{"title": "Developing Topography and Ocular Dominance Using Two aVLSI Vision Sensors and a Neurotrophic Model of Plasticity", "book": "Advances in Neural Information Processing Systems", "page_first": 1155, "page_last": 1162, "abstract": null, "full_text": "Developing Topography and Ocular Dominance\n\nUsing two aVLSI Vision Sensors and a\n\nNeurotrophic Model of Plasticity\n\nTerry Elliott\n\nDept. Electronics & Computer Science\n\nUniversity of Southampton\n\nHigh\ufb01eld\n\nSouthampton, SO17 1BJ\n\nUnited Kingdom\nte@ecs.soton.ac.uk\n\nJ\u00a8org Kramer\n\nInstitute of Neuroinformatics\n\nUniversity of Z\u00a8urich and ETH Z\u00a8urich\n\nWinterthurerstrasse 190\n\n8057 Z\u00a8urich\nSwitzerland\n\nkramer@ini.phys.ethz.ch\n\nAbstract\n\nA neurotrophic model for the co-development of topography and ocular\ndominance columns in the primary visual cortex has recently been pro-\nposed. In the present work, we test this model by driving it with the\noutput of a pair of neuronal vision sensors stimulated by disparate mov-\ning patterns. We show that the temporal correlations in the spike trains\ngenerated by the two sensors elicit the development of re\ufb01ned topogra-\nphy and ocular dominance columns, even in the presence of signi\ufb01cant\namounts of spontaneous activity and \ufb01xed-pattern noise in the sensors.\n\n1 Introduction\n\nA large body of evidence suggests that the development of the retinogeniculocortical path-\nway, which leads in higher vertebrates to the emergence of eye-speci\ufb01c laminae in the\nlateral geniculate nucleus (LGN), the formation of ocular dominance columns (ODCs) in\nthe striate cortex and the establishment of retinotopic representations in both structures, is a\ncompetitive, activity-dependent process (see Ref. [1] for a review). Experimental \ufb01ndings\nindicate that at least in the case of ODC formation, this competition may be mediated by\nretrograde neurotrophic factors (NTFs) [2]. A computational model for synaptic plasticity\nbased on this hypothesis has recently been proposed [1]. This model has successfully been\napplied to the development and re\ufb01nement of retinotopic representations in the LGN and\nstriate cortex, and to the formation of ODCs in the striate cortex due to competition be-\ntween the eye-speci\ufb01c laminae of the LGN. In this model, the activity within the afferent\ncell sheets was simulated either as interocularly uncorrelated spontaneous retinal waves or,\nas a coarse model of visually evoked activity, as interocularly correlated Gaussian noise.\nGaussian noise, however, is not a realistic model of evoked retinal activity, nor do the in-\nterocular correlations introduced adequately capture the correlations that arise due to the\nspatial disparity between the two retinas.\n\nFor this study, we tested the ability of the plasticity model to generate topographic re\ufb01ne-\nment and ODCs in response to afferent activity provided by a pair of biologically-inspired\n\n\farti\ufb01cial vision sensors. These sensors capture some of the properties of biological retinas.\nThey convert optical images into analog electrical signals and perform brightness adapta-\ntion and logarithmic contrast-encoding. Their output is encoded in asynchronous, binary\nspike trains, as provided by the retinal ganglion cells of biological retinas. Mismatch of\nprocessing elements and temporal noise are a natural by-product of biological retinas and\nsuch vision sensors alike. One goal of this work was to determine the robustness of the\nmodel towards such nonidealities. While the re\ufb01nement of topography from the temporal\ncorrelations provided by one vision sensor in response to moving stimuli has already been\nexplored [3], the present work focuses on the co-development of topography and ODCs\nin response to the correlations between the signals from two vision sensors stimulated by\ndisparate moving bars. In particular, the dependence of ODC formation on disparity and\nnoise is considered.\n\n2 Vision Sensor\n\nThe vision sensor used in the experiments is a two-dimensional array of 16 16 pixels\nfabricated with standard CMOS technology, where each pixel performs a two-way recti\ufb01ed\ntemporal high-pass \ufb01ltering operation on the incoming visual signal in the focal plane [4, 5].\nThe sensor adapts to background illuminance and responds to local positive and negative\nilluminance transients at separately coded terminals. The transients are converted into a\nstream of asynchronous binary pulses, which are multiplexed onto a common, arbitrated\naddress bus, where the address encodes the location of the sending pixel and the sign of\nthe transient. In the absence of any activity on the communication bus for a few hundred\nmilliseconds the bus address decays to zero. A block diagram of a reduced-resolution\narray of pixels with peripheral arbitration and communication circuitry is shown in Fig. 1.\nHandshaking with external data acquisition circuitry is provided via the request (\u0001\u0003\u0002\u0005\u0004\n)\nand acknowledge (\n\n) terminals.\n\n\u0006\b\u0007\u0003\t\n\nArbiter tree\n\nHandshaking\n\n0\n0\n0\n\n1\n0\n0\n\n0\n1\n0\n\n1\n1\n0\n\n0\n0\n1\n\n1\n0\n1\n\n0\n1\n1\n\n1\n1\n1\n\nF\nF\nO\n\nN\nO\n\nF\nF\nO\n\nN\nO\n\nF\nF\nO\n\nN\nO\n\nF\nF\nO\n\nN\nO\n\nX address\nY address\n\nACK\n\nREQ\n\nH\na\nn\nd\ns\nh\na\nk\nn\ng\n\ni\n\nA\nr\nb\n\ni\nt\n\ne\nr\n \nt\nr\ne\ne\n\n00\n\n01\n\n10\n\n11\n\nFigure 1: Block diagram of the sensor architecture (reduced resolution).\n\nIf the array is used for imaging purposes under constant or slowly-varying ambient light-\ning conditions, it only responds to boundaries or edges of moving objects or shadows of\nsuf\ufb01cient contrast and not to static scenes. Depending on the settings of different bias con-\ntrols the imager can be used in different modes. Separate gain controls for ON and OFF\ntransients permit the imager to respond to only one type of transient or to both types with\nadjustable weighting. Together with these gain controls, a threshold bias sets the contrast\n\n\fresponse threshold and the rate of spontaneous activity. For suf\ufb01ciently large thresholds,\nspontaneous activity is completely suppressed. Another bias control sets a refractory pe-\nriod that limits the maximum spike rate of each pixel. For short refractory periods, each\ncontrast transient at a given pixel triggers a burst of spikes; for long refractory periods, a\ntypical transient only triggers a single spike in the pixel, resulting in a very ef\ufb01cient, one-bit\nedge coding.\n\n3 Sensor-Computer Interface\n\nThe two vision sensors were coupled to a computer via two parallel ports. The handshaking\nterminals of each chip were shorted, so that the sensors could operate at their own speed\nwithout being arti\ufb01cially slowed down by the computer. This avoided the risk of overload-\ning the multiplexer and thereby distorting the data. Furthermore, this scheme was simpler\nto implement than a handshaking scheme. The lack of synchronization entailed several\nproblems: missing out on events, reading events more than once, and reading spurious zero\naddresses in the absence of recent activity in the sensors. The \ufb01rst two problems could\nsatisfactorily be solved by choosing a long refractory period, so that each moving-edge\nstimulus only evoked a single spike per pixel. For a typical stimulus this resulted in inter-\nspike intervals on the multiplexed bus of a few milliseconds, which made it unlikely that\nevents would be missed. Furthermore, the refractory period prevented any given pixel from\nspiking more than once in a row in response to a moving edge, so that multiple reads of\nthe same address were always due to the same event being read several times and therefore\ncould be discarded. The ambiguity of the (0,0) address readings, namely whether such a\nreading meant that the (0,0) pixel was active or that the address on the bus had decayed to\nzero due to lack of activity, could not be resolved. It was therefore decided to ignore the\n(0,0) address and to exclude the (0,0) cell from each map. Using this strategy it was found\nthat the data read by the computer re\ufb02ected the optical stimuli with a small error rate.\n\n4 Visual Stimulation\n\nTwo separate windows within the display of the LCD monitor of the computer used for data\nacquisition were each imaged onto one of the vision chips via a lens to provide the optical\nstimulation. The stimuli in each window consisted in eight separate sequences of images\nthat were played without interruption, each new sequence being selected randomly after the\ncompletion of the previous one. Each sequence simulated a white bar sweeping across a\nblack background. The sequences were distinguished only by the orientation and direction\nof motion of the bar, while the speed, as measured perpendicularly to the bar\u2019s orientation,\nwas constant and identical for each sequence. The bar could have four different orienta-\ntions, aligned to the rows or columns of the vision sensor or to one of the two diagonals,\nand move in either direction. The bars had a \ufb01nite width of 20 pixels on the LCD display,\ncorresponding to about 8 pixel periods on the image sensors, and they were suf\ufb01ciently\nlong entirely to \ufb01ll the \ufb01eld of view of the chips. The displays in the two windows stimu-\nlating the two chips were identical save for a \ufb01xed relative displacement between the bars\nalong the direction of motion during the entire run, simulating the disparity seen by two\neyes looking at the same object. The used displacements were 0, 10, and 15 pixels on the\nLCD display, corresponding to no disparity and disparities of 1/2 the bar width (4 sensor\npixels) and 3/4 of the bar width (6 sensor pixels), respectively. The speed of the bar was\nlargely unimportant, because the output spikes of the chip were sampled into bins of \ufb01xed\nsizes, rather than bins representing \ufb01xed time windows. The chosen white bar on a black\nbackground stimulated the vision sensor with a leading ON edge and a trailing OFF edge.\nHowever, because the spurious activity of the chip, mainly in the form of crosstalk, was\nincreased if both ON and OFF responses were activated and because we required only the\nresponse to one edge type for this work, the ON responses from the chip were suppressed.\n\n\f5 Neurotrophic Model of Plasticity\n\nis a simple model for the number of NTF receptors supported by an afferent cell, where\n\nlabel the\nlabel target cells. The two afferent sheets represent the\ntwo chips\u2019 arrays of pixels and are therefore 16  16 square arrays of cells. For convenience,\nactivity. For each time step of simulated development, we capture a \ufb01xed number of spikes\n\nLet the letters and\u0001\nlabel afferent cells within an afferent sheet, letters\u0002 and\u0003\nafferent sheets, and letters\u0004 and\u0005\n\t denote an afferent cell\u2019s\nthe target array is also a 16 16 square array of cells. Let\u0006\b\u0007\n\t\f\u000b\u000e\r , while one that has gives\u0006\u000f\u0007\n\t\f\u000b\u0011\u0010 .\nfrom each chip. A pixel that has not spiked gives\u0006\n\u0007\n\t represents the number of synapses projected from cell\nIf\u0012\u0013\u0007\nin afferent sheet\u0002\n\t evolves according to the equation\n, then\u0012\u0013\u0007\n$'&\n154\n+0/\n132\n\t\b \"!\n\u0012\u0016\u0007\n\u0006\u001d\u001c\u001e\u0006\u001f\u0007\n\u0010:9<;\n\u000b\u000e\u0019\n\u0015\u0018\u0017\n&\u0011687\n&*),+.-\n#%$,&\n#%$'&\n \"!\n\u0006(\u001c\u001e\u0006\nHere,132 and154 represent, respectively, an activity-independent and a maximum activity-\ndependent release of NTF from target cells; the parameter\u0006 a resting NTF uptake capacity\n+ a function characterising NTF diffusion between target cells, which\nby afferent cells;-\n. The function!\n\t>\u000b@?\n\t\bB\nwe take for convenience to be a Gaussian of width=\n\u0006A\u0007\n\u0012\u0013\u0007\n\t denotes average afferent activity. The parameter\u0019 sets the overall rate of development.\n\u000bD\r ,1\n\u000b\u000e\rE;IHKJ ,1\n\u000bM\u0010 .\n\u000bLF,\r and\u0006\n\rGF ,=\nConsistent with previous work [3], we set\u0019C\u000bD\rE;\nmethod [8]. For a given afferent cell, let\u0015 be the distance between some target cell and the\ntarget cell to which the afferent cell would project were topography perfect; let\u0015ENPORQ be the\n\u0015\u0018NPOTQ3U\n\rEWZ\u0010\\[\nwhereV>X8Y\ncells. The parameter\u0003\nits topographically preferred target cell, and\u0003\nprojections. Here we set\u0003\n\n \"VPW\n\u0003\u001eS\n\u000b^\u0010\nX]Y\n\r\u000fWZ\u0010Z[ determines the quality of the projections, with\u0003\n\u000b_\r giving initially completely random\n\u000b`\r\u000f;IJ ; the impact of decreasing\u0003 on the \ufb01nal structure of the\n\nThe topographic representation of an afferent sheet on the target sheet is depicted using\nstandard methods [1, 8]: the centres of mass of afferent projections to all target cells are\ncalculated, and these are then connected by lines that preserve the neighbourhood relations\namong the target cells.\n\nAlthough this model appears complex, it can be shown to be equivalent to a non-linear\nHebbian rule with competition implemented via multiplicative synaptic normalisation [6].\nFor a full discussion, derivation and justi\ufb01cation of the model, see Ref. [7].\n\nBoth afferent sheets initially project roughly equally to all cells in the target sheet.\nThe initial pattern of connectivity between the sheets is established following Goodhill\u2019s\n\nis a randomly selected number for each such pair of afferent and target\n\ngiving initially greatest topographical bias, so that an afferent cell projects maximally to\n\nto target\n\n(1)\n\n(2)\n\nmaximum such distance. Then the number of synapses projected by the afferent cell to this\ntarget cell is initially set to be proportional to\n\ntopographic map has been thoroughly explored elsewhere [3].\n\n6 Results\n\nFor each iteration step of the algorithm a \ufb01xed number of spikes was captured. The bin\nsize determines the correlation space constants of the afferent cell sheets and therefore\nin\ufb02uences the \ufb01nal quality of the topographic mapping [3]. Unless otherwise noted the bin\nsize was 32 per sensor, which corresponds to about two successive pixel rows stimulated\nby a moving contrast boundary. The presented simulations were performed for 15,000 to\n20,000 iteration steps, suf\ufb01cient for map development to be largely complete.\n\n\u0014\n\u0004\n\u0014\n\u0015\n\u0014\n\t\n\u0012\n\u0007\n\u0014\n\t\n\u001a\n\u001b\n\u0007\n\t\n\u0012\n$\n\u0014\n&\n\u001b\n$\n&\n$\n\u0014\n\u001c\n#\n\u0012\n$\n+\n&\n\u0006\n$\n&\n\u0012\n$\n+\n\u0014\n\u0007\n#\n\u0014\n\u0014\n\t\n?\n\u0006\n\u0007\n2\n4\n\u0010\n7\n\u0015\n\u001c\n\u001b\n\u0010\n7\n\u0003\n\f(a)\n\n(b)\n\n(c)\n\nFigure 2: Distribution of ODCs in the target cell sheet for different disparities between the\nbar stimuli driving the two afferent sheets. The gray level of each target cell indicates the\nrelative strengths of projections from the two afferent sheets, where \u2018black\u2019 represents one\nand \u2018white\u2019 the other afferent sheet. (a) No disparity; (b) disparity: 50% of bar width (4\nsensor pixels); (c) disparity: 75% of bar width (6 sensor pixels).\n\nSeveral runs were performed for the three different disparities of the stimuli presented to\nthe two sensors. Since the results for a given disparity were all qualitatively similar, we\nonly show the results of one representative run for each value. The distribution of the\nformed ODCs in the target sheet is shown in Fig. 2, where the shading of each neuron\nindicates the relative numbers of projections from the two afferent sheets. In the absence\nof any disparity the formation of ODCs was suppressed. The residual ocular dominance\nmodulations may be attributed to a small misalignment of the two chips with respect to\nthe display. With the introduction of a disparity a very clear structure of ODCs emerges.\nThe distribution of ODCs strongly depends on the disparity and does not vary signi\ufb01cantly\nbetween runs for a given disparity. With increasing disparity the boundaries between ODCs\nbecome more distinct [9, 10]. The obtained maps are qualitatively similar to those obtained\nwith simulated afferent inputs [1].\n\nr\ne\nw\no\nP\n\n0.3\n\n0.25\n\n0.2\n\n0.15\n\n0.1\n\n0.05\n\n0\n\n0\n\n2\n\n4\n\n6\n\n8\n\nFrequency\n\n10\n\n12\n\n14\n\n16\n\nFigure 3: Power spectra of the spatial frequency distribution of ODCs in the target cell\nsheet for different disparities and data sets. A \u2018solid\u2019 line denotes data with disparity of\n75% of bar width (6 sensor pixels); a \u2018dashed\u2019 line denotes a disparity of 50% of bar width\n(4 sensor pixels); a \u2018dotted\u2019 line denotes no disparity.\n\n\fThe power spectra obtained from two-dimensional Fourier transforms of the ODC distri-\nbutions, represented in Fig. 3, show that the spatial frequency content of the ODCs is a\nfunction of disparity, consistent with experimental \ufb01ndings in the cat [8, 11, 12, 13], and\nthat its variability between different runs of the same disparity is signi\ufb01cantly smaller than\nbetween different disparities. The principal spatial frequency along each dimension of the\ntarget sheet is mainly determined by the NTF diffusion parameter [1] and the disparity. For\nthe NTF diffusion parameter used here, it ranges between two and four cycles; increas-\ning (decreasing) the diffusion parameter decreases (increases) the spatial frequency. The\nheights of the peaks show the degree of segregation, which increases with disparity, as\nalready mentioned.\n\n(a)\n\n(b)\n\n(c)\n\nFigure 4: Topographic mapping between afferent sheets and target sheet for different dis-\nparities between the stimuli driving the two afferent sheets. The data are from the same\nruns as the ODC data of Fig. 2. (a) No disparity; (b) disparity: 50% of bar width (4 sensor\npixels); (c) disparity: 75% of bar width (6 sensor pixels).\n\nThe resulting topographic maps for the same runs are shown in Fig. 4. In the absence of\ndisparity the topographic map is almost perfect, with nearly one-to-one mapping between\nthe afferent sheets and the target sheet, apart from remaining edge effects. However, dis-\nruptions appear at ODC boundaries in the runs with disparate stimuli, these disruptions\nbecoming more distinct with increasing disparity due to the increasing sharpness of ODC\nboundaries.\n\nThe data presented above were obtained under suppression of spontaneous \ufb01ring, so that\neach pixel generated exactly one spike in response to each moving bright-to-dark contrast\nboundary with an error rate of about 5%. By turning up the spontaneous \ufb01ring rate we can\ntest the robustness of the system to increased noise levels. We set the spontaneous \ufb01ring\nrate to approximately 50%, so that roughly half of all spikes are not associated with an\nedge event. We also increased the bin size from 32 to 48 spikes per chip to compensate\nfor the reduced intraocular correlations as a result of increased noise [3]. Fig. 5 shows a\ntypical pattern of ODCs and the corresponding topographic map in the presence of 50%\nspontaneous activity. Although there are some distortions in the topographic map, in gen-\neral it compares very favourably to maps developed in the absence of spontaneous activity.\nAt an approximately 60% level of noise major disruptions in topographic map formation\nand attenuated ODC development are exhibited. Increasing the level of noise still further\ncauses a complete breakdown of topographic and ODC map formation (data not shown).\n\n\f(a)\n\n(b)\n\nFigure 5: The pattern of ODCs and the topographic map that develop in the presence of\napproximately 50% noise. (a) The OD map; (b) the topographic map. The disparity is 50%\nof the bar width (4 sensor pixels).\n\n7 Discussion\n\nThe re\ufb01nement of topography and the development of ODCs can be robustly simulated\nwith the considered hybrid system, consisting of an integrated analog visual sensing system\nthat captures some of the key features of retinal processing and a mathematical model\nof activity-dependent synaptic competition. Despite the different structure of the input\nstimuli and the different noise characteristics of the real sensors from those used in the\npure simulations [1], the results are comparable.\n\nSeveral parameters of the vision sensors, such as refractory period and spontaneous \ufb01ring\nrate, can be continuously varied with input bias voltages. This facilitates the evaluation of\nthe performance of the model under different input conditions. The sensors were operated\nat long refractory periods, so that each pixel responded with a single spike to a contrast\nboundary moving across it. In this non-bursting mode the coding of the stimulus is very\nsparse, which makes the topographic re\ufb01nement process more ef\ufb01cient [3].\n\nThe noise induced by the vision sensors manifests itself in occasionally missing responses\nof some pixels to a moving edge, in temporal jitter and a tunable level of spontaneous ac-\ntivity. With an optimal suppression of spontaneous \ufb01ring, the error rate (number of missed\nand spurious events divided by total number of events) can be reduced to approximately\n5%. Increased spontaneous activity levels show a strongly anisotropic distribution across\nthe sensing arrays because of the inherent \ufb01xed-pattern noise present in the integrated sen-\nsors due to random mismatches in the fabricated circuits. This type of inhomogeneity has\nnot been modeled in previous work. Spontaneous activity and mismatches between cells\nwith the same functional role are prominent features of biological neural systems and bio-\nlogical information processing systems therefore have to deal with these nonidealities. The\nplasticity algorithm proves to be suf\ufb01ciently robust with respect to these types of noise.\n\nThe developed ODC and topographic maps depend quite strongly on the disparity between\nthe two sensors. At zero disparity, the formation of ODCs is practically suppressed and\ntopography becomes very smooth. As the disparity increases, the period of the resulting\nODCs increases, consistent with experimental results in the cat [8, 11, 12, 13], and, as\nexpected, the degree of segregation also increases [9, 10]. In the presence of high levels\nof spontaneous activity in the afferent pathways, with as much as half of all spikes not\nbeing stimulus\u2013related, the maps continue to exhibit well developed ODCs and topography.\nAlthough there are indications of distortions in the topographic maps in the presence of\n\n\fapproximately 50% spontaneous activity, the maps remain globally well structured. As\nspontaneous activity is increased further, map development becomes increasingly disrupted\nuntil it breaks down completely.\n\n8 Conclusions\n\nWe examined the re\ufb01nement of topographic mappings and the formation of ocular dom-\ninance columns by coupling a pair of integrated vision sensors to a neurotrophic model\nof synaptic plasticity. We have shown that the afferent input from real sensors looking at\nmoving bar stimuli yields similar results as simulated partially randomized input and that\nthese results are insensitive to the presence of signi\ufb01cant noise levels.\n\nAcknowledgments\n\nTragically, J\u00a8org Kramer died in July, 2002. TE dedicates this work to his memory.\n\nTE thanks the Royal Society for the support of a University Research Fellowship. JK was supported\nin part by the Swiss National Foundation Research SPP grant. We thank David Lawrence of the\nInstitute of Neuroinformatics for his invaluable help with interfacing the chip to the PC.\n\nReferences\n[1] T. Elliott and N. R. Shadbolt, \u201cA neurotrophic model of the development of the retinogeniculo-\ncortical pathway induced by spontaneous retinal waves,\u201d Journal of Neuroscience, vol. 19, pp.\n7951\u20137970, 1999.\n\n[2] A.K. McAllister, L.C. Katz, and D.C. Lo, \u201cNeurotrophins and synaptic plasticity,\u201d Annual\n\nReview of Neuroscience, vol. 22, pp. 295\u2013318, 1999.\n\n[3] T. Elliott and J. Kramer, \u201cCoupling an aVLSI neuromorphic vision chip to a neurotrophic\nmodel of synaptic plasticity: the development of topography,\u201d Neural Computation, vol. 14,\npp. 2353\u20132370, 2002.\n\n[4] J. Kramer, \u201cAn integrated optical transient sensor,\u201d IEEE Trans. Circuits and Systems II: Analog\n\nand Digital Signal Processing, 2002, submitted.\n\n[5] J. 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Tumosa, \u201cAlternating monocular exposure increases the spacing of ocular-\n\nity domains in area 17 of cats,\u201d Visual Neuroscience, vol. 14, pp. 929\u2013938, 1997.\n\n\f", "award": [], "sourceid": 2326, "authors": [{"given_name": "Terry", "family_name": "Elliott", "institution": null}, {"given_name": "J\u00f6rg", "family_name": "Kramer", "institution": null}]}