[机械模具数控自动化专业毕业设计外文文献及翻译]【期刊】PCNN模型及其应用-外文文献

480 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 10, NO. 3, MAY 1999PCNN Models and ApplicationsJohn L. Johnson and Mary Lou Padgett, Member, IEEEAbstractThe pulse coupled neural network (PCNN) modelsare described. The linking field modulation term is shown to bea universal feature of any biologically grounded dendritic model.Applications and implementations of PCNNs are reviewed. Ap-plication based variations and simplifications are summarized.The PCNN image decomposition (factoring) model is describedin new detail.Index TermsDendritic model, PCNN factoring, pulse coupledneural networks.I. INTRODUCTIONTHE STUDY of the electrochemical dynamics of neurons,from the seminal work of Hodgkin and Huxley 1 tothe most recent work on internal dendritic pulse generation2, has led to increasingly accurate and more detailed models3. The transcription of the biological models to algorithmicmodels has led to an extensive literature of data processingsystems, most of which have been primarily concerned withutilizing adaptive algorithms for data classifiers. The studyof systems of pulsed neurons as dynamical networks, withand without adaptation, is more recent. One of the earlypapers 4 described a dynamic linking architecture based onan excitatory-inhibitory pair of coupled oscillators. Researchinto more biologically grounded pulsed network dynamics wasspurred by the experimental observations of synchronous pulsebursts in the cat visual cortex 5, 6.The 1990 Eckhorn linking field network 7 was intro-duced as a phenomenological model of a system exhibitingsynchronous pulse bursts. It used a pulse generator calleda neuromime 8, a modulatory coupling term, and synapticconnections modeled as leaky capacitors. Its central newconcept was the introduction of a secondary receptive field,the linking field, whose integrated input modulated the primaryfeeding receptive field input by means of an internal cellularcircuit. It provided a simple, effective simulation tool forstudying synchronous pulse dynamics in networks, and wassoon recognized as having significant applications in imageprocessing 911. A number of modifications and variationswere introduced to the linking field model in order to tailorits performance as image processing algorithms, and theseManuscript received November 8, 1997; revised December 27, 1998. Thiswork was supported in part by AF under Contract 8530-94-1-0002, AFOSRunder Contract SREP F9620-C-0063, and NCCOSC under Contract N66001-97-C-8612.J. L. Johnson is with the U.S. Army, MICOM, Photonics and OpticalScience, Redstone Arsenal, AL 35898-5248 USA.M. L. Padgett can be contacted at Publisher Item Identifier S 1045-9227(99)03191-4.became known collectively as pulse coupled neural networks,or PCNNs 12. The linking modulation was shown to enablehigher order networks 13 and a new form of image fusion(Broussard and Rodgers, this issue), and further to allow theconstruction of arbitrarily complex fuzzy logical rule systemson a single neuron 14.The two fundamental properties of the PCNN are theuse of pulses and pulse products. The latter property comesdirectly from the original linking field model as the basiccoupling mechanism. It is an asymmetric modulation of oneneuronal input by another. The choice of a modulatory cou-pling rather than the more-common additive coupling has theadvantage that a neuron with no primary input can not beactivated by the coupling input, a feature that is importantin image processing. While additive coupling is a primarybiologically grounded mechanism in that synaptic currentsare in parallel and thus additive, there is some experimentalevidence that pulse products and temporal encoding of spatialinformation can be of equal importance 15. A candidatemechanism yielding multiplicative coupling is derived belowfrom the dendritic computational dynamics of a compartmentalmodel.Section II begins with a detailed inspection of a compart-mental model having two inputs, the minimum number fora PCNN. It shows the modulatory coupling of the inputs,and how even very simple model cells can provide an elegantmeans of uniquely encoding information as time signals. Thepulse generator mechanism is then discussed, and it is shownthat there is a significant difference between the neuromimeand the integrate-and-fire (I&F) models in the generationof pulse bursts. Section III reviews the basic linking fieldmodel on which most PCNNs are based. Multiple pulseand single pulse regimes are described, and a number ofuseful aspects of PCNNs given. These include logical rules,image fusion, scale definition by linking strength, iconic timesignals, PCNN histograms, and chaotic structure. Section IVis a short review that describes PCNN techniques and givesdefinitions of different variations, and Section V is devotedto PCNN applications and implementations. Because PCNNsare generally used as nonadaptive processors, the connectivityrequirements are low, and it is practical to build them as high-speed electronic chips. Section VI, an algorithmic descriptionof PCNNs, is included for those interested in developing sim-ple software code versions. It shows the major simplificationsand shortcuts used in many image processing applications. Thepseudocode presented includes new details for the factoringmodel. Section VII gives examples of the application of thesevariations, and features PCNN factoring.10459227/99$10.00 1999 IEEEJOHNSON AND PADGETT: PCNN MODELS AND APPLICATIONS 481(a)(b)Fig. 1. The two-compartment model neuron: (a) compartmental model and (b) equivalent circuit.II. THE PARTS OF THE BASIC MODEL,ITSORIGIN, AND RELATION TO BIOLOGICAL MODELSA. Pulse Products in a Dendritic ModelThe purpose of this analysis is to show that the shunting-induced modulatory coupling is a generic and pervasive bi-ological pulse-coupling mechanism. It is not the exclusivemechanism for pulse products. A nonlinear enhancement effectamong closely spaced synaptic inputs along a dendrite hasrecently been experimentally confirmed. It is one of severalactive-channel interactions in which the conductance has avoltage dependence. It provides a multiplicative effect amonginputs to complex cells, and is related to the sodium spikesin active dendrites 16. Like the shunting effect, it allowsfor additive as well as multiplicative coupling. Rather thanchoosing either additive coupling or multiplicative coupling,nature has chosen both.A major distinction between PCNNs and the standardHodgkinHuxley 1 neuronal model is in the choice of thepulse generator. The neuromime used in the original Eckhornmodel is very similar in overall performance to the biologicalintegrate-and-fire pulse generator, but it has some fundamentaldifferences. These differences are discussed later in moredetail.The PCNN is based on having at least two distinct in-puts. A compartmental model cell 17 consisting of a singledendrite compartment and a second compartment containingthe integrate-and-fire pulse generator, with a single synapticinput to each compartment, provides the right combination ofmathematical transparency and adequacy. This model containsnumerous simplifications and approximations of the morebiologically accurate models, and they in turn are incompletemodels of real neurons 3. Some of the factors not consideredhere are multiple ionic synaptic channels, active channels,cellular aging, long and short term adaptation, continuousdendritic geometries and branches, refractory period (exceptas an add-on term), and temperature effects.Each compartment is a leaky capacitor. The leakage hasthree major parts: intrinsic, synaptic, and active. Only the firsttwo are used here. A synapse can receive either a pulse inputor a steady-state input. The somatic compartment generatesthe output pulse. The compartments are connected by a seriesresistance. There is no axon compartment. Fig. 1(a) shows thecell body and the dendrite compartments, and their synapticinput conductances labeled and , respectively. Fig. 1(b)shows the equivalent circuit. The box labeled representsthe pulse generator. is the resting potential inside the cell,nominally about 70 mV, is the synaptic back poten-tial, typically 20 mV, , and are the compartmentalcapacitances, on the order of nanoFarads, while , ,and are the membrane intrinsic leakage conductances andthe longitudinal conductance, respectively. The synaptic andintrinsic conductances are of the order of megaMhos, whilethe longitudinal conductance can range from ten to a thousandtimes larger 18.The compartmental voltages are described by the relation(1)whereandSynaptic conductance waveforms are often modeled as thealpha function 19 , where . This isrepresentative of an input pulse. The conductance can haveother forms as well. It can be a constant, a square pulse, ora delta function. Likewise, the output pulse function canhave several forms. The step function Stepis useful for constant-step discrete-time simulations, formingthe pulse in two time steps. is the threshold for pulse482 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 10, NO. 3, MAY 1999initiation. A variation is to use the step function as a gate fora pulse train which is set at the maximum allowed pulse rate,as suggested by Eckhorn 7. A third representation is to usea sum of delta functions taken over the firing times, , whichare defined as the times when exceeds(2)The modulation terms due to the synaptic shunting are mosteasily seen in the steady-state case where the internal activityhas reached an equilibrium level below the threshold for firing.For constant inputs and , and no pulses ,the modulation products are immediately obtained from thenullcline ( ) of (1) which is of the formwhereThis is a saturable activity function. It has an intrinsic leakageterm, linear terms, and a product term. Because is negativeand is positive, the leakage term is negative and sets athreshold for firing. Since , the coefficient of thelinear linking term in the numerator is positive, as are theremaining terms. In size, the conductance dominates theintrinsic and input conductances. This makes the constant andlinear terms of the numerator and the denominator all of thesame order of magnitude, while the product coefficients arein the ratio of the leakage conductance to the longitudinalconductance. These correspond to the linking strength factor, and are of the order of 0.1 to 0.001 or less. It is seen that thesynaptic shunting terms lead to both linear and multiplicativeterms for the internal activity, and that the latter can be ofa significant strength. Linking strength factors of 0.1 give asubstantial modification to a pulse activity pattern 20. Themodulation is symmetric in the inputs (unlike that of theoriginal linking field model), and the activity will saturate forlarge inputs.The nullcline of (1) for a general dendritic system withnumerous inputs, many branches, channels, and trees willlikewise give a combination of linear and multiplicative termsin a saturable ratio. However, it will be much more complex.It will contain all possible combinations of products and sums,and in fact will comprise a general higher order model neuronwhose order equals the total number of inputs to the entireneuron, which can be several thousand inputs. The highest-level products will be attenuated due to the separation of themost distant synapses on the dendritic tree, with modulationsamong local groups being more pronounced.Now consider the case for which the cell generates pulses, still with constant inputs and . The solutionis easily obtained by diagonalization of the 2 2 matrix .The diagonalizing transform matrix for the general 2 2matrix iswhereNote that ,so .The solution of (1) is then(3)where the time dependence of is in the pulse functionof (2). and are the eigenvalues of the diagonalizedmatrix.Despite the simplicity of the two-compartment, two-inputsystem, it is not usually solved analytically. Bressloff and Tay-lor 21 review the general problem, including shunting effects,and an iterative approach involving time-ordered operators isgiven. In the example section, however, only a one-input, two-compartment nonshunting solution is presented. Accordingly,the existence of the modulation products is not discussed there,nor by Bressloff 22, an extension of the latter reference21. Rall 17 and others 16, 18 place the emphasis onnumerical methods. For this case in which modulation productsare obtained, the analytical solution is again ignored. This isdespite the experimental evidence 15 for products of pulsetrain time signals.These modulation products provide the critical function ofthe logical AND conjunction, thus allowing the constructionof large, complex logical rule systems on a single neuron andthe biological implementation of sigma-pi nets, higher ordernets, and the PCNN nets.The internal activity due to the Eckhorn linking fieldsmodulatory coupling is seen to be an asymmetric version ofthe steady-state internal activity of the standard compartmentalmodel, thus providing a basic biological grounding of thelinking field and all the PCNNs adapted from it. It furthersupports the experimental findings of McClurkin et al. 15,by showing that there is an explicit generic mechanism forforming products of input time signals in the standard cellmodel.Even the restricted case of constant inputs shows someinteresting dynamical properties. This case would correspondto the retinal ganglion cells that receive nonpulsed inputs fromthe earlier retinal layers, the inputs being roughly constantduring periods of visual fixation. Only the outline of thealgebraic solution is given, as the details, while straightforward, are tedious and lengthy.Integrate (3) from just after the th pulse to just afterthe th pulse. Apply the condition that the voltage inJOHNSON AND PADGETT: PCNN MODELS AND APPLICATIONS 483compartment 1 just after reset is at its minimum .This gives two distinct equations for the voltage in thedendrite compartment, each a function of the inputs and ,and of the th interspike time interval .One equation is at time ; the other is at timeThese can be combined to give each interspike time intervalin terms of the inputs, cellular geometry and electrochemicalstructure, and the previous interspike time interval(4)For the conductance and voltage value regimes given earlier,these functions are approximatelyandwhere the -functions are terms involving the inputs and thecompartmental geometry. Fig. 2 illustrates the possible cases.For case (a), if , the curves do notintersect and there is only one pulse. For cases (b) and (c),if the curves intersect. In that case, iffurther (b) , the pulse sequence can reach apoint attractor, a limit cycle, or can terminate after a finitenumber of pulses, while if (c) , the sequencewill be either a point attractor or a limit cycle.Consideration of this recurrence relation shows that evenfor constant inputs the cell will generate a complex outputspike train pattern with information encoded in the interspikestructure. This agrees with the findings of McClurkin etal. 15that each color hue has its own pulse time signal structure,an experimental result that is difficult to explain otherwise.Further, the time signal also contains information about thestructure of the cell from which it originated, information thatcan be viewed as an identifying code for that cell or cell type.Finally, since as noted by Bressloff 22 the cellular responseis the temporal convolution of the input time signal and thecells response function it is an inescapable conclusion thatreal neurons have the capability to generate, transmit, receive,and respond to information-bearing time signals.B. Pulse Generators: The Neuromime VersusIntegrate and Fire (I&F)1) Coupled Oscillators: These are more general and com-plex oscillatory signal generators that contain the other twoas special cases. The output signals can be nearly pure har-monic functions, skewed periodic functions that are boundary-matched exponential decays/excitation, or sharp, spike-likefunctions, all depending on the choice of the model parametersand response functions. They consist of two “cells,” eachhaving its own response function. The first cell receives thesystem input, then transmits its output to the second cell whichin turn sends a signal back to the first cell. Generally, thesecond cell inhibits the first cell, and has a slower, longer-lasting effect on it than the first cell had on it.(a)(b)(c)Fig. 2. Recursive relationship of successive pulse periods for a single neuronwith constant inputs. (a) Null case. (b) and (c) The pulse periods can approacha point attractor, a limit cycle, or terminate after a finite number of pulsesdepending on the values of the cell structural parameters.If the response of the first cell is assumed to be instantaneous(a step function) and the response of the second cell is madeto be that of a leaky capacitor, the system is a neuromime.Similarly, a coupled oscillator with a linear excitatory rateto a leaky capacitor for the first cell and a fast step-likeinhibitory output from the second cell is an integrate-and-fire-pulse generator.A coupled oscillator signal generator, installed inside amodel neuron, can exhibit coupled synchronous activity. Itis more complex and general than the synchronizations ofthe other pulse generators. For example, it can be perturbedto oscillate about its synchronous lock-in phase point with asimilar coupled-oscillator signal, while a neuromime cannot(once two neuromimes with the same frequency lock together,they cannot be perturbed by low-level fluctuations).2) The Neuromime: The neuromime is described by theinteraction of an inhibitory threshold and an excitatory stepfunctionstep484 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 10, NO. 3, MAY 1999For an input, , the neuromime produces pulses at a rate(5)Strictly speaking, it is a second-order system with an implicitlyunders