# Recent Advances in Pulse-Coupled Neural Networks with Applications in Image Processing

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## Abstract

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## 1. Introduction

## 2. Fundamentals of PCNN

#### 2.1. Original Pulse-Coupled Neural Network

#### 2.2. Intersecting Cortical Model

#### 2.3. Spiking Cortical Model

#### 2.4. Modified SPCNN

#### 2.5. Fire-Controlled MSPCNN

#### 2.6. Sine–Cosine PCNN

#### 2.7. Quasi-Continuous Model

#### 2.8. Heterogeneous PCNN

- Neurons with different weights, but the same structure.
- Neurons with different structures, but the same weight.
- Both structure and weight are different for different neurons.

#### 2.9. Continuous-Coupled Neural Network

## 3. Applications

#### 3.1. Color Image Processing

#### 3.2. Diagnosis and Computer Vision

#### 3.3. Image Fusion

#### 3.4. Other Recent Advances

#### 3.5. Summary

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Freeman, W.J.; van Dijk, B.W. Spatial patterns of visual cortical fast EEG during conditioned reflex in a rhesus monkey. Brain Res.
**1987**, 422, 267–276. [Google Scholar] [CrossRef] - Eckhorn, R.; Bauer, R.; Jordan, W.; Brosch, M.; Kruse, W.; Munk, M.; Reitboeck, H.J. Coherent oscillations: A mechanism of feature linking in the visual cortex? Biol. Cybern.
**1988**, 60, 121–130. [Google Scholar] [CrossRef] [PubMed] - Hodgkin, A.L.; Huxley, A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol.
**1952**, 117, 500–544. [Google Scholar] [CrossRef] [PubMed] - Eckhorn, R.; Reitboeck, H.J.; Arndt, M.; Dicke, P. Feature Linking via Synchronization among Distributed Assemblies: Simulations of Results from Cat Visual Cortex. Neural Comput.
**1990**, 2, 293–307. [Google Scholar] [CrossRef] - Johnson, J.L. Pulse-coupled neural nets: Translation, rotation, scale, distortion, and intensity signal invariance for images. Appl. Opt.
**1994**, 33, 6239–6253. [Google Scholar] [CrossRef] [PubMed] - Ranganath, H.S.; Kuntimad, G.; Johnson, J.L. Pulse coupled neural networks for image processing. In Proceedings of the Proceedings IEEE Southeastcon ‘95. Visualize the Future, Raleigh, NC, USA, 26–29 March 1995; pp. 37–43. [Google Scholar]
- Gu, X.; Yu, D.; Zhang, L. Image shadow removal using pulse coupled neural network. IEEE Trans. Neural Netw.
**2005**, 16, 692–698. [Google Scholar] [CrossRef] [PubMed] - Liu, M.; Zhao, F.; Jiang, X.; Zhang, H.; Zhou, H. Parallel binary image cryptosystem via spiking neural networks variants. Int. J. Neural Syst.
**2021**, 32, 2150014. [Google Scholar] [CrossRef] [PubMed] - Ranganath, H.S.; Kuntimad, G. Object detection using pulse coupled neural networks. IEEE Trans. Neural Netw.
**1999**, 10, 615–620. [Google Scholar] [CrossRef] - Yu, B.; Zhang, L. Pulse-coupled neural networks for contour and motion matchings. IEEE Trans. Neural Netw.
**2004**, 15, 1186–1201. [Google Scholar] [CrossRef] - Jason, M.K. Simplified pulse-coupled neural network. In Applications and Science of Artificial Neural Networks; SPIE: Bellingham, WA, USA, 1996. [Google Scholar]
- Johnson, J.L.; Padgett, M.L. PCNN models and applications. IEEE Trans. Neural Netw.
**1999**, 10, 480–498. [Google Scholar] [CrossRef] - Ekblad, U.; Kinser, J.M.; Atmer, J.; Zetterlund, N. The intersecting cortical model in image processing. Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip.
**2004**, 525, 392–396. [Google Scholar] [CrossRef] - Zhan, K.; Zhang, H.; Ma, Y. New Spiking Cortical Model for Invariant Texture Retrieval and Image Processing. IEEE Trans. Neural Netw.
**2009**, 20, 1980–1986. [Google Scholar] [CrossRef] - Huang, Y.; Ma, Y.; Li, S.; Zhan, K. Application of heterogeneous pulse coupled neural network in image quantization. J. Electron. Imaging
**2016**, 25, 61603. [Google Scholar] [CrossRef] - Huang, Y.; Ma, Y.; Li, S. A new method for image quantization based on adaptive region related heterogeneous PCNN. In Proceedings of the International Symposium on Neural Networks, Jeju, Korea, 15–18 October 2015; pp. 269–278. [Google Scholar]
- Duan, P.; Kang, X.; Li, S.; Ghamisi, P. Multichannel Pulse-Coupled Neural Network-Based Hyperspectral Image Visualization. IEEE Trans. Geosci. Remote Sens.
**2020**, 58, 2444–2456. [Google Scholar] [CrossRef] - Yang, Z.; Dong, M.; Guo, Y.; Gao, X.; Wang, K.; Shi, B.; Ma, Y. A new method of micro-calcifications detection in digitized mammograms based on improved simplified PCNN. Neurocomputing
**2016**, 218, 79–90. [Google Scholar] [CrossRef] - Yang, Z.; Guo, Y.; Gong, X.; Ma, Y. A Non-integer Step Index PCNN Model and Its Applications. In Medical Image Understanding and Analysis; Springer: Cham, Switzerland, 2017; pp. 780–791. [Google Scholar]
- Liu, J.; Lian, J.; Sprott, J.C.; Liu, Q.; Ma, Y. The Butterfly Effect in Primary Visual Cortex. IEEE Trans. Comput.
**2022**, 1. [Google Scholar] [CrossRef] - Liu, J.; Lian, J.; Sprott, J.C.; Ma, Y. A Novel Neuron Model of Visual Processor. arXiv
**2012**, arXiv:2104.07257. [Google Scholar] - Wang, Z.; Ma, Y.; Cheng, F.; Yang, L. Review of pulse-coupled neural networks. Image Vis. Comput.
**2010**, 28, 5–13. [Google Scholar] [CrossRef] - Yang, Z.; Lian, J.; Guo, Y.; Li, S.; Wang, D.; Sun, W.; Ma, Y. An Overview of PCNN Model’s Development and Its Application in Image Processing. Arch. Comput. Methods Eng.
**2019**, 26, 491–505. [Google Scholar] [CrossRef] - Liu, H.; Cheng, Y.; Zuo, Z.; Sun, T.; Wang, K. Discrimination of neutrons and gamma rays in plastic scintillator based on pulse-coupled neural network. Nucl. Sci. Tech.
**2021**, 32, 82. [Google Scholar] [CrossRef] - Liu, H.-R.; Zuo, Z.; Li, P.; Liu, B.-Q.; Chang, L.; Yan, Y.-C. Anti-noise performance of the pulse coupled neural network applied in discrimination of neutron and gamma-ray. Nucl. Sci. Tech.
**2022**, 33, 75. [Google Scholar] [CrossRef] - Lian, J.; Yang, Z.; Sun, W.; Guo, Y.; Zheng, L.; Li, J.; Shi, B.; Ma, Y. An image segmentation method of a modified SPCNN based on human visual system in medical images. Neurocomputing
**2019**, 333, 292–306. [Google Scholar] [CrossRef] - Chen, Y.; Park, S.; Ma, Y.; Ala, R. A New Automatic Parameter Setting Method of a Simplified PCNN for Image Segmentation. IEEE Trans. Neural Netw.
**2011**, 22, 880–892. [Google Scholar] [CrossRef] [PubMed] - Otsu, N. A threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern.
**1979**, 9, 62–66. [Google Scholar] [CrossRef][Green Version] - Lian, J.; Yang, Z.; Sun, W.; Zheng, L.; Qi, Y.; Shi, B.; Ma, Y. A fire-controlled MSPCNN and its applications for image processing. Neurocomputing
**2021**, 422, 150–164. [Google Scholar] [CrossRef] - Yang, Z.; Lian, J.; Li, S.; Guo, Y.; Ma, Y. A study of sine–cosine oscillation heterogeneous PCNN for image quantization. Soft Comput.
**2019**, 23, 11967–11978. [Google Scholar] [CrossRef] - Lindblad, T.; Kinser, J.M.; Lindblad, T.; Kinser, J. Image Processing Using Pulse-Coupled Neural Networks; Springer: Berlin/Heidelberg, Germany, 2005. [Google Scholar]
- Ma, Y.; Wang, Z.; Zheng, J.Z.; Lu, L.; Wang, G.; Li, P.; Ma, T.; Xie, Y. Extracting Micro-calcification Clusters on Mammograms for Early Breast Cancer Detection. In Proceedings of the 2006 IEEE International Conference on Information Acquisition, Weihai, China, 20–23 August 2006; pp. 499–504. [Google Scholar]
- Beer, R.; Chiel, H.; Sterling, L.S. Heterogeneous neural networks for adaptive behavior in dynamic environments. Adv. Neural Inf. Process. Syst.
**1988**, 1, 577–585. [Google Scholar] - Selverston, A.I. A consideration of invertebrate central pattern generators as computational data bases. Neural Netw.
**1988**, 1, 109–117. [Google Scholar] [CrossRef] - Kuffler, S.W.; Nicholls, J.G. From Neuron to Brain, a Cellular Approach to the Function of the Nervous System; Stephen, W., Kuffler, J., Nicholls, G., Eds.; Sinauer Associates: Sunderland, MA, USA, 1976. [Google Scholar]
- Yang, Z.; Lian, J.; Li, S.; Guo, Y.; Qi, Y.; Ma, Y. Heterogeneous SPCNN and its application in image segmentation. Neurocomputing
**2018**, 285, 196–203. [Google Scholar] [CrossRef] - Siegel, R.M. Non-linear dynamical system theory and primary visual cortical processing. Phys. D Nonlinear Phenom.
**1990**, 42, 385–395. [Google Scholar] [CrossRef] - Jia, H.; Xing, Z.; Song, W. Three Dimensional Pulse Coupled Neural Network Based on Hybrid Optimization Algorithm for Oil Pollution Image Segmentation. Remote Sens.
**2019**, 11, 1046. [Google Scholar] [CrossRef][Green Version] - He, K.; Wang, R.; Tao, D.; Cheng, J.; Liu, W. Color Transfer Pulse-Coupled Neural Networks for Underwater Robotic Visual Systems. IEEE Access
**2018**, 6, 32850–32860. [Google Scholar] [CrossRef] - Lian, J.; Liu, J.; Yang, Z.; Qi, Y.; Zhang, H.; Zhang, M.; Ma, Y. A Pulse-Number-Adjustable MSPCNN and Its Image Enhancement Application. IEEE Access
**2021**, 9, 161069–161086. [Google Scholar] [CrossRef] - Shanker, R.; Bhattacharya, M. Automated Diagnosis system for detection of the pathological brain using Fast version of Simplified Pulse-Coupled Neural Network and Twin Support Vector Machine. Multimed. Tools Appl.
**2021**, 80, 30479–30502. [Google Scholar] [CrossRef] - Altaf, M.M. A hybrid deep learning model for breast cancer diagnosis based on transfer learning and pulse-coupled neural networks. Math. Biosci. Eng.
**2021**, 18, 5029–5046. [Google Scholar] [CrossRef] - Thyagharajan, K.K.; Kalaiarasi, G. Pulse coupled neural network based near-duplicate detection of images (PCNN–NDD). Adv. Electr. Comput. Eng.
**2018**, 18, 87–97. [Google Scholar] [CrossRef] - Lian, J.; Yang, Z.; Liu, J.; Sun, W.; Zheng, L.; Du, X.; Yi, Z.; Shi, B.; Ma, Y. An Overview of Image Segmentation Based on Pulse-Coupled Neural Network. Arch. Comput. Methods Eng.
**2021**, 28, 387–403. [Google Scholar] [CrossRef] - Qi, Y.; Yang, Z.; Sun, W.; Lou, M.; Lian, J.; Zhao, W.; Deng, X.; Ma, Y. A Comprehensive Overview of Image Enhancement Techniques. Arch. Comput. Methods Eng.
**2022**, 29, 583–607. [Google Scholar] [CrossRef] - Jiang, L.; Zhang, D.; Che, L. Texture analysis-based multi-focus image fusion using a modified Pulse-Coupled Neural Network (PCNN). Signal Process. Image Commun.
**2021**, 91, 116068. [Google Scholar] [CrossRef] - Du, C.; Gao, S. Multi-focus image fusion algorithm based on pulse coupled neural networks and modified decision map. Optik
**2018**, 157, 1003–1015. [Google Scholar] [CrossRef] - Ramlal, S.D.; Sachdeva, J.; Ahuja, C.K.; Khandelwal, N. Multimodal medical image fusion using non-subsampled shearlet transform and pulse coupled neural network incorporated with morphological gradient. Signal Image Video Process.
**2018**, 12, 1479–1487. [Google Scholar] [CrossRef] - Li, L.; Ma, H. Pulse Coupled Neural Network-Based Multimodal Medical Image Fusion via Guided Filtering and WSEML in NSCT Domain. Entropy
**2021**, 23, 591. [Google Scholar] [CrossRef] [PubMed] - Rajalingam, B.; Priya, R. Hybrid multimodality medical image fusion based on guided image filter with pulse coupled neural network. Int. J. Sci. Res. Sci. Eng. Technol.
**2018**, 5, 86–99. [Google Scholar] - Qin, X.; Ban, Y.; Wu, P.; Yang, B.; Liu, S.; Yin, L.; Liu, M.; Zheng, W. Improved Image Fusion Method Based on Sparse Decomposition. Electronics
**2022**, 11, 2321. [Google Scholar] [CrossRef] - Ban, Y.; Liu, M.; Wu, P.; Yang, B.; Liu, S.; Yin, L.; Zheng, W. Depth Estimation Method for Monocular Camera Defocus Images in Microscopic Scenes. Electronics
**2022**, 11, 2012. [Google Scholar] [CrossRef] - Chen, T.; Wang, H.; Cao, J. Research on Auto-focusing Method Based on Pulse Coupled Neural Network. J. Phys. Conf. Ser.
**2021**, 1848, 012158. [Google Scholar] [CrossRef] - Dong, J.; Xia, Z.; Yan, W.; Zhao, Q. Dynamic gesture recognition by directional pulse coupled neural networks for human-robot interaction in real time. J. Vis. Commun. Image Represent.
**2019**, 63, 102583. [Google Scholar] [CrossRef]

**Figure 2.**Schematic of the pulse-coupled neural network. (

**a**) Connection between the internal activity ${\mathit{U}}_{ij}$, timing pulse sequence $\mathit{Y}$, and dynamic threshold ${\mathit{\theta}}_{ij}$. (

**b**) Schematic of the PCNN. (

**c**) Activity of the internal activity ${\mathit{U}}_{ij}$ and dynamic threshold ${\mathit{\theta}}_{ij}$ under stimulation of multipule pulses.

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**MDPI and ACS Style**

Liu, H.; Liu, M.; Li, D.; Zheng, W.; Yin, L.; Wang, R. Recent Advances in Pulse-Coupled Neural Networks with Applications in Image Processing. *Electronics* **2022**, *11*, 3264.
https://doi.org/10.3390/electronics11203264

**AMA Style**

Liu H, Liu M, Li D, Zheng W, Yin L, Wang R. Recent Advances in Pulse-Coupled Neural Networks with Applications in Image Processing. *Electronics*. 2022; 11(20):3264.
https://doi.org/10.3390/electronics11203264

**Chicago/Turabian Style**

Liu, Haoran, Mingzhe Liu, Dongfen Li, Wenfeng Zheng, Lirong Yin, and Ruili Wang. 2022. "Recent Advances in Pulse-Coupled Neural Networks with Applications in Image Processing" *Electronics* 11, no. 20: 3264.
https://doi.org/10.3390/electronics11203264