO-PCNN. One can see that PSO-
Fig. 3. Original infrared image of high-voltage joint between insulator and cable. 195
Optik - International Journal for Light and Electron Optics 187 (2019) 193–197
B. Wang, et al.
Fig. 4. Segmented image of high-voltage joint based on PSO-PCNN.
Fig. 5. Segmented image of high-voltage joint based on MSAPSO-PCNN.
PCNN needs 19 iterations to finish the search of optimum parameters, and MSAPSO-PCNN just requires 15 iterations to obtain the optimum parameters. In addition, it can be noted that the final fitness based on MSAPSO-PCNN is 0.9930, which is bigger than 0.9914 based on PSO-PCNN, and STDEV based on MSAPSO-PCNN is 0.01014, which is smaller than 0.05243 based on PSO-PCNN. These mean that our method can search for optimum with better convergence property. 5. Conclusion The paper has studied the image segmentation issue based on PCNN. As the optimization operator of membrane computing, a simulated annealing particle swarm optimization has been proposed, and applied in image segmentation successfully. At last some typical numerical examples have been included to show the effectiveness of the method given. Acknowledgments This work is partially supported by the Key Laboratory of Fluid and Power Machinery of the Ministry of Education, and the Graduate Innovation Fund of Xihua University (ycjj2018015). 196
Optik - International Journal for Light and Electron Optics 187 (2019) 193–197
B. Wang, et al.
Table 1 Fitness based on PSO-PCNN and MSAPSO-PCNN. Iterations
MSAPSO-PCNN
PSO-PCNN
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Final optimum STDEV
0.9412 0.9589 0.9593 0.9605 0.9902 0.9909 0.9910 0.9915 0.9916 0.9927 0.9930 0.9930 0.9930 0.9930 0.9930 0.9930 0.9930 0.01014
0.8513 0.8779 0.8787 0.8859 0.9063 0.9261 0.933 0.9413 0.9538 0.9551 0.9602 0.9901 0.9904 0.9906 0.9914 0.9914 0.9914 0.05243
References [1] R. Eckhorn, H.J. Reitboeck, M. Arndt, Feature linking via synchronization among distributed assemblies: simulation of results from cat cortex, Neural Comput. 2 (1990) 293–307. [2] C.H. Zhao, G.F. Shao, L.J. Ma, X. Zhang, Image fusion algorithm based on redundant-lifting NSWMDA and adaptive, PCNN Optik 125 (2014) 6247–6255. [3] Y. Cheng, L. Tian, C. Yin, Research on crack detection applications of improved PCNN algorithm in MOI nondestructive test method, Neurocomputing 277 (2017) 249–259. [4] Y. Guo, Z. Yang, Y. Ma, Saliency motivated improved simplified PCNN model for object segmentation, Neurocomputing 275 (2017) 2179–2190. [5] X.Z. Xu, Multimodal medical image fusion using PCNN optimized by the QPSO algorithm, Appl. Soft Comput. 46 (2016) 588–595. [6] A.K. Helmy, G.S. El-Tawee, Image segmentation scheme based on SOM–PCNN in frequency domain, Appl. Soft Comput. 40 (2016) 405–415. [7] H. Li, X. Jin, N. Yang, The recognition of landed aircrafts based on PCNN model and affine moment invariants, Pattern Recognit. Lett. 51 (2015) 23–29. [8] S. Wei, Q. Hong, M. Hou, Automatic image segmentation based on PCNN with adaptive threshold time constant, Neurocomputing 74 (2011) 1485–1491. [9] W. Xie, Y. Li, Y. Ma, PCNN-based level set method of automatic mammographic image segmentation, Opt. Int. J. Light Electron. Opt. 127 (2016) 1644–1650. [10] J. Garcia, C. Pope, F. Altimiras, A Distributed K-Means Segmentation Algorithm Applied to Lobesia botrana Recognition, Complexity (2017) 5137317. [11] B. Wang, L.L. Chen, Y.Z. Liu, New results on contrast enhancement for infrared images, Optik 178 (2019) 1264–1269. [12] B. Wang, J. Cheng, S. Zhong, Bounded input bounded output stability for Lurie system with time-varying delay, Adv. Difference Equations 57 (2018) 1–13. [13] B. Wang, L.L. Chen, New results on the control for a kind of Uncertain chaotic systems based on fuzzy logic, Complexity (2019) 8789438. [14] B. Wang, L.L. Chen, J. Cheng, New result on maximum entropy threshold image segmentation based on P system, Optik 163 (2018) 81–85. [15] P. Viet-Thanh, S. Jafari, C. Volos, Simulation and experimental implementation of a line-equilibrium system without linear term, Chaos Solitons Fractals 120 (2019) 213–221. [16] B. Wang, New results on fuzzy synchronization for a kind of disturbed memristive chaotic system, Complexity (2018) 3079108. [17] B. Wang, L.L. Chen, Z.Y. Zhang, A novel method on the edge detection of infrared image, Optik 180 (2019) 610–614. [18] B. Wang, D. Zhang, J. Cheng, et al., Fuzzy model-based nonfragile control of switched discrete-time systems, Nonlinear Dyn. 93 (2018) 2461–2471. [19] P. Viet-Thanh, Christos Volos, S. Jafari, A novel cubic-equilibrium chaotic system with coexisting hidden attractors: analysis, and circuit implementation, J. Circuits Syst. Comput. 27 (2018) 1850066. [20] B. Wang, J. Cheng, F. Zou, Stochastic finite time H∞ filtering for nonlinear Markovian jump systems with partly known transition probabilities, Proc. Inst. Mech. Eng. Part I 33 (2019) 31–43. [21] B. Wang, Y. Liu, X. Zhang, A New Memristive Chaotic System and the Generated Random Sequence, IEICE transactions on fundamentals of electronics, Commun. Comp. Sci. E102A (2019) 665–667. [22] B. Wang, X.H. Zhang, X.C. Dong, Novel secure communication based on chaos synchronization, IEICE transactions on fundamentals of electronics, Commun. Comp. Sci. E101-A (2018) 1132–1135. [23] B. Wang, Results on a Novel Piecewise-Linear Memristor-Based Chaotic System, Complexity (2019) 8948656.
197