{"title": "A Neuromorphic Multi-chip Model of a Disparity Selective Complex Cell", "book": "Advances in Neural Information Processing Systems", "page_first": 1051, "page_last": 1058, "abstract": "", "full_text": "A Neuromorphic Multi-chip Model of a Disparity \n\nSelective Complex Cell\n\nEric K. C. Tsang and Bertram E. Shi\n\nDept. of Electrical and Electronic Engineering\n\nHong Kong University of Science and Technology\n\nKowloon, HONG KONG SAR\n\n{eeeric,eebert}@ust.hk\n\nAbstract\n\nThe relative depth of objects causes small shifts in the left and right ret-\ninal positions of these objects, called binocular disparity. Here, we\ndescribe a neuromorphic implementation of a disparity selective com-\nplex cell using the binocular energy model, which has been proposed to\nmodel the response of disparity selective cells in the visual cortex. Our\nsystem consists of two silicon chips containing spiking neurons with\nmonocular Gabor-type spatial receptive fields (RF) and circuits that\ncombine the spike outputs to compute a disparity selective complex cell\nresponse. The disparity selectivity of the cell can be adjusted by both\nposition and phase shifts between the monocular RF profiles, which are\nboth used in biology. Our neuromorphic system performs better with\nphase encoding, because the relative responses of neurons tuned to dif-\nferent disparities by phase shifts are better matched than the responses\nof neurons tuned by position shifts.\n\n1 Introduction\n\nThe accurate perception of the relative depth of objects enables both biological organisms\nand artificial autonomous systems to interact successfully with their environment. Binocu-\nlar disparity, the positional shift between corresponding points in two eyes or cameras\ncaused by the difference in their vantage points, is one important cue that can be used to\ninfer depth. \n\nIn the mammalian visual system, neurons in the visual cortex combine signals from the\nleft and right eyes to generate responses selective for a particular disparity [1]. Ohzawa et\nal.[2] proposed the binocular energy model to explain the responses of binocular complex\ncells in the cat visual cortex, and found that the predictions of this model are in good\nagreement with measured data. This model also matches data from the macaque [3].\n\nIn the energy model, a neuron achieves its particular disparity tuning by either a position\nor a phase shift between its monocular receptive field (RF) profiles for the left and right\neyes. Based on an analysis of a population of binocular cells, Anzai et al. [4] suggest that\nthe cat primarily encodes disparity via a phase shift, although position shifts may play a\nlarger role at higher spatial frequencies. Computational studies show that it is possible to\nestimate disparity from the relative responses of model complex cells tuned to different\ndisparities [5][6].\n\n\fThis paper describes a neuromorphic implementation of disparity tuned neurons con-\nstructed according to the binocular energy model. Section 2 reviews the binocular energy\nmodel and the encoding of disparity by position and phase shifts. Section 3 describes our\nimplementation. Section 4 presents measured results from the system illustrating better\nperformance for neurons tuned by phase than by position. This preference arises because\nthe position-tuned neurons are more sensitive to the mismatch in the circuits on the Gabor-\ntype filter chip than the phase-tuned neurons. We have characterized the mismatch on the\nchip, as well as its effect on the complex cell outputs, and found that the phase model least\nsensitive to the parameters that vary most. Section 5 summarizes our results.\n\n2 The Binocular Energy Model\n\nOhzawa et al. [2] proposed the binocular energy model to explain the response of binocu-\nlar complex cells measured in the cat. Anzai et al. further refined the model in a series of\npapers [4][7][8]. In this model, the response of a binocular complex cell is the linear com-\nbination of the outputs of four binocular simple cells, as shown in Figure 1. The response\nof a binocular simple cell is computed by applying a linear binocular filter to the input\n)2\nfrom the two eyes, followed by a half squaring nonlinearity: \n is the positive half-wave rectifying nonlinearity. The linear bin-\nwhere \nocular filter output is the sum of two monocular filter outputs\n,\n\n,\n(\nb xR xL\n\nmax b 0,{\n\n) +\nL\n\nb +\n\n,\nR\n\nrs\n\n\u03c6\n\n\u03c6\n\n\u03c6\n\n\u03c6\n\n\u03c6\n\n\u03c6\n\n=\n\n=\n\n}\n\n(\n\n,\n\n,\n\n,\n\n,\n\n(\nb cR cL\n\n+\n) m cL\nwhere the monocular filters linearly combine image intensity, \nfield profile\n\n)\nL\n\n=\n\nR\n\n(\n\n,\nm cR\n\n(\n\n,\nR IR\n\n,\n)\nL IL\nI x( )\n\n, with a Gabor receptive\n\n(1)\n\nm c \u03c6 I\n,\n\n(\n\n,\n\n)\n\ng x c \u03c6\n(\n)\n\n,\n\n,\n\n=\n\n=\n\n\u03a3\n\n,\n\n(\n\n,\nxg x c \u03c6\n1\nc\u2013(\n--- x\n2\n\n\u2013\n\n\u03bae\n\n)I x( )\n\n)TC 1\u2013\n\nc\u2013(\nx\n\n)\n\ncos\n\n(\n\n\u2126T x\n\nc\u2013(\n\n)\n\n\u03c6+\n\n)\n\nx ZZ2\u2208\n\n indexes pixel position. The subscripts R and L denote parameters or image\nwhere \n\u2126 IR2\u2208\nintensities from the right or left eye. The parameters \n control the\n\u03ba\n controls the gain. These parameters\nspatial frequency and bandwidth of the filter and \nare assumed to be the same in all of the simple cells that make up a complex cell. How-\nIR2\u2208\nIR\u2208\never, the center position, \n vary, both between the two eyes\nand among the four simple cells. \n\n and the phase \n\nC IR2\n\n and \n\n2\u00d7\n\n\u2208\n\n\u03c6\n\nc\n\nLinear\n\nBinocular\n\nFilter\n\nEven\n\nOdd\n\nLeft\n\nRight\n\nHalf-squaring\n\n\u03a3\n\n\u03a3\n\n\u03a3\n\n\u03a3\n\n+\n\n+\n\n+\n\n+\n\n+\n+\n\n+\n+\n\nCx\n\n+\n\n+\n\n+\n\n+\n\nBinocular\n\nComplex Cell\n\nBinocular Simple Cells\n\nFig. 1: Binocular energy model of a complex cell. \n\n\fWhile the response of simple cells depends heavily upon the stimulus phase and contrast,\nthe response of complex cells is largely independent of the phase and contrast. The binoc-\nular energy model posits that complex cells achieve this invariance by linearly combining\nthe outputs of four simple cell responses whose binocular filters are in quadrature phase,\nbeing identical except that they differ in phase by \n. Because filters that differ in phase\nby \n are identical except for a change in sign, we only require two unique binocular fil-\nters, the four required simple cell outputs being obtained by positive and negative half\nsquaring their outputs.\n\n\u03c0 2\u2044\n\n\u03c0\n\nComplex cells constructed according to the binocular energy model respond to disparities\nin the direction orthogonal to their preferred orientation. Their disparity tuning in this\ndirection depends upon the relative center positions and the relative phases of the monoc-\nular filters. A binocular complex cell whose monocular filters are shifted by\n\u2206c\n and \n will respond maximally for an input disparity\ncR cL\u2013\n=\n\u2206c \u2206\u03c6 \u2126\u2044\n\u2248\n). Disparity is encoded by a position shift if\n\u2013\nDpref\n\u2206c\n\u2206\u03c6\n0\u2260\n and \n. The\n0=\n0\u2260\ncell uses a hybrid encoding if both \n. Phase encoding and position\n\u2206c\nencoding are equivalent for the zero disparity tuned cell (\n\n\u2206\u03c6\n (i.e. \n. Disparity is encoded by a phase shift if \n\n\u03c6\n\u03c6\n=\nL\u2013\nR\n\u2248\nIR x( )\nIL x Dpref\n0\u2260\n\n\u2013(\n\u2206c\n\n and \n\n0=\n\n).\n\n0=\n\n and \n\n0=\n\n and \n\n\u2206\u03c6\n\n\u2206c\n\n\u2206\u03c6\n\n0\u2260\n\n)\n\n\u2206\u03c6\n\n3 Neuromorphic Implementation\n\nFigure 2 shows a block diagram of our binocular cell system, which uses a combination of\nanalog and digital processing. At this time, we use a pattern generator to supply left and\nright eye input. This gives us precise electronic control over spatial shift between the left\nand right eye inputs to the orientation selective neurons. We plan to replace the pattern\ngenerator with silicon retinae in the future. The left and right eye inputs are processed by\ntwo Gabor-type chips that contain retinotopic arrays of spiking neuron circuits whose spa-\ntial RF profiles are even and odd symmetric Gabor-type functions. The address filters\nextract spikes from four neurons in each chip whose output spike rates represent the posi-\ntive and negative components of the odd and even symmetric filters centered at a desired\nretinal location. These spike trains are combined in the binocular combination block to\nimplement the summation in (1). The complex cell computation block performs the half\nsquaring nonlinearity and linear summation. In the following, we detail the design of the\nmajor building blocks. \n\nPattern\n\nGenerator\n\nMixed A/D\nAER chips\n\nXilinx CPLDs\n\nMCU\n\nGabor\nChip\n\nAddress\n\nFilter\n\nLeft Eye\n\nLeft Retina Address\n\nGabor\nChip\n\nAddress\n\nFilter\n\nRight Eye\n\nRight Retina Address\n\ne+\ne-\no+\no-\n\ne+\ne-\no+\no-\n\nBinocular\n\nCombination\n\nB1+\nB1-\n\nB2+\nB2-\n\nComplex Cell\nComputation\n\nComplex Cell\n\nResponse\n\nPhase Encoding Selection\n\nFig. 2: System block diagram of a neuromorphic complex cell. The opposite direction\narrows represent the AER handshaking protocol. The three groups of four parallel arrows\nrepresent spiking channels. The labels \u201ce/o\u201d and \u201c+/-\u201d represent EVEN/ODD and ON/\nOFF. The top labels indicate the type of hardware used to implement each stage.\n\n\f3.1 Gabor-type filtering chip\n\n\u03c6\n\nIL\n\nIR\n\n or \n\n0=\n\n,\nL IL\n\n,\nm cL\n\n), each chip computes outputs (\n\n filter as the EVEN symmetric filter and the \n\nImages from each eye are passed to a Gabor-type filtering chip [9] that implements the\nmonocular filtering required by the simple cells. Given a spike rate encoded 32 x 64 pixel\n\u03c6\n,\n,\n) corre-\nimage (\n(\n)\nm cR\nR IR\n\u03c0 2\u2044\u2013\n. All filters are\nsponding to a 32 x 64 array of center positions and two phases, 0 and \ndesigned to have the same gain, spatial frequency tuning and bandwidth. We refer to the\n\u03c6\n filter as the ODD symmet-\nric filter. Figure 3 shows the RF profile of the EVEN and ODD filters, which differ from a\nGabor function because the function that modulates the cosine function is not a Gaussian;\nit decays faster at the origin and slower at the tails. This difference should not affect the\nresulting binocular complex cell responses significantly. Qian and Zhu [5] show that the\nbinocular complex cell responses in the energy model are insensitive to the exact shape of\nthe modulating envelope.\n\n\u03c0 2\u2044\u2013=\n\n or \n\n)\n\n(\n\n\u03c6\n\nThe positive and negative components of each filter output are represented by a spike rate\non separate ON and OFF channels. For example, for the right eye at center position \n,\ncR\nand the EVEN-OFF spike rate\nthe EVEN-ON spike rate is proportional to \nto \n. Spikes are encoded on a single asynchronous digital bus using the\naddress event representation (AER) communication protocol. The AER protocol signals\nthe occurrence of a spike in the array by placing an address identifying the cell that spiked\non the bus [10]. \n\nm cR 0 IR\n\ncR 0 IR\n\nm\u2013\n\n) +\n\n) +\n\n(\n\n(\n\n,\n\n,\n\n,\n\n,\n\nFig. 3: The measured RF profile of the EVEN and ODD symmetric filters at the center\npixel.\n\n3.2 AER Address Filter\n\nEach AER address filter extracts only those spikes corresponding to the four neurons\nwhose RF profiles are centered at a desired retinal location and demultiplexes the spikes\nas voltage pulses on four separate wires. In our addressing scheme, every neuron is\nassigned a unique X (column) and Y (row) address. As addresses appear on the AER bus,\ntwo latches latch the row and column address of each spike, which are compared with the\nrow and column address of the desired retinal location, which is encoded on bits 1-6 of the\naddress. Bit 0 (the LSB) encodes the type of filter: EVEN/ODD on the row address and\nON/OFF on the column address. Once the filter detects a spike from the desired retinal\nlocation, it generates a voltage pulse which is demultiplexed onto one of four output lines,\ndepending upon the LSB of the latched row and column address.\n\nTo avoid losing events, we minimize the time the AER address filter requires to process\neach address by implementing it using a Xilinx XC9500 series Complex Programmable\nLogic Device (CPLD). We chose this series because of its speed and flexibility. The block\ndelay in each macrocell is 7ns. The series supports in system programming, enabling rapid\ndebugging during system design. Because the AER protocol is asynchronous, we paid par-\nticular attention to the timing in the signal path to ensure that addresses are latched cor-\nrectly and to avoid glitches that could be interpreted as output spikes.\n\n\f3.3 Binocular combination block\n\n)\n\n(\n\n0=\n\n\u2206c\n\nThe binocular combination block combines eight spike trains to implement the summation\noperation in Eq. (1) for two phase quadrature binocular filters. To compute the two binoc-\nular filter outputs required for a zero disparity tuned cell, we first set the AER address fil-\nters so that they extract spikes from monocular neurons with the same RF centers in the\nleft and right eyes \n. To compute the output of the first binocular filter B1, the\nbinocular combination block sums the outputs of the left and right eye EVEN filters by\nmerging spikes from the left and right EVEN-ON channels onto a positive output line,\nB1+ (shown in Fig. 2), and merging spikes from the left and right EVEN-OFF channels\nonto a negative output line, B1-. The difference between the spike rates on B1+ and B1-\nencodes the B1 filter output. However, the B1+ and B1- spike rates do not represent the\nON (positive half-wave rectified) and OFF (negative half-wave rectified) components of\nthe binocular filter outputs, since they may both be non-zero at the same time. To compute\nthe output of the second filter, B2, the binocular combination block merges spikes from\nthe left and right ODD channels similarly. \n\n\u2206c\n\n0\u2260\n\nThe system can also implement binocular filter outputs for neurons tuned to non-zero dis-\nparities. For position encoding, we change the relative addresses selected by the AER\naddress filters to set \n, but leave the binocular combination block unchanged. If we\nfix the center location of the right eye RF to the center column of the chip (32), we can\ndetect position disparities between -31 and 32 in unit pixel steps. For phase encoding, we\nleave the AER address filters unchanged and alter the routing in the binocular combina-\ntion block. Because the RF profiles of the Gabor-type chips have two phase values, alter-\ning the routing as shown in Table 1 results in four distinct binocular filters with monocular\nfilter phase shifts of \n, which correspond to the tuned far, tuned\nexcitatory, tuned near and tuned inhibitory disparity cells identified by Poggio et al. [11] \n\n0 \u03c0 2\u2044\n,\n\n\u03c0 2\u2044\u2013\n\n and \n\n\u2206\u03c6\n\n\u03c0\n\n=\n\n,\n\nThe binocular combination block uses the same type of Xilinx CPLD as the AER filter.\nInputs control the monocular phase shift of the resulting binocular filter by modifying the\nrouting. For simplicity, we implement the merge using inclusive OR gates without arbitra-\ntion. Although simultaneous spikes on the left and right channels will be merged into a\nsingle spike, the probability that this will happen is negligible, since the width of the volt-\nage pulse that represents each spike (~32ns) is much smaller than the inter-spike intervals,\nwhich are on the order of milliseconds. \n\nTable 1: Signal combinations for phase disparity encoding. Each table entry represents the \ncombination of right/left eye inputs combined in a binocular output line to achieve a \ndesired phase shift of \n\n. We abbreviate EVEN/ODD by e/o and ON/OFF by +/-.\n\n\u2206\u03c6\n\n\u2206\u03c6\n\n\u03c0 2\u2044\u2013\n\n0\n\u03c0 2\u2044\n\u03c0\n\nB1+\ne+/o-\ne+/e+\ne+/o+\ne+/e-\n\n3.4 Complex cell output\n\nBinocular output line\nB1-\nB2+\no+/e+\ne-/o+\no+/o+\ne-/e-\ne-/o-\no+/e-\no+/o-\ne-/e+\n\nB2-\no-/e-\no-/o-\no-/e+\no-/o+\n\nSince the spike rates at the four outputs of the binocular combination block are relatively\nlow, e.g. 10-1000Hz, we implement the final steps using an 8051 microcontroller (MCU)\nrunning at 24 MHz. Integrators count the number of spikes from each channel in a fixed\ntime window, e.g. \n, to estimate the average spike rate on each of the four lines.\nWe generate the four binocular simple cell responses by positive and negative half squar-\n\n40ms\n\n=\n\nT\n\n\fing the spike rate differences (B1+ - B1-) and (B2+ - B2-), and sum them to obtain the bin-\nocular complex cell output. The MCU computes one set of four simple cell and one\ncomplex cell outputs every \n\n is the time window of the integration. \n\n seconds, where \n\nT\n\nT\n\n4 RESULTS\n\nWe use a pattern generator to supply the left and right eye inputs, which gives us precise\ncontrol over the input disparity. In a loose biological analogy, we directly stimulate the\noptic nerve. The pattern generator simultaneously excites a pair of pixels in the left and\nright Gabor-type chips. The two pixels lie in the same row but are displaced by half the\ninput disparity to the right of the center pixel in the right chip and by half the input dispar-\nity to the left of the center pixel in the left chip. The integration time window was 40ms.\n\nFigure 4(a) shows the response of binocular complex cells tuned to three different dispari-\nties by phase encoding. The AER address filters selected spikes from the retina locations\n(32,16) in both chips. Consistent with theoretical predictions, the peaks of the non-zero\ndisparity tuned cells are approximately the same height, but smaller than the peak of the\nzero disparity tuned filter because of the smaller size of the side peaks in the ODD filter\nresponse in comparison with the center peak in the EVEN filter. Figure 4(a) shows the\nresponse of binocular complex cells tuned to similar disparities by position encoding. The\nnegative-disparity tuned cell combines the outputs of pixels (33,16) in the left chip and\n(31,16) in the right chip. The positive-disparity tuned cell combines the outputs of pixel\n(31,16) in the left chip and pixel (33,16) in the right chip. The zero-disparity tuned cells\nfor position and phase encoding are identical. Theoretically, the position model should\nresult in three identical peaks that are displaced in disparity. However, the measurements\nshow a wide variation in the peak sizes. The responses of the phase-tuned neurons exhibit\nbetter matching, because they were all computed from the same two sets of pixel outputs.\nIn contrast, the three position-tuned neurons combine the responses of the Gabor-type chip\nat six different pixels. \n\nDecreasing the time over which we integrate the spike outputs of the binocular combina-\ntions stage results in faster disparity update. However, Figure 4(c) shows that this also\nincreases variability in the response, when measured as a percentage of the mean\nresponse. \n\ne\ns\nn\no\np\ns\ne\nr\n \nl\nl\ne\nc\n \nx\ne\nl\np\nm\no\nc\n\n1.5\n\n1\n\n0.5\n\n0\n-15\n\n-5\n\n-10\n10\ninput disparity (pixels)\n\n5\n\n0\n\ne\ns\nn\no\np\ns\ne\nr\n \nl\nl\ne\nc\n \n\nx\ne\nl\np\nm\no\nc\n\n3\n\n2\n\n1\n\n0\n-15\n\n15\n\n-5\n\n-10\n10\ninput disparity (pixels)\n\n0\n\n5\n\n6\n\n4\n\n2\n\n.\n\nv\ne\nd\n\n \n.\n\nd\nt\nS\n%\n\n \n\n15\n\n0\n-15\n\n-5\n\n-10\n10\ninput disparity (pixels)\n\n0\n\n5\n\n15\n\n(a)\n\n(b)\n\n(c)\n\nFig. 4: (a) Response of three binocular complex cells tuned to three different disparities by\nphase encoding. (b) Response of three binocular complex cells tuned to three different\ndisparities by position encoding. (c) Standard deviation of the response of zero disparity\ncomplex cell expressed as a percentage of the mean response at zero disparity for two\nintegration windows of \n (dashed line). Statistics\nT\ncomputed over 80 samples.\n\n (solid line) and \n\n40ms\n\n20ms\n\n=\n\n=\n\nT\n\nAlthough they are nominally identical, the gain, damping (bandwidth), spatial frequency\nand offset of neurons from different retinal locations on the same chip vary due to transis-\n\n\ftor mismatch in the circuits used to implement them. We performed a numerical sensitiv-\nity analysis on the effect of variation in these parameters on the complex cell responses, by\nexamining how much variations in them affected the locations at which the disparity tun-\ning curves for neurons tuned to left and right disparities crossed the disparity tuning curve\nfor the neuron tuned to zero disparity. These two locations form decision boundaries\nbetween near, zero and far disparities if we classify stimuli according to disparity tuned\nneuron with the maximum response. We found that the variation in the distance between\nthese points varied much more than their centroid. Figure 5(a) shows the sensitivity coeffi-\ncients for the distance between these points, where the sensitivity coefficient is defined as\nthe percentage variation in the distance per percentage variation in a RF parameter. We\nconsider the response to be robust to variations if the sensitivity coefficient is less than 1.\nIn most cases, we find that the position model is less robust than the phase model.\n\nIn addition, we characterized the variability in the RF parameters for neurons from differ-\nent positions on the chip. We probed the response of seven individual spiking neurons to\ndifferent spatial impulse inputs and fitted parameterized Gabor-type functions to the\nresponses. We then computed the standard deviation in the parameters across the neurons\nprobed, which we express as a percentage of the mean value. Figure 5(b) shows that the\nphase model is least sensitive to variations in the parameters that vary the most. \n\nPosition Model\nPhase Model\n\ny\nt\ni\nv\ni\nt\ni\ns\nn\ne\nS\n\n2.5\n\n2\n\n1.5\n\n1\n\n0.5\n\n0\n\ny\nt\ni\nv\ni\nt\ni\ns\nn\ne\nS\n\n0.8\n0.7\n0.6\n0.5\n0.4\n0.3\n0.2\n0.1\n0\n\n70\n60\n50\n40\n30\n20\n10\n0\n\nn\no\ni\nt\na\ni\nr\na\nV\n \np\nh\nC\n\ni\n\nON-OFF\n\nDamping\n\nGain\n\nSpatial\n\nFrequency\n\nOffset\n\nON-OFF Gain\n\nDamping\n\nSpatial\n\nFrequency\n\nOffset\n\n(a)\n\n(b)\n\nFig. 5: (a) Sensitivity of the phase and position models to variations in the RF parameters\nof the neurons. (b) A comparison of the sensitivity of phase model to the variability in the\nRF parameters. The line indicates the percentage standard deviation in the RF parameters.\nErrors bars indicate the 95% confidence interval. Solid bars show the sensitivity of the\nphase model from (a).\n\n5 CONCLUSION\n\nWe have replicated the disparity selectivity of complex cells in the visual cortex in a neu-\nromorphic system based upon the disparity energy model. This system contains four sili-\ncon chips containing retinotopic arrays of neurons which communicate via the AER\ncommunication protocol, as well as circuits that combine the outputs of these chips to gen-\nerate the response of a model binocular complex cell. We exploit the capability of AER\nprotocol for point to point communication, as well as the ability to reroute spikes. \n\nOur measurements indicate that our binocular complex cells are disparity selective and\nthat their selectivity can be adjusted through both position and phase encoding. However,\nthe relative responses of neurons tuned by phase encoding exhibit better matching than the\nrelative responses of neurons tuned by position encoding, because neurons tuned to differ-\nent disparities by position encoding integrate outputs from different pixels while neurons\ntuned by phase encoding integrate output from the same pixels.\n\nThis implementation is an initial step towards the development of a multi-chip neuromor-\nphic system capable of extracting depth information about the visual environment using\nsilicon neurons with physiologically-based functionality. The next step will be to extend\n\n\fthe system from a single disparity tuned neuron to a set of retinotopic arrays of disparity\ntuned neurons. In order to do this, we will develop a mixed analog-digital chip whose\narchitecture will be similar to that of the orientation tuned chip, which will combine the\noutputs from left and right eye orientation-tuned chips to compute an array of neurons\ntuned to the same disparity but different retinal locations. The tuned disparity can be con-\ntrolled by address remapping, so additional copies of the same chip could represent neu-\nrons tuned to other disparities. This chip will increase the number of neurons we compute\nsimultaneously, as well as decreasing the power consumption required to compute each\nneuron. In the current implementation, the digital circuits required to combine the monoc-\nular responses consume 1.2W. In contrast, the Gabor chips and their associated external\nbias and interface circuits consume only 62mW, with only about 4mW required for each\nGabor chip. We expect the power consumption of the binocular combination chip to be\ncomparable. Computing the neuron outputs in parallel will enable us to investigate the\nroles of additional processing steps such as pooling [5], [6] and normalization [12], [13].\n\nAcknowledgements\n\nThis work was supported in part by the Hong Kong Research Grants Council under Grant\nHKUST6218/01E. It was inspired by a project with Y. Miyawaki at the 2002 Telluride\nNeuromorphic Workshop. The authors would like to thank K. A. Boahen for helpful dis-\ncussions and for supplying the receiver board used in this work, and T. Choi for his assis-\ntance in building the system.\n\nReferences\n\n[1]\n\n[2]\n\n[3]\n\n[4]\n\n[5]\n\n[6]\n\n[7]\n\n[8]\n\n[9]\n\n[10]\n\n[11]\n\n[12]\n\n[13]\n\nBarlow, H. B., Blackemore, C., & Pettigrew, J. D. (1967) The neural mechanism of binocu-\nlar depth discrimination. J. Physiol. Lond., 193, 327-342.\nOhzawa, I., Deangelis, G. C., & Freeman, R. D. (1990) Stereoscopic depth discrimination in\nthe visual cortex: neurons ideally suited as disparity detectors. 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Visual Neuro-\nscience, 9, 181-197.\n\n\f", "award": [], "sourceid": 2446, "authors": [{"given_name": "Bertram", "family_name": "Shi", "institution": null}, {"given_name": "Eric", "family_name": "Tsang", "institution": null}]}