Cellular neural network: Difference between revisions

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{{short description|Parallel computing paradigm}}

In [[computer science]] and [[machine learning]], '''cellular neural networks''' ('''CNN)''') or '''cellular nonlinear networks''' ('''CNN)''') are a [[parallel computing]] paradigm similar to [[Artificial neural network|neural networks]], with the difference that communication is allowed between neighbouring units only. Typical applications include [[image processing]], analyzing 3D surfaces, solving [[partial differential equation]]s, reducing non-visual problems to [[Geometry|geometric]] maps, modelling biological [[visual system|vision]] and other [[Sensory-motor coupling|sensory-motor]] organs.<ref>{{Cite book|last=Slavova|first=A.|url=https://books.google.com/books?id=bt4PUx8CZXIC&q=Cellular+neural+network|title=Cellular Neural Networks: Dynamics and Modelling|date=2003-03-31|publisher=Springer Science & Business Media|isbn=978-1-4020-1192-4|language=en}}</ref>

CNN is not to be confused with [[Convolutionalconvolutional neural networknetworks]] (also colloquially called CNN).

==CNN architecture==

Due to their number and variety of [[Computer architecture|architectures]], it is difficult to give a precise definition for a CNN processor. From an architecture standpoint, CNN processors are a system of finite, fixed-number, fixed-___location, fixed-topology, locally interconnected, multiple-input, single-output, nonlinear processing units. The nonlinear processing units are often referred to as [[neurons]] or [[cell (biology)|cells]]. Mathematically, each cell can be modeled as a [[Dissipation|dissipative]], nonlinear [[dynamical system]] where information is encoded via its initial state, inputs and variables used to define its behavior. Dynamics are usually continuous, as in the case of [[Discrete time and continuous time|Continuous-Time]] CNN (CT-CNN) processors, but can be discrete, as in the case of [[Discrete time and continuous time|Discrete-Time]] CNN (DT-CNN) processors.<ref>S. Malki, Y. Fuqiang, and L. Spaanenburg, "Vein Feature Extraction Using DT-CNNs", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>H. Harrer and J.Nossek, "Discrete-Time Cellular Neural Networks", [[International Journal of Circuit Theory and Applications]], 20:453-467, 1992.</ref><ref>M. Brugge, "Morphological Design of Discrete−Time Cellular Neural Networks", University of Groningen Dissertation, 2005.</ref>

Each cell has one output, by which it communicates its state with both other cells and external devices. Output is typically [[Real number|real-valued]], but can be [[Complex number|complex]] or even [[quaternion]], i.e. a Multi-Valued CNN (MV-CNN). Most CNN processors, processing units are identical, but there are applications that require non-identical units, which are called Non-Uniform Processor CNN (NUP-CNN) processors, and consist of different types of cells.

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The idea of CNN processors was introduced by [[Leon Chua]] and Lin Yang in 1988.<ref>https://www.researchgate.net/publication/3183706_Cellular_neural_networks_Theory ("Cellular Neural Networks: Theory" and "Cellular Neural Networks: Applications" in IEEE Transactions on Circuits and Systems)</ref> In these articles, Chua and Yang outline the underlying mathematics behind CNN processors. They use this mathematical model to demonstrate, for a specific CNN implementation, that if the inputs are static, the processing units will converge, and can be used to perform useful calculations. They then suggest one of the first applications of CNN processors: image processing and pattern recognition (which is still the largest application to date). [[Leon O. Chua|Leon Chua]] is still active in CNN research and publishes many of his articles in the [[International Journal of Bifurcation and Chaos]], of which he is an editor. Both [[IEEE Circuits and Systems Society|IEEE Transactions on Circuits and Systems]] and the International Journal of Bifurcation also contain a variety of useful articles on CNN processors authored by other knowledgeable researchers. The former tends to focus on new CNN architectures and the latter more on the dynamical aspects of CNN processors.

In 1993, [[:nl:Tamás Roska|Tamas Roska]] and Leon Chua introduced the first algorithmically programmable analog CNN processor in the world.<ref name=":3">{{Cite journal|last1=Roska|first1=T.|last2=Chua|first2=L.O.|date=March 1993|title=The CNN universal machine: an analogic array computer|url=http://dx.doi.org/10.1109/82.222815|journal=IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing|volume=40|issue=3|pages=163–173|doi=10.1109/82.222815|issn=1057-7130|url-access=subscription}}</ref> The multi-national effort was funded by the [[Office of Naval Research]], the [[National Science Foundation]], and the [[Hungarian Academy of Sciences]], and researched by the Hungarian Academy of Sciences and the [[University of California, Berkeley|University of California]]. This article proved that CNN processors were producible and provided researchers a physical platform to test their CNN theories. After this article, companies started to invest into larger, more capable processors, based on the same basic architecture as the CNN Universal Processor. Tamas Roska is another key contributor to CNNs. His name is often associated with biologically inspired information processing platforms and algorithms, and he has published numerous key articles and has been involved with companies and research institutions developing CNN technology.

=== Literature ===

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=== Boolean functions ===

Like CA, computations can be performed through the generation and propagation of signals that either grow or change over time. [[Computation]]s can occur within a signal or can occur through the interaction between signals. One type of processing, which uses signals and is gaining momentum is [[Signal processing|wave processing]], which involves the generation, expanding, and eventual collision of waves. Wave processing can be used to measure distances and find optimal paths. Computations can also occur through particles, gliders, solutions, and filterons localized structures that maintain their shape and velocity.{{clarify|date=August 2023|what are these things? what is a filteron?}} Given how these structures interact/collide with each other and with static signals, they can be used to store information as states and implement different [[Boolean functions]]. Computations can also occur between complex, potentially growing or evolving localized behavior through worms, ladders, and pixel-snakes. In addition to storing states and performing [[Boolean function]]s, these structures can interact, create, and destroy static structures.<ref name=":1">{{Cite journalbook|last1=Chen|first1=F.|last2=He|first2=G.|last3=Xu|first3=X.|last4=Chen|first4=G.|date=August 2006|title=Implementation of Arbitrary Boolean Functions via CNN|url=https://ieeexplore.ieee.org/document/4145881|journal=2006 10th International Workshop on Cellular Neural Networks and Their Applications |chapter=Implementation of Arbitrary Boolean Functions via CNN |date=August 2006|pages=1–6|doi=10.1109/CNNA.2006.341641|isbn=1-4244-0639-0|s2cid=9648461}}</ref>

The applications of CNNs to Boolean functions is discussed in the paper by Fangyue Chen, Guolong He, Xiubin Xu, and [[Chen Guanrong|Guanrong Chen]], "Implementation of Arbitrary Boolean Functions via CNN".<ref name=":1" />

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In the 2000s, AnaFocus, a mixed-signal semiconductor company from the [[University of Seville]], introduced their ACE prototype CNN processor product line. Their first ACE processor contained 20x20 B/W processor units; and subsequent processors provided 48x48 and 128x128 grayscale processor units, improving the speed and processing elements. AnaFocus also had a multilayer CASE prototype CNN processors line. Their processors allowed real-time interaction between the sensing and processing. In 2014, AnaFocus had been sold to e2v technologies.<ref>{{Cite web|title=Acquisition of AnaFocus: Fast-growing CMOS imaging business to be integrated into High Performance Imaging division|url=https://www.teledyne-e2v.com/news/acquisition-of-anafocus-fast-growing-cmos-imaging-business-to-be-integrated-into-high-performance-imaging-division/|access-date=2020-12-27|website=e2v}}</ref>

Another company, AnaLogic Computers was founded in 2000 by many of the same researchers behind the first algorithmically programmable CNN Universal Processor. In 2003, AnaLogic Computers developed a PCI-X visual processor board that included the ACE 4K processor,<ref>{{Cite web|title=StackPath|url=https://www.vision-systems.com/home/article/16738443/cellular-device-processes-at-ultrafast-speeds|access-date=2020-12-27|website=www.vision-systems.com|date=February 2003 }}</ref> with a [[Texas Instruments|Texas Instrument]] DIP module and a high-speed frame-grabber. This allowed CNN processing to be easily included in a desktop computer. In 2006, AnaLogic Computers developed their Bi-I Ultra High Speed Smart Camera product line, which includes the ACE 4K processor in their high-end models.<ref>A. Rodríguez-Vázquez, G. Liñán-Cembrano, L. Carranza, E. Roca-Moreno, R. Carmona-Galán, F. Jiménez-Garrido, R. Domínguez-Castro, and S. Meana, "ACE16k: The Third Generation of Mixed-Signal SIMD-CNN ACE Chips Toward VSoCs," IEEE Trans. on Circuits and Systems - I, 51(5): 851-863, 2004.</ref>

In 2006, Roska et al. published a paper on designing a Bionic Eyeglass for AnaLogic. The Bionic Eyeglass is a dual-camera, wearable platform, based on the Bi-I Ultra High Speed Smart Camera, designed to provide assistance to blind people. Some of its functions include route number recognition and color processing.<ref>{{Cite journalbook|last1=Roska|first1=T.|last2=Balya|first2=D.|last3=Lazar|first3=A.|last4=Karacs|first4=K.|last5=Wagner|first5=R.|last6=Szuhaj|first6=M.|datetitle=May2006 IEEE International Symposium on Circuits and Systems 2006|titlechapter=System aspects of a bionic eyeglass |url=https://ieeexplore.ieee.org/document/1692547|journaldate=May 2006 IEEE International Symposium on Circuits and Systems|pages=4 pp.–164|doi=10.1109/ISCAS.2006.1692547|isbn=0-7803-9389-9|s2cid=3842486}}</ref><ref>K. Karacst and T. Roskatt, "Route Number Recognition of Public Transport Vehicles via the Bionic Eyeglass", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>R. Wagner and M. Szuhajt, "Color Processing in Wearable Bionic Glasses"</ref>

=== Analog CNN processors ===

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=== Image processing ===

CNN processors were designed to perform image processing; specifically, real-time ultra-high frame-rate (>10,000 frame/s) processing for applications like particle detection in jet engine fluids and spark-plug detection. Currently, CNN processors can achieve up to 50,000 frames per second, and for certain applications such as missile tracking, flash detection, and spark-plug diagnostics these microprocessors have outperformed a conventional [[supercomputer]]. CNN processors lend themselves to local, low-level, processor intensive operations and have been used in feature extraction,<ref>O. Lahdenoja, M. Laiho and A. Paasio, "Local Binary Pattern Feature Vector Extraction with CNN", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref> level and gain adjustments, color constancy detection,<ref>L. Torok and A. Zarandy, "CNN Based Color Constancy Algorithm", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref> contrast enhancement, [[deconvolution]],<ref>L. Orzo, "Optimal CNN Templates for Deconvolution", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006</ref> [[image compression]],<ref>P. Venetianer and T. Roska, "Image Compression by Cellular Neural Networks," IEEE Trans. Circuits Syst., 45(3): 205-215, 1998.</ref><ref>R. Dogarut, R. Tetzlaffl and M. Glesner, "Semi-Totalistic CNN Genes for Compact Image Compression", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> [[motion estimation]],<ref name="Y. Cheng, J. Chung 2005">Y. Cheng, J. Chung, C. Lin and S. Hsu, "Local Motion Estimation Based On Cellular Neural Network Technology for Image Stabilization Processing", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref><ref>A. Gacsadi, C. Grava, V. Tiponut, and P. Szolgay, "A CNN Implementation of the Horn & Schunck Motion Estimation Method", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> image encoding, image decoding, [[image segmentation]],<ref>S. Chen, M. Kuo and J. Wang, "Image Segmentation Based on Consensus Voting", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref><ref>G. Grassi, E. Sciascio, A. Grieco and P. Vecchio, "A New Object-oriented Segmentation Algorithm based on CNNs - Part II: Performance Evaluation", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref> orientation preference maps,<ref>J. Wu, Z. Lin and C. Liou, "Formation and Variability of Orientation Preference Maps in Visual Cortex: an Approach Based on Normalized Gaussian Arrays", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref> pattern learning/recognition,<ref name=":2" /><ref>C. Wu and S. Tsai, "Autonomous Ratio-Memory Cellular Nonlinear Network (ARMCNN) for Pattern Learning and Recognition", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> multi-target tracking,<ref>G. Timar and C. Rekeczky, "Multitarget Tracking Applications of the Bi-I Platform: Attention-selection, Tracking and Navigation", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> [[image stabilization]],<ref name="Y. Cheng, J. Chung 2005"/> resolution enhancement,<ref>T. Otake, T. Konishi, H. Aomorit, N. Takahashit and M. Tanakat, "Image Resolution Upscaling Via Two-Layered Discrete Cellular Neural Network", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> image deformations and mapping, image inpainting,<ref>A. Gacsadi and P. Szolgay, "Image Inpainting Methods by Using Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref> optical flow,<ref>B. Shi, T. Roska and L. Chua, "Estimating Optical Flow with Cellular Neural Networks," Int’l Journal of Circuit Theory and Applications, 26: 344-364, 1998.</ref> contouring,<ref>Szalka, G. Soos, D. Hillier, L. Kek, G. Andrassy and C. Rekeczky, "Space-time Signature Analysis of 2D Echocardiograms Based on Topographic Cellular Active Contour Techniques", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>T. Szabot and P. Szolgay, "CNN-UM-Based Methods Using Deformable Contours on Smooth Boundaries", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> [[moving object detection]],<ref>G. Costantini, D. Casali, and R. Perfetti, "Detection of Moving Objects in a Binocular Video Sequence", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> axis of symmetry detection,<ref>G Costantini, D. Casafi., and R. Perfetti, "A New CNN-based Method for Detection of the Axis of Symmetry.", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> and [[image fusion]].<ref>I. Szatmari, P. Foldesy, C. Rekeczky and A. Zarandy, "Image Processing Library for the Aladdin Computer", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref><ref>I. Szatmari, P. Foldesy, C. Rekeczky and A. Zarandy, "Image processing library for the Aladdin Visual Computer", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref><ref>K. Wiehler, M. Perezowsky, R. Grigat, "A Detailed Analysis of Different CNN Implementations for a Real-Time Image Processing System", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.</ref>

Due to their processing capabilities and flexibility, CNN processors have been used and [[prototype]]dprototyped for novel field applications such as flame analysis for monitoring combustion at a waste [[Incineration|incinerator]],<ref>L. Bertucco, A. Fichaa, G. Nmari and A. Pagano, "A Cellular Neural Networks Approach to Flame Image Analysis for Combustion Monitoring", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.</ref> mine-detection using [[infrared]] imagery, [[calorimeter]] cluster peak for [[high energy physics]],<ref>C. Baldanza, F. Bisi, M. Bruschi, I. D’Antone, S. Meneghini, M. Riui, M. Zufa, "A Cellular Neural Network For Peak Finding In High-Energy Physics", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.</ref> anomaly detection in potential field maps for geophysics,<ref>E. Bilgili, O. Ucan, A. Albora and I. Goknar, "Potential Anomaly Separation Using Genetically Trained Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref> laser dot detection,<ref>C. Rekeczky and G. Timar "Multiple Laser Dot Detection and Localization within an Attention Driven Sensor Fusion Framework", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.</ref> metal inspection for detecting manufacturing defects,<ref>Z. Szlavikt, R. Tetzlaff, A. Blug and H. Hoefler, "Visual Inspection of Metal Objects Using Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> and [[Seismology|seismic]] horizon picking. They have also been used to perform [[Biometrics|biometric]] functions<ref>R. Dogaru and I. Dogaru, "Biometric Authentication Based on Perceptual Resonance Between CNN Emergent Patterns and Humans", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref> such as [[fingerprint recognition]],<ref>T. Su, Y. Du, Y. Cheng, and Y. Su, "A Fingerprint Recognition System Using Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> vein feature extraction, face tracking,<ref>S. Xavier-de-Souza, M. Van Dyck, J. Suykens and J. Vandewalle, "Fast and Robust Face Tracking for CNN Chips: Application to Wheelchair Driving", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> and generating visual stimuli via emergent patterns to gauge perceptual [[resonance]]s.

=== Biology and medicine ===

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There is an ongoing effort to incorporate CNN processors into sensory-computing-actuating machines as part of the emerging field of [[Cellular Machines]]. The basic premise is to create an integrated system that uses CNN processors for the sensory signal-processing and potentially the decision-making and control. The reason is that CNN processors can provide a low power, small size, and eventually low-cost computing and actuating system suited for Cellular Machines. These Cellular Machines will eventually create a Sensor-Actuator Network (SAN),<ref>M. Haenggi, "Mobile Sensor-Actuator Networks: Opportunities and Challenges", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.</ref> a type of Mobile Ad Hoc Networks (MANET) which can be used for military intelligence gathering, surveillance of inhospitable environments, maintenance of large areas, planetary exploration, etc.

CNN processors have been proven versatile enough for some control functions. They have been used to optimize function via a genetic algorithm,<ref>D. Balya and V. Galt, "Analogic Implementation of the Genetic Algorithm", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref> to measure distances, to perform optimal path-finding in a complex, dynamic environment, and theoretically can be used to learn and associate complex stimuli. They have also been used to create antonymous gaits and low-level motors for robotic [[nematode]]s, spiders, and lamprey gaits using a Central Pattern Generator (CPG). They were able to function using only feedback from the environment, allowing for a robust, flexible, biologically inspired robot motor system. CNN-based systems were able to operate in different environments and still function if some of the processing units are disabled.<ref>{{cite arxivarXiv|last1=Asli|first1=A. E. Niaraki|last2=Roghair|first2=J.|last3=Jannesari|first3=A.|date=2020-03-11|title=Energy-aware Goal Selection and Path Planning of UAV Systems via Reinforcement Learning|class=eess.SP|eprint=1909.12217}}</ref><ref>I. Gavrilut, V. Tiponut, and A. Gacsadi, "Path Planning of Mobile Robots by Using Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref><ref>P. Arena, P. Crucitti, L. Fortuna, M. Frasca, D. Lombardo and L. Patane, "Perceptive Patterns For Mobile Robots via RD-CNN and Reinforcement Learning", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.</ref>

=== Communication systems ===

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*W. Yen, R. Chen and J. Lai, "Design of Min/Max Cellular Neural Networks in CMOS Technology", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.

*Z. Gallias and M. Ogorzalek, "Influence in System Nonuniformity on Dynamic Phenomenon in Arrays of Coupled Nonlinear Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002

*A. PaasiotPaasio and J. PoilkonentPoikonen, "Programmable DiitalDigital Nested CNN", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

*M. ZnggiHanggi, R. Dogaru, and L. Chua, "Physical Modeling of RTD-Based CNN Cells", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.

*Z. VoroshazitVoroshazi, Z. NagytNagy, A. Kiss and P. Szolgay, "An Embedded CNN-UM Global Analogic Programming Unit Implementation on FPGA", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

*A. Loncar, R. Kunz and R. Tetzaff, "SCNN 2000 - Part I: Basic Structures and Features of the Simulation System for Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.

*V. Tavsanoglu, "Jacobi’s Iterative Method for Solving Linear Equations and the Simulation of Linear CNN", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

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*S. Chen, M. Kuo and J. Wang, "Image Segmentation Based on Consensus Voting", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.

*Y. Cheng, J. Chung, C. Lin and S. Hsu, "Local Motion Estimation Based On Cellular Neural Network Technology for Image Stabilization Processing", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.

*P. KorbeltKorbel and K. SlotiSlot, "Modeling of Elastic Inter-node Bounds in Cellular Neural Network-based Implementation of the Deformable Grid Paradigm", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

*C. Amenta, P. Arena, S. Baglio, L. Fortuna, D. Richiura, M.Xibilia and L. Vu, "SC-CNNs for Sensors Data Fusion and Control in Space Distributed Structures", Int’l Workshop on Cellular Neural Networks and Their Applications, 2000.

*T. Su, Y. Du, Y. Cheng, and Y. Su, "A Fingerprint Recognition System Using Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

*M. Bucolo, L. Fortuna, M. Frasca, M. La Rosa, D. Shannahoff-Khalsa, "A CNN Based System to Blind Sources Separation of MEG Signals", Int’l Workshop on Cellular Neural Networks and Their Applications, 2002.

*F. DohlertDohler, A. Chernihovskyi, F. Mormann, C. Elger, and K. Lehnertz, "Detecting Structural Alterations in the Brain using a Cellular Neural Network based Classification of Magnetic Resonance Images", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

*L. Fortuna, P. Arena, D. Balya, and A. Zarandy, "Cellular Neural Networks: A Paradigm for Nonlinear Spatio-Temporal Processing", IEEE Circuits and Systems Magazine, 1(4): 6-21, 2001.

*L. Goras, L. Chua, and D. Leenearts, "Turing Patterns in CNNs – Part I: Once Over Lightly", IEEE Trans. on Circuits and Systems – I, 42(10):602-611, 1995.

*L. Goras, L. Chua, and D. Leenearts, "Turing Patterns in CNNs – Part II: Equations and Behavior", IEEE Trans. on Circuits and Systems – I, 42(10):612-626, 1995.

*L. Goras, L. Chua, and D. Leenearts, "Turing Patterns in CNNs – Part III: Computer Simulation Results", IEEE Trans. on Circuits and Systems – I, 42(10):627-637, 1995.

*L. KomatowskitKornatowski, K. Slot, P. DqbiecDȩbiec, and H. Kim, "Generation of Patterns with Predefined Statistical Properties using Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

*C. Lin and S. Chen, "Biological Visual Processing for Hybrid-Order Texture Boundary Detection with CNN-UM", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

*G. Costantini, D. Casali, and M. Carota, "A Pattern Classification Method Based on a Space-Variant CNN Template", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

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*R. Chen and J. Lai, "Data Encryption Using Non-uniform 2-D Von Neumann Cellular Automata", Int’l Workshop on Cellular Neural Networks and Their Applications, 2005.

*A. Chernihovskyi, C. Elger, and K. Lehnertz, "Effect of in Inhibitory Diffusive Coupling on Frequency-Selectivity of Excitable Media Simulated With Cellular Neural Networks", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

*P. Arena, M. BediatBedia, L. Fortuna, D. Lombardo, L. Patane, and M. Velardet, "Spatio-temporal Patterns in CNNs for Classification: the Winnerless Competition Principle", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.

*V. Perez-Munuzuri, A. P. Munuzuri, M. Gomez-Gesteria, V. Perez-Villar, L. Pivka, and L. Chua, "Nonlinear Waves, Patters, and Spatio-Temporal Chaos in Cellular Neural Networks," Phil. Trans. R. Soc. Lond. A, (353): 101-113, 1995.

*M. Ercsey-Ravasz, T. Roska and Z. Neda, "Random Number Generator and Monte Carlo type Simulations on the CMM-UM", Int’l Workshop on Cellular Neural Networks and Their Applications, 2006.