Cellular neural networks and visual computing: foundation and applications

410 Pages·2002·4.552 MB·English

by  Leon O. Chua, Tamas Roska

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Cellular neural networks and visual computing
Cellular Nonlinear/neural Network (CNN) technology is both a revolutionary concept and an
experimentallyprovennewcomputingparadigm.AnalogiccellularcomputersbasedonCNNsare
settochangethewayanalogsignalsareprocessedandarepavingthewaytoanentirenewanalog
computingindustry.
Thisuniqueundergraduate-leveltextbookincludesmanyexamplesandexercises,includingCNN
simulatoranddevelopmentsoftwareaccessibleviatheInternet.ItisanidealintroductiontoCNNs
and analogic cellular computing for students, researchers, and engineers from a wide range of
disciplines.Althoughitsprimefocusisonvisualcomputing,theconceptsandtechniquesdescribed
inthebookwillbeofgreatinteresttothoseworkinginotherareasofresearch,includingmodeling
ofbiological,chemical,andphysicalprocesses.
Leon Chua is a Professor of Electrical Engineering and Computer Science at the University of
California,BerkeleywherehecoinventedtheCNNin1988andholdsseveralpatentsrelatedtoCNN
Technology.HereceivedtheNeuralNetworkPioneerAward,2000.
Tama´s Roska is a Professor of Information Technology at the Pa´zma´ny P. Catholic University of
Budapest and head of the Analogical and Neural Computing Laboratory of the Computer and
AutomationResearchInstituteoftheHungarianAcademyofSciences,Budapestandwasanearly
pioneer of CNN technology and a coinventor of the CNN Universal Machine as an analogic
supercomputer, He has also spent 12 years as a part-time visiting scholar at the University of
CaliforniaatBerkeley.

Cellular neural networks
and visual computing
Foundation and applications
Leon O. Chua
and
Tama´s Roska
         
The Pitt Building, Trumpington Street, Cambridge, United Kingdom
  
The Edinburgh Building, Cambridge CB2 2RU, UK
40 West 20th Street, New York, NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
Ruiz de Alarcón 13, 28014 Madrid, Spain
Dock House, The Waterfront, Cape Town 8001, South Africa
http://www.cambridge.org
©Cambridge University Press 2004
First published in printed format 2002
ISBN 0-511-04051-2 eBook (netLibrary)
ISBN 0-521-65247-2 hardback
Toourwives,DianaandZsuzsa

Contents
Acknowledgements pagexi
1 Introduction 1
2 Notation,definitions,andmathematicalfoundation 7
2.1 Basicnotationanddefinitions 7
2.2 Mathematicalfoundations 14
3 CharacteristicsandanalysisofsimpleCNNtemplates 35
3.1 Twocasestudies:theEDGEandEDGEGRAYtemplates 35
3.2 ThreequickstepsforsketchingtheshiftedDPplot 49
3.3 Someotherusefultemplates 50
4 SimulationoftheCNNdynamics 100
4.1 IntegrationofthestandardCNNdifferentialequation 100
4.2 Imageinput 101
4.3 Softwaresimulation 102
4.4 Digitalhardwareaccelerators 110
4.5 AnalogCNNimplementations 111
4.6 Scalingthesignals 113
4.7 Discrete-timeCNN(DTCNN) 114
vii
viii Contents
5 BinaryCNNcharacterizationviaBooleanfunctions 115
5.1 BinaryanduniversalCNNtruthtable 115
5.2 Booleanandcompressedlocalrules 122
5.3 Optimizingthetruthtable 124
6 UncoupledCNNs:unifiedtheoryandapplications 139
6.1 Thecompletestabilityphenomenon 139
6.2 ExplicitCNNoutputformula 140
6.3 ProofofcompletelystableCNNtheorem 142
6.4 TheprimaryCNNmosaic 155
6.5 Explicitformulafortransientwaveformandsettlingtime 156
6.6 WhichlocalBooleanfunctionsarerealizablebyuncoupledCNNs? 161
6.7 Geometricalinterpretations 162
6.8 HowtodesignuncoupledCNNswithprescribedBooleanfunctions 166
6.9 Howtorealizenon-separablelocalBooleanfunctions? 173
7 IntroductiontotheCNNUniversalMachine 183
7.1 Globalclockandglobalwire 184
7.2 Setinclusion 184
7.3 Translationofsetsandbinaryimages 188
7.4 Openingandclosingandimplementinganymorphologicaloperator 190
7.5 ImplementinganyprescribedBooleantransitionfunctionbynotmorethan
256templates 195
7.6 Minimizing the number of templates when implementing any possible
Booleantransitionfunction 198
7.7 Analog-to-digitalarrayconverter 201
8 Backtobasics:Nonlineardynamicsandcompletestability 205
8.1 Aglimpseofthingstocome 205
8.2 AnoscillatoryCNNwithonlytwocells 205
8.3 AchaoticCNNwithonlytwocellsandonesinusoidalinput 210
8.4 SymmetricAtemplateimpliescompletestability 214
8.5 Positiveandsign-symmetricAtemplateimpliescompletestability 219