{"title": "A Contrast Sensitive Silicon Retina with Reciprocal Synapses", "book": "Advances in Neural Information Processing Systems", "page_first": 764, "page_last": 772, "abstract": null, "full_text": "A Contrast Sensitive Silicon Retina with \n\nReciprocal Synapses \n\nKwabena A. Boahen \n\nComputation and Neural Systems \nCalifornia Institute of Technology \n\nPasadena, CA 91125 \n\nAndreas G. Andreou \n\nElectrical and Computer Engineering \n\nJohns Hopkins University \n\nBaltimore, MD 21218 \n\nAbstract \n\nThe goal of perception is to extract invariant properties of the underly(cid:173)\ning world. By computing contrast at edges, the retina reduces incident \nlight intensities spanning twelve decades to a twentyfold variation. In one \nstroke, it solves the dynamic range problem and extracts relative reflec(cid:173)\ntivity, bringing us a step closer to the goal. We have built a contrast(cid:173)\nsensitive silicon retina that models all major synaptic interactions in the \nouter-plexiform layer of the vertebrate retina using current-mode CMOS \ncircuits: namely, reciprocal synapses between cones and horizontal cells, \nwhich produce the antagonistic center/surround receptive field, and cone \nand horizontal cell gap junctions, which determine its size. The chip has \n90 x 92 pixels on a 6.8 x 6.9mm die in 2/lm n-well technology and is fully \nfunctional. \n\n1 \n\nINTRODUCTION \n\nRetinal cones use both intracellular and extracellular mechanisms to adapt their \ngain to the input intensity level and hence remain sensitive over a large dynamic \nrange. For example, photochemical processes within the cone modulate the pho(cid:173)\nto currents while shunting inhibitory feedback from the network adjusts its mem(cid:173)\nbrane conductance. Adaptation makes the light sensitivity inversely proportional \nto the recent input level and the membrane conductance proportional to the back(cid:173)\nground intensity. As a result, the cone's membrane potential is proportional to the \nratio between the input and its spatial or temporal average, i.e. contrast. We have \n\n764 \n\n\fA Contrast Sensitive Silicon Retina with Reciprocal Synapses \n\n765 \n\ndeveloped a contrast- sensitive silicon retina using shunting inhibition. \n\nThis silicon retina is the first to include variable inter-receptor coupling, allowing \none to trade-off resolution for enhanced signal-to-noise ratio, thereby revealing \nlow-contrast stimuli in the presence of large transistor mismatch. In the vertebrate \nretina, gap junctions between photoreceptors perform this function [5]. At these \nspecialized synapses, pores in the cell membranes are juxtaposed, allowing ions \nto diffuse directly from one cell to another [6]. Thus, each receptor's response is a \nweighted average over a local region. The signal-to-noise ratio increases for features \nlarger than this region-in direct proportion to the space constant [5]. \n\nOur chip achieves a four-fold improvement in density over previous designs [2]. \nWe use innovative current-mode circuits [7] that provide very high functionality \nwhile faithfully modeling the neurocircuitry. A bipolar phototransistor models the \nphoto currents supplied by the outer-segment of the cone. We use a novel single(cid:173)\ntransistor implementation of gap junctions that exploits the physics of MaS tran(cid:173)\nsistors. Chemical synapses are also modeled very efficiently with a single device. \n\nMahowald and Mead's pioneering silicon retina [2] coded the logarithm of contrast. \nHowever, a logarithmic encoding degrades the signal-to-noise ratio because large \nsignals are compressed more than smaller ones. Mead et. al. have subsequently \nimproved this design by including network-level adaptation [4] and adaptive pho(cid:173)\ntoreceptors [3, 4] but do not implement shunting inhibition. Our silicon retina was \ndesigned to encode contrast directly using shunting inhibition. \n\nThe remainder of this paper is organized as follows. The neurocircuitry of the \ndistal retina is described in Section 2. Diffusors and the contrast-sensitive sili(cid:173)\ncon retina circuit are featured in Section 3. We show that a linearized version of \nthis circuit computes the regularized solution for edge detection. Responses from a \none-dimensional retina showing receptive field organization and contrast sensitiv(cid:173)\nity, and images from the two-dimensional chip showing spatial averaging and edge \nenhancement are presented in Section 4. Section 5 concludes the paper. \n\nCones \n\nI \n_____ X \n\nSynapses \n\n) Hog:n:tal \n\n~ Gap Junctions \n\nFigure 1: Neurocircuitry of the outer-plexiform layer. The white and black \ntriangles are excitatory and inhibitory chemical synapses, respectively. The \ngrey regions between adjacent cells are electrical gap junctions. \n\n\f766 \n\nBoahen and Andreou \n\n2 THE RETINA \n\nThe outer plexiform layer of the retina produces the well-known antagonistic cen(cid:173)\nter/surround receptive field organization first described in detail by Kuffler in the \ncat [11). The functional neurocircuitry, based on the red cone system in the tur(cid:173)\ntle [10, 8, 6], is shown in Figure 1. Cones and horizontal cells are coupled by gap \njunctions, forming two syncytia within which signals diffuse freely. The gap junc(cid:173)\ntions between horizontal cells are larger in area (larger number of elementary pores), \nso signals diffuse relatively far in the horizontal cell syncytium. On the other hand, \nsignals diffuse poorly in the cone syncytium and therefore remain relatively strong \nlocally. When light falls on a cone, its activity increases and it excites adjacent hor(cid:173)\nizontal cells which reciprocate with inhibition. Due to the way signals spread, the \nexcitation received by nearby cones is stronger than the inhibition from horizontal \ncells, producing net excitation in the center. Beyond a certain distance, however, \nthe reverse is true and so there is net inhibition in the surround. \n\nThe inhibition from horizontal cells is of the shunting kind and this gives rise to \nto contrast sensitivity. Horizontal cells depolarize the cones by closing chloride \nchannels while light hyperpolarizes them by closing sodium channels [9, I). The \ncone's membrane potential is given by \n\nv = gNaENa + gD Vnet \ngNa + gCI + gD \n\n(1) \n\nwhere the conductances are proportional to the number of channels that are open \nand voltages are referred to the reversal potential for chloride. gD and Vnet describe \nthe effect of gap junctions to neighboring cones. Since the horizontal cells pool \nsignals over a relatively large area, gCI will depend on the background intensity. \nTherefore, the membrane voltage will be proportional to the ratio between the \ninput, which determines gNa, and the background. \n\n(a) \n\n(b) \n\nFigure 2: (a) Diffusor circuit. (b) Resistor circuit. The diffusor circuit simu(cid:173)\nlates the currents in this linear resistive network. \n\n\fA Contrast Sensitive Silicon Retina with Reciprocal Synapses \n\n767 \n\n3 SILICON MODELS \n\nIn the subthreshold region of operation, a MOS transistor mimics the behavior of a \ngap junction. Current flows by diffusion: the current through the channel is linearly \nproportional to the difference in carrier concentrations across it [2]. Therefore, the \nchannel is directly analogous to a porous membrane and carrier concentration is the \nanalog of ionic species concentration. In conformity with the underlying physics, we \ncall transistors in this novel mode of operation diffusors. The gate modulates the \ncarrier concentrations at the drain and the source multiplicatively and therefore sets \nthe diffusivity. In addition to offering a compact gap junction with electronically \nadjustable 'area,' the diffusor has a large dynamic range-at least five decades. \n\nA current-mode diffusor circuit is shown in Figure 2a. The currents through the \ndiode-connected well devices Ml and M2 are proportional to the carrier concen(cid:173)\ntrations at either end of the diffusor M3 \u2022 Consequently, the diffusor current is pro(cid:173)\nportional to the current difference between Ml and M 2 \u2022 Starting with the equation \ndescribing subthreshold conduction [2, p. 36], we obtain an expression for the cur(cid:173)\nrent IpQ in terms of the currents Ip and IQ, the reference voltage Vre / and the bias \nvoltage VL : \n\n(2) \nFor simplicity, voltages and currents are in units of VT = kT/q, and 10 , the zero \nbias current, respectively; all devices are assumed to have the same Ii and 10 \u2022 The \nineffectiveness of the gate in controlling the channel potential, measured by Ii ~ 0.75, \nintrod uces a small nonideality. There is a direct analogy between this circuit and \nthe resistive circuit shown in Figure 2b for which I pQ == (Cz/Cl){IQ - Ip). The \ncurrents in these circuits are identical if Cz/Cl == exp(IiVL - Vre /) and Ii == l. \nIncreasing VL or reducing Vre / has the same effect as increasing C 2 or reducing C l . \nChemical synapses are also modeled using a single MOS transistor. Synaptic inputs \nto the turtle cone have a much higher resistance, typically O.6GO or more [1], \nthan the input conductance of a cone in the network which is 50MO or less [8]. \nThus the synaptic inputs are essentially current sources. This also holds true for \nhorizontal cells which are even more tightly coupled. Accordingly, chemical synapses \nare modeled by a MOS transistor in saturation. In this regime, it behaves like a \ncurrent source driving the postsynapse controlled by a voltage in the presynapse. \nThe same applies to the light-sensitive input supplied by the cone outer-segment; \nits peak conductance is about OAGO in the tiger salamander [9]. Therefore, the \ncone outer-segment is modeled by a bipolar phototransistor, also in saturation, \nwhich produces a current proportional to incident light intensity. \n\nShunting inhibition is not readily realized in silicon because the 'synapses' are cur(cid:173)\nrent sources. However, to first order, we achieve the same effect by modulating the \ngap junction diffusitivity gD (see Equation 1). In the silicon retina circuit, we set \nVL globally for a given diffusitivity and control Vre / locally to implement shunting \ninhibition. \n\nA one-dimensional version of the current-mode silicon retina circuit is shown in \nFigure 3. This is a direct mapping of the neurocircuitry of the outer-plexiform \nlayer (shown in Figure 1) onto silicon using one transistor per chemical synapse/gap \njunction. Devices Ml and M2 model the reciprocal synapses. M4 and Ms model \n\n\f768 \n\nBoahen and Andreou \n\nVDD \n\nI \n\nFigure 3: Current-mode Outer-Plexiform Circuit. \n\nthe gap junctions; their diffusitivities are set globally by the bias voltages VG and \nVF. The phototransistor M6 models the light-sensitive input from the cone outer \nsegment. The transistor M 3 , with a fixed gate bias Vu, is analogous to a leak in \nthe horizontal cell membrane that counterbalances synaptic input from the cone. \nThe circuit operation is as follows. The currents Ic and IH represent the responses \nof the cone and the horizontal cell, respectively. These signals are actually in \nthe post-synaptic circuit-the nodes with voltage Vc and VH correspond to the \npresynaptic signals but they encode the logarithm of the response. Increasing the \nphotocurrent will cause Vc to drop, turning on M2 and increasing its current Ic; \nthis is excitation. Ic pulls VH down, turning on Ml and increasing its current IH; \nanother excitatory effect. I H , in turn, pulls Vc up, turning off M2 and reducing its \ncurrent Ic; this is inhibition. \n\nThe diffusors in this circuit behave just like those in Figure 2 although the well \ndevices are not diode- connected. The relationship between the currents given by \nEquation 2 still holds because the voltages across the diffusor are determined by the \ncurrents through the well devices. However, the reference voltage for the diffusors \nbetween 'cones' (M4) is not fixed but depends on the 'horizontal cell' response. Since \nIH = exp(VDD - KVH ), the diffusitivity in the cone network will be proportional to \nthe horizontal cell response. This produces shunting inhibition. \n\n3.1 RELATION TO LINEAR MODELS \n\nAssuming the horizontal cell activities are locally very similar due to strong cou(cid:173)\npling, we can replace the cone network diffusitivity by g = (IH)g, where (IH) is the \nlocal average. Now we treat the diffusors between the 'cones' as if they had a fixed \n\n\fA Contrast Sensitive Silicon Retina with Reciprocal Synapses \n\n769 \n\ndiffusitivity fJ; the diffusitivity in the 'horizontal cell' network is denoted by h. Then \nthe equations describing the full two-dimensional circuit on a square grid are: \n\nI(xm,Yn) + fJ L {Ic(xi,Yj) - Ic(xm,Yn)} \n\ni = m\u00b1 1 \nj = n \u00b1 1 \n\nIu + h L {IH(xm,Yn) - IH(xi,Yj)} \n\ni= m \u00b11 \nj = n \u00b1 1 \n\n(3) \n\n(4) \n\nThis system is a special case of the dual layer outer plexiform model proposed by \nVagi [12]-we have the membrane admittances set to zero and the synaptic strengths \nset to unity. Using the second-difference approximation for the laplacian, we obtain \nthe continuous versions of these equations \n\nIH(x, y) \nIc(x,y) \n\nI(x, y) + fJV 2 Ic(x, y) \nIu - hV2 IH(x, y) \n\nwith the internode distance normalized to unity. Solving for IH(x, Y), we find \n\n)..V2V 2IH(x,y) +IH(x,y) = I(x,y) \n\n(5) \n(6) \n\n(7) \n\nThis is the biharmonic equation used in computer vision to find an optimally smooth \ninterpolating function 'IH(x,y)' for the noisy, discrete data 'I(x,y)' [13]. The co(cid:173)\nefficient).. = fJh is called the regularizing parameter; it determines the trade-off \nbetween smoothing and fitting the data. In this context, the function of the hori(cid:173)\nzontal cells is to compute a smoothed version of the image while the cones perform \nedge detection by taking the laplacian of the smoothed image as given by Equation 6. \nThe space constant of the solutions is )..1/4 [13]. This predicts that the receptive \nfield size of our retina circuit will be weakly dependent on the input intensity since \nfJ is proportional to the horizontal cell activity. \n\n4 CHIP PERFORMANCE \n\nData from the one-dimensional chip showing receptive field organization is in Fig(cid:173)\nure 4. As the 'cone' coupling increases, the gain decreases and the excitatory and \ninhibitory subregions of the receptive field become larger. Increasing the 'horizontal \ncell' coupling also enlarges the receptive field but in this case the gain increases. This \nis because stronger diffusion results in weaker signals locally and so the inhibition \ndecreases. Figure 5(a) shows the variation of receptive field size with intensity(cid:173)\nroughly doubling in size for each decade. This indicates a one-third power depen(cid:173)\ndence which is close to the theoretical prediction of one-fourth for the linear model. \nThe discrepancy is due to the body effect on transistor M2 (see Figure 3) which \nmakes the diffusor strength increase with a power of 1/ K,2. \n\nContrast sensitivity measurements are shown in Figure 5(b). The S-shaped curves \nare plots of the Michaelis-Menten equation used by physiologists to fit responses of \ncones [6]: \n\nv - V. \n\n-\n\nIn \n\nmaz In + un \n\n(8) \n\n\f770 \n\nBoahen and Andreoli \n\n55 \n\n50 \n-\n45 \n--d 35 \nii 40 \n\nv \n~ 30 \nu 25 \n~ \n.fr 20-+--~~ \n:= \no 15 \n10 \n\n~~\"In \n\n50 \n\n(a) \n\n5 \n\n10 \n\n15 \nNode Position \n\n20 \n\n25 \n\n50 \n\n45 \n\n-.40 \n-< \n535 \n..., \n~ 30 \n'\"' '\"' 825 \n..., \nE.. 20 \n..., \n:= \n015 \n\n10 \n\n50 \n\n5 \n\n10 \n\n15 \nNode Position \n\n(b) \n\n20 \n\n25 \n\nFigure 4: Receptive fields measured for 25 x 1 pixel chip; arrows indicate \nincreasing diffu80r gate voltages. The inputs were 50DA at the center and \nlOnA elsewhere, and the output current Iu was set to 20nA. (a) Increasing \ninter-receptor diffusor voltages in l5mV steps. (b) Increasing inter-horizontal \ncell diffusor voltages in 50m V steps. \n\n60 \n\n50 \n\n--\n40 \n--\n-< \n= 30 \n..., \n:= \n~ ..., \n:= \n0 \n\n20 \n\n10 \n\n0 \n\n-10 \n0 \n(a) \n\n50 \n\n40 \n\n-.30 \n--\n< \n= \n:; 20 \n..., \n~ \n:= \n010 \n\n0 \n\n5 \n\n10 \n\n15 \nN ode Position \n\n20 \n\n25 \n\n-10 \n10- 11 \n(b) \n\n10-10 \n\n10- 9 \n\nInput (A) \n\n10-8 \n\n10-7 \n\nFigure 5: (a) Dependence of receptive field on intensity; arrows indicate in(cid:173)\ncreasing intensity. Center inputs were 500pA, 5nA, 15nA, 50nA, and 500nA. \nThe background input was always one-fifth of the center input. (b) Contrast \nsensitivity measurements at two background intensity levels. Lines are fits of \nthe Michaelis-Menten equation. \n\n\f", "award": [], "sourceid": 466, "authors": [{"given_name": "Kwabena", "family_name": "Boahen", "institution": null}, {"given_name": "Andreas", "family_name": "Andreou", "institution": null}]}