{"title": "Adaptive Retina with Center-Surround Receptive Field", "book": "Advances in Neural Information Processing Systems", "page_first": 678, "page_last": 684, "abstract": null, "full_text": "Adaptive Retina with  Center-Surround \n\nReceptive Field \n\nShih-Chii Lin and Kwabena Boahen \n\nComputation and Neural  Systems \n\n139-74 California Institute of Technology \n\nPasadena, CA  91125 \n\nshih@pcmp.caltech.edu,  buster@pcmp.caltech.edu \n\nAbstract \n\nBoth vertebrate and invertebrate retinas are highly efficient  in ex(cid:173)\ntracting contrast independent of the background intensity over five \nor  more  decades.  This  efficiency  has  been  rendered  possible  by \nthe adaptation of the DC operating point to the background inten(cid:173)\nsity while maintaining high gain  transient responses.  The center(cid:173)\nsurround properties of the retina allows the system  to extract in(cid:173)\nformation at the edges in the image.  This silicon retina models the \nadaptation properties of the receptors and the antagonistic center(cid:173)\nsurround properties of the laminar cells  of the invertebrate retina \nand the outer-plexiform layer of the vertebrate retina.  We also illus(cid:173)\ntrate the spatio-temporal responses of the silicon retina on moving \nbars.  The  chip  has  59x64  pixels  on  a  6.9x6.8mm2  die  and  it  is \nfabricated in 2 J-tm  n-well  technology. \n\n1 \n\nIntroduction \n\nIt has  been observed previously that the initial  layers of the vertebrate and inver(cid:173)\ntebrate retina systems  perform  very  similar processing  functions  on  the  incoming \ninput  signal[1].  The response versus log intensity curves of the receptors in inver(cid:173)\ntebrate  and  vertebrate  retinas  look  similar.  The  curves  show  that  the  receptors \nhave a  larger gain for  changes in illumination than to steady illumination,  i.e,  the \nreceptors  adapt.  This adaptation  property allows  the  receptor  to respond over  a \nlarge input range without  saturating. \n\nAnatomically, the eyes of invertebrates differ greatly from  that of vertebrates.  Ver-\n\n\fAdaptive Retina with Center-Surround Receptive Field \n\n679 \n\ntebrates  normally  have  two  simple  eyes  while  insects  have  compound  eyes.  Each \ncompound  eye  in  the  fly  consists  of 3000-4000 ommatidia and  each ommatidium \nconsists of 8  photoreceptors.  Six  of these  receptors  (which  are also  called  RI-R6) \nare in a single spectral class.  The other two receptors, R7 and R8 provide channels \nfor  wavelength discrimination and polarization. \n\nThe vertebrate eye is divided into the outer-plexiform layer and the inner-plexiform \nlayer.  The  outer-plexiform  layer  consists  of the  rods  and  cones,  horizontal  cells \nand  bipolar  cells.  Invertebrate receptors  depolarise  in  response  to an  increase in \nlight, in contrast to vertebrate receptors, which hyperpolarise to an increase in light \nintensity.  Both vertebrate and invertebrate receptors show light adaptation over at \nleast five  decades of background illumination.  This adaptation property allows the \nretina to maintain a high transient gain to contrast over a wide range of background \nintensities. \n\nThe invertebrate receptors project to the next layer which is called the lamina layer. \nThis layer consists primarily of monopolar cells which show a  similar response ver(cid:173)\nsus  log  intensity  curve  to  that  of vertebrate  bipolar  cells  in  the  outer-plexiform \nlayer.  Both cells respond with graded potentials to changes in illumination.  These \ncells  also show a  high  transient  gain to changes in illumination while  ignoring the \nbackground intensity  and  they  possess  center-surround receptive  fields.  In  verte(cid:173)\nbrates,  the cones  which  are excited  by  the incoming  light,  activate  the  horizontal \ncells which in tum inhibit the cones.  The horizontal cells  thus mediate the lateral \ninhibition  which  produces  the  center-surround  properties.  In  insects,  a  possible \nprocess  of this  lateral  inhibition  is  done  by  current  flow  from  the  photoreceptors \nthrough  the  epithelial  glial  cells  surrounding  an  ommatidium  or  the  modulation \nof the local field  potential in  the lamina to influence  the transmembrane potential \nof the photoreceptor[2].  The center-surround receptive fields  allow  contrasts to be \naccentuated since the surround computes a  local mean and subtracts that from  the \ncenter signal. \n\nMahowald[3]  previously described a silicon retina with adaptive photoreceptors and \nBoahen  et al.[4]  recently  described  a  compact  current-mode  analog  model  of the \nouter-plexiform  layer  of the  vertebrate  retina  and  analysed  the  spatio-temporal \nprocessing  properties  of  this  retina[5].  A  recent  array  of  photoreceptors  from \nDelbriick[6]  uses  an adaptive photoreceptor circuit that adapts its operating point \nto  the  background  intensity  so that  the  pixel  shows  a  high  transient  gain  over  5 \ndecades  of background  illumination.  However  this  retina  does  not  have  spatial \ncoupling between pixels. \n\nThe  pixels  in  the  silicon  retina  described  here  has  a  compact  circuit  that  incor(cid:173)\nporates  both  spatial  and  temporal  filtering  with  light  adaptation  over  5  decades \nof background intensity.  The network  exhibits center-surround behavior.  Boahen \net  al.[4]  in  their  current-mode  diffusor  retina,  draw  an  analogy  between  parts of \nthe  diffusor  circuit  and the  different  cells  in  the outer-plexiform  layer.  While  the \nsame analogy  cannot  be  drawn from  this  silicon  retina to the invertebrate retina \nsince the function of the cells  are not completely understood, the output responses \nof the  retina circuit are  similar  to the output responses of the photoreceptor and \nmonopolar cells in invertebrates. \n\nThe  circuit  details  are  described  in  Section  2  and  the spatio-temporal  processing \nperformed by the retina on stimulus moving at different speeds is shown  in Section \n\n\f680 \n\n3. \n\n2  Circuit \n\nVI \n\n1 \n\nVh \n.1. \n\nVb \np1 \n\nVI\u00b7I \n\nVI \n\n1 \n\nVh \n.1. \n\nM4 \n\nVI \n\n.bel \n\nVr \n\nMI \n\n(a) \n\nS.-C. LIU, K.  BOAHEN \n\n------\n\nVI+I \n\n---------\n\nim.l \n\nrrr \n\niia \n\niI ... I \n\nrrr \n\nrrr \n\n'II \n\n(b) \n\n'II \n\nFigure  1:  (a)  One-dimensional version of the retina.  (b)  Small-signal equivalent of \ncircuit in (a). \n\nA one-dimensional version of the retina is shown in Figure l(a).  The retina consists \nof an  adaptive photoreceptor circuit  at each pixel  coupled together with  diffusors, \ncontrolled by voltages, Vg  and Vh.  The output of this network can either be obtained \nat the voltage output, V,  or at the current output, 10  but the outputs have different \nproperties.  Phototransduction  is  obtained  by  using  a  reverse-biased  photodiode \nwhich produces current that is proportional to the incident light.  The logarithmic \nproperties are obtained by operating the feedback  transistor shown in Figure  l(a) \nin  the subthreshold region.  The voltage change at the output photoreceptor,  V r ,  is \nproportional to a  small  contrast since \n\nUT \n\nUTdI  UT  i \nVr = -d(logl) = - - = - -\nK,  h g \nK,  1 \n\nK, \n\nwhere  UT  is  the  thermal  voltage,  K,  =  CO:rCd  ' Coz  is  the oxide  capacitance and \nCd  is  the  depletion  capacitance of a  transistor.  The  circuit  works  as  follows:  If \nthe photocurrent through  the photodiode increases,  Vr  will  be pulled low  and the \noutput  voltage  at  V,  increases  by  VI  =  AVr  where  A  is the  amplifier  gain  of the \noutput  stage.  This  output  change  in  V,  is  coupled  into  Vel  through  a  capacitor \n\n\fAdaptive Retina with Center-Surround Receptive Field \n\n681 \n\ndivider  ratio,  Cl~2C2.  The  feedback  transistor,  M4,  operates  in  the  subthreshold \nregion and supplies the current necessary to offset  the photocurrent.  The increase \nin  Vel  (i.e.  the gate voltage of M4)  causes the current supplied  by  M3  to increase \nwhich  pulls  the node  voltage,  Vr ,  back  to the  voltage  level  needed  by  Ml  to sink \nthe bias current from  transistor, M2. \n\n3.5 \n\n3.45 \n\n3.4 \n\n... -= 0 \n~ \u2022  3.35 \n\u2022 \nQ. \u2022 \u2022 a: \n\nc \n0 \n\n3.3 \n\n-2 \n\n-1 \n\n3.25 \n\n0 \n\n3.2 \n0 \n\n5 \n\n10 \n\n15 \n\n20 \n\n25 \n\nTime (Sec) \n\nFigure  2:  This figure  shows  the  output  response of the receptor  to a  variation of \nabout 40%  p-p in the intensity of a  flickering  LED  light  incident on the chip.  The \nresponse shows  that the high sensitivity of the receptor to the  LED  is maintained \nover  5  decades of differing background intensities.  The numbers on  the section of \nthe curve indicate the log intensity of the mean value.  0 log is the absolute intensity \nfrom  the LED. \n\nThe  adaptive  element,  M3,  has  an  I-V  curve  which  looks  like  a  hyperbolic  sine. \nThe  small  slope  of the I-V  curve  in  the  middle  means  that  for  small  changes  of \nvoltages across M3,  the element  looks  like  an open-circuit.  With large  changes of \nvoltage across M3, the current through M3  becomes exponential and Vel  is charged \nor discharged almost instantaneously. \n\nFigure 2 shows the output response of the photoreceptor to a square-wave variation \nof about  40%  p-p in  the intensity of a  red LED  (635  nm).  The results show  that \nthe circuit is able to discern  the small contrast over five  decades of background in(cid:173)\ntensity while the steady-state voltage of the photoreceptor output varies only about \n15mV.  Further  details  of the photoreceptor  circuit  and its  adaptation  properties \nare described in Delbriick[6]. \n\n3  Spatio-Temporal Response \n\nThe spatio-temporal response of the network to different moving stimuli is explored \nin this section.  The circuit shown in Figure l(a) can be transferred to an equivalent \nnetwork of resistors and capacitors as shown  in Figure  l(b)  to obtain the  transfer \nfunction  of the  circuit.  The  capacitors at  each  node  are  necessary  to  model  the \n\n\f682 \n\nS.-C. LIU, K. BOAHEN \n\n8.5 \n\ni \n~ 7.5 \n:; ... :; \no \ni \nI \n~ r. ... \n\n1 \nlJ; \n\n0.4 \n\n0.6 \n\n0.8 \n\n1.2 \n\n1.4 \n\n(a) \n\nTime (Sec) \n\n3.8 ~_---:-\":--_--::'= __  ':\"':-_--::':-_--::,'::-_--.J \n\n0.7 \n\n0.8 \n\n0.5 \n\n0 .6 \nTime (Sec) \n\n0.3 \n\n0.4 \n\n(b) \n\nFigure 3:  (a)  Response  of a  pixel  to a  grey  strip  2  pixels  wide  of gray-level  \"0.4\" \non  a  dark  background of level  \"0\"  moving  past  the  pixel  at different  speeds.  (b) \nResponse of a pixel to a dark strip of gray-level \"0.6\" on a white background of level \n\"1\"  moving past the pixel at different speeds.  The voltage shown on these curves is \nnot the direct measurement of the voltage at V,  but rather V,  drives a current-sensing \ntransistor and this current is then sensed by an offchip  current sense-amplifier. \n\n\fAdaptive Retina with Center-Surround Receptive Field \n\n683 \n\ntemporal responses of the circuit. \n\nThe chip results from  the experiments below illustrate the center-surround proper(cid:173)\nties of the network and the difference in time-constants between the surround and \ncenter. \n\n3.1  Chip Results \n\nData from  the  2D  chip is  shown in the next few  figures.  In these experiments, we \nare only looking at one pixel of the 2D array.  A rotating circular fly-wheel stimulus \nwith  strips of alternating contrasts is  mounted above  the chip.  The stimulus was \ncreated using Mathematica.  Figure 3a shows the spati~temporal impulse response \nof one pixel measured at V,  with a small strip at level  \"0.4\" on a dark background of \nlevel  \"0\"  moving past the pixels on  the row.  At slow speeds,  the impulse response \nshows a  center-surround behavior where  the pixel first  receives inhibition from  the \npreceding pixels  which  are excited  by the  stimulus.  When  the stimulus moves  by \nthe pixel  of interest, it is  excited and then it is inhibited by the subsequent pixels \nseeing the stimulus. \n\nI o \nf \nI \ni \n\nTim. (Sec) \n\nFigure 4:  Response of a  pixel to a  strip of varying contrasts on a  dark  background \nmoving past the pixel at a constant speed. \n\nAt faster  speeds,  the initial inhibition in the response grows smaller until  at some \neven faster speed, the initial inhibition is no longer observed.  This response comes \nabout because the inhibition from the surround has a longer-time constant than the \ncenter.  When the stimulus moves past the pixel of interest, the inhibition from  the \npreceding pixels excited by the stimulus does not have time to inhibit  the pixel of \ninterest.  Hence the excitation is seen first  and then the inhibition comes into place \nwhen  the stimulus passes  by.  Note that in  these figures  (Figures  3-4),  the  curves \nhave  been  displaced  to show  the  pixel  response  at different  speeds  of the  moving \nstimulus.  The voltage shown on these curves is  not the direct measurement of the \nvoltage  at V,  but  rather V,  drives  a  current-sensing transistor and  this  current  is \nthen sensed by an off-chip  current sense-amplifier. \n\nFigure 3b  shows  the  spati~temporal impulse  response of one pixel  with  a  similar \n\n\f684 \n\ns.-c. LlU, K. BOAHEN \n\nsize  strip of level  \"0.6\"  on a  light  background of level  \"1\"  moving past the row of \npixels.  The  same inhibition  behavior is  seen  for  increasing  stimulus  speeds.  Fig(cid:173)\nure 4 shows the output response at V,  for  the same stimulus of gray-levels varying \nfrom  \"0.2\"  to  \"0.8\"  on  a  dark  background of level  \"0\"  moving at one speed.  The \npeak excitation response is plotted against the contrast in Figure 5.  A level of \"0.2\" \ncorresponds to a irradiance of 15mW/m2 while a level of \"0.8\" corresponds to a irra(cid:173)\ndiance of 37.4mW/m2.  These measurements are done with a photometer mounted \nabout 1.5in above a piece of paper with the contrast which is  being measured.  The \nirradiance varies exponentially with increasing level. \n\n4  Conclusion \n\nIn  this  paper,  we  described  an  adaptive  retina  with  a  center-surround  receptive \nfield.  The system properties of this retina allows it to model functionally either the \nresponses of the laminar cells in the invertebrate retina or the outer-plexiform layer \nof vertebrate retina.  We  show  that  the  circuit  shows  adaptation  to changes over \n5 decades of background intensities.  The center-surround property of the network \ncan  be  seen  from  its spatio-temporal  response  to  different  stimulus  speeds.  This \nproperty serves to remove redundancy in space and time of the input signal. \n\nAcknowledgements \n\nWe  thank Carver Mead for his support and encouragement.  SC Liu is supported by \nan  NIMH  fellowship  and K  Boahen is  supported by  a  Sloan fellowship.  We  thank \nTobias  Delbriick for  the inspiration and help  in  testing the  design.  We  also thank \nRahul  Sarpeshkar and Bradley Minch  for  comments.  Fabrication was  provided  by \nMOSIS. \n\nReferences \n\n[1]  S.  B. Laughlin,  \"Coding efficiency and design in retinal processing\", In:  Facets \nof Vision (D. G. Stavenga and R.  C.  Hardie, eds) pp. 213-234. Springer, Berlin, \n1989. \n\n[2]  S.  R.  Shaw,  \"Retinal resistance barriers and electrica1lateral inhibition\",  Na(cid:173)\n\nture,  Lond.255,:  480-483,  1975. \n\n[3]  M.  A.  Mahowald,  \"Silicon  Retina  with  Adaptive  Photoreceptors\" \n\nin \nSPIE/SPSE Symposium  on  Electronic Science  and  Technology:  From  Neurons \nto  Chips.  Orlando, FL,  April  1991. \n\n[4]  K.  A.  Boahen and A.  G.  Andreou,  \"A  Contrast Sensitive Silicon Retina with \n\nReciprocal Synapses\", In D.  S.  Touretzky  (ed.),  Advances  in Neural Informa(cid:173)\ntion Processing  Systems 4,  764-772. San Mateo, CA:  Morgan Kaufmann,  1992. \n[5]  K.  A.  Boahen,  \"Spatiotemporal  sensitivity  of the  retina:  A physical  model\", \nCNS Memo  CNS-TR-91-06,  California Institute of Technology,  Pasadena, CA \n91125, June 1991. \n\n[6]  T.  Delbriick,  \"Analog  VLSI  Phototransduction  by  continous-time,  adaptive, \nlogarithmic photoreceptor circuits\",  CNS Memo  No.30,  California Institute of \nTechnology,  Pasadena, CA  91125,  1994. \n\n\f", "award": [], "sourceid": 1055, "authors": [{"given_name": "Shih-Chii", "family_name": "Liu", "institution": null}, {"given_name": "Kwabena", "family_name": "Boahen", "institution": null}]}