CELLULAR NEURAL NETWORKS AND VISUAL COMPUTING
CONTENTS INTRODUCTION NOTATION,DEFINITIONS,ANDMATHEMATICALFOUNDATION BASIC NOTATION AND DE?NITIONS MATHEMATICAL FOUNDATIONS CHARACTERISTICSANDANALYSISOFSIMPLECNNTEMPLATES TWO CASE STUDIES: THE EDGE AND EDGEGRAY TEMPLATES THREE QUICK STEPS FOR SKETCHING THE SHIFTED DP PLOT SOME OTHER USEFUL TEMPLATES SIMULATIONOFTHECNNDYNAMICS INTEGRATION OF THE STANDARD CNN DIFFERENTIAL EQUATION IMAGE INPUT SOFTWARE SIMULATION DIGITAL HARDWARE ACCELERATORS ANALOG CNN IMPLEMENTATIONS SCALING THE SIGNALS DISCRETE-TIME CNN (DTCNN) BINARYCNNCHARACTERIZATIONVIABOOLEANFUNCTIONS BINARY AND UNIVERSAL CNN TRUTH TABLE BOOLEAN AND COMPRESSED LOCAL RULES OPTIMIZING THE TRUTH TABLE UNCOUPLEDCNNS:UNIFIEDTHEORYANDAPPLICATIONS THE COMPLETE STABILITY PHENOMENON EXPLICIT CNN OUTPUT FORMULA PROOF OF COMPLETELY STABLE CNN THEOREM THE PRIMARY CNN MOSAIC EXPLICIT FORMULA FOR TRANSIENT WAVEFORM AND SETTLING TIME WHICH LOCAL BOOLEAN FUNCTIONS ARE REALIZABLE BY UNCOUPLED CNNS? GEOMETRICAL INTERPRETATIONS HOW TO DESIGN UNCOUPLED CNNS WITH PRESCRIBED BOOLEAN FUNCTIONS HOW TO REALIZE NON-SEPARABLE LOCAL BOOLEAN FUNCTIONS? INTRODUCTIONTOTHECNNUNIVERSALMACHINE GLOBAL CLOCK AND GLOBAL WIRE SET INCLUSION TRANSLATION OF SETS AND BINARY IMAGES OPENING AND CLOSING AND IMPLEMENTING ANY MORPHOLOGICAL OPERATOR IMPLEMENTING ANY PRESCRIBED BOOLEAN TRANSITION FUNCTION BY NOT MORE THAN 256 TEMPLATES MINIMIZING THE NUMBER OF TEMPLATES WHEN IMPLEMENTING ANY POSSIBLE BOOLEAN TRANSITION FUNCTION ANALOG-TO-DIGITAL ARRAY CONVERTER BACKTOBASICS:NONLINEARDYNAMICSANDCOMPLETESTABILITY A GLIMPSE OF THINGS TO COME AN OSCILLATORY CNN WITH ONLY TWO CELLS A CHAOTIC CNN WITH ONLY TWO CELLS AND ONE SINUSOIDAL INPUT SYMMETRIC A TEMPLATE IMPLIES COMPLETE STABILITY POSITIVE AND SIGN-SYMMETRIC A TEMPLATE IMPLIES COMPLETE STABILITY POSITIVE AND CELL-LINKING A TEMPLATE IMPLIES COMPLETE STABILITY STABILITY OF SOME SIGN-ANTISYMMETRIC CNNS A APPENDIX TO CHAPTER THECNNUNIVERSALMACHINE(CNN-UM) THE ARCHITECTURE A SIMPLE EXAMPLE IN MORE DETAIL A VERY SIMPLE EXAMPLE ON THE CIRCUIT LEVEL LANGUAGE, COMPILER, OPERATING SYSTEM TEMPLATEDESIGNTOOLS 10 1 VARIOUS DESIGN TECHNIQUES 10 2 BINARY REPRESENTATION, LINEAR SEPARABILITY, AND SIMPLE DECOMPOSITION 10 3 TEMPLATE OPTIMIZATION 10 4 TEMPLATE DECOMPOSITION TECHNIQUES CNNSFORLINEARIMAGEPROCESSING 11 1 LINEAR IMAGE PROCESSING WITH B TEMPLATES IS EQUIVALENT TO SPATIAL CONVO- LUTION WITH FIR KERNELS 11 2 SPATIAL FREQUENCY CHARACTERIZATION 11 3 A PRIMER ON PROPERTIES AND APPLICATIONS OF DISCRETE-SPACE FOURIER TRANS- FORM (DSFT) 11 4 LINEAR IMAGE PROCESSING WITH A AND B TEMPLATES IS EQUIVALENT TO SPATIAL CONVOLUTION WITH IIR KERNELS COUPLEDCNNWITHLINEARSYNAPTICWEIGHTS 12 1 ACTIVE AND INACTIVE CELLS, DYNAMIC LOCAL RULES 12 2 BINARY ACTIVATION PATTERN AND TEMPLATE FORMAT 12 3 A SIMPLE PROPAGATING TYPE EXAMPLE WITH B/W SYMMETRICAL RULE 12 4 THE CONNECTIVITY PROBLEM UNCOUPLEDSTANDARDCNNSWITHNONLINEARSYNAPTICWEIGHTS 13 1 DYNAMIC EQUATIONS AND DP PLOT STANDARDCNNSWITHDELAYEDSYNAPTICWEIGHTSANDMOTIONANALYSIS 14 1 DYNAMIC EQUATIONS 14 2 MOTION ANALYSIS – DISCRETE TIME AND CONTINUOUS TIME IMAGE ACQUISITION VISUAL MICROPROCESSORS – ANALOG AND DIGITAL VLSI IMPLEMENTATION OF THE CNN UNIVERSAL MACHINE 15 1 THE ANALOG CNN CORE 15 2 ANALOGIC CNN-UM CELL 15 3 EMULATED DIGITAL IMPLEMENTATION 15 4 THE VISUAL MICROPROCESSOR AND ITS COMPUTATIONAL INFRASTRUCTURE 15 5 COMPUTING POWER COMPARISON CNNMODELSINTHEVISUALPATHWAYANDTHE‘‘BIONICEYE” 16 1 RECEPTIVE ?ELD ORGANIZATION, SYNAPTIC WEIGHTS, AND CLONING TEMPLATE 16 2 SOME PROTOTYPE ELEMENTARY FUNCTIONS AND CNN MODELS OF THE VISUAL PATHWAY 16 3 A SIMPLE QUALITATIVE “ENGINEERING” MODEL OF A VERTEBRATE RETINA 16 4 THE “BIONIC EYE” IMPLEMENTED ON A CNN UNIVERSAL MACHINE NOTES