A Contrast Sensitive Silicon Retina with 
Reciprocal Synapses 
Kwabena A. Boahen 
Computation and Neural Systems 
California Institute of Technology 
Pasadena, CA 91125 
Andreas G. Andreou 
Electrical and Computer Engineering 
Johns Hopkins University 
Baltimore, MD 21218 
Abstract 
The goal of perception is to extract invariant properties of the underly- 
ing world. By computing contrast at edges, the retina reduces incident 
light intensities spanning twelve decades to a twentyfold variation. In one 
stroke, it solves the dynamic range problem and extracts relative reflec- 
tivity, bringing us a step closer to the goal. We have built a contrast- 
sensitive silicon retina that models all major synaptic interactions in the 
outer-plexiform layer of the vertebrate retina using current-mode CMOS 
circuits: namely, reciprocal synapses between cones and horizontal cells, 
which produce the antagonistic center/surround receptive field, and cone 
and horizontal cell gap junctions, which determine its size. The chip has 
90 x 92 pixels on a 6.8 x 6.9mm die in 2pm n-well technology and is fully 
functional. 
I INTRODUCTION 
Retinal cones use both intracellular and extracellular mechanisms to adapt their 
gain to the input intensity level and hence remain sensitive over a large dynamic 
range. For example, photochemical processes within the cone modulate the pho- 
tocurrents while shunting inhibitory feedback from the network adjusts its mem- 
brane conductance. Adaptation makes the light sensitivity inversely proportional 
to the recent input level and the membrane conductance proportional to the back- 
ground intensity. As a result, the cone's membrane potential is proportional to the 
ratio between the input and its spatial or temporal average, i.e. contrast. We have 
764 
A Contrast Sensitive Silicon Retina with Reciprocal Synapses 765 
developed a contrast-sensitive silicon retina using shunting inhibition. 
This silicon retina is the first to include variable inter-receptor coupling, allowing 
one to trade-off resolution for enhanced signal-to-noise ratio, thereby revealing 
low-contrast stimuli in the presence of large transistor mismatch. In the vertebrate 
retina, gap junctions between photoreceptors perform this function [5]. At these 
specialized synapses, pores in the cell membranes are juxtaposed, allowing ions 
to diffuse directly from one cell to another [6]. Thus, each receptor's response is a 
weighted average over a local region. The signal-to-noise ratio increases for features 
larger than this region--in direct proportion to the space constant [5]. 
Our chip achieves a four-fold improvement in density over previous designs [2]. 
We use innovative current-mode circuits [7] that provide very high functionality 
while faithfully modeling the neurocircuitry. A bipolar phototransistor models the 
photocurrents supplied by the outer-segment of the cone. We use a novel single- 
transistor implementation of gap junctions that exploits the physics of MOS tran- 
sistors. Chemical synapses are also modeled very efficiently with a single device. 
Mahowald and Mead's pioneering silicon retina [2] coded the logarithm of contrast. 
However, a logarithmic encoding degrades the signal-to-noise ratio because large 
signals are compressed more than smaller ones. Mead et. al. have subsequently 
improved this design by including network-level adaptation [4] and adaptive pho- 
toreceptors [3, 4] but do not implement shunting inhibition. Our silicon retina was 
designed to encode contrast directly using shunting inhibition. 
The remainder of this paper is organized as follows. The neurocircuitry of the 
distal retina is described in Section 2. Diffusors and the contrast-sensitive sili- 
con retina circuit are featured in Section 3. We show that a linearized version of 
this circuit computes the regularized solution for edge detection. Responses from a 
one-dimensional retina showing receptive field organization and contrast sensitiv- 
ity, and images from the two-dimensional chip showing spatial averaging and edge 
enhancement are presented in Section 4. Section 5 concludes the paper. 
Cones 
k Synapses 
Horizontal 
Cells 
Junctions 
Figure 1: Neurocircuitry of the outer-plexiform layer. The white and black 
triangles are excitatory and inhibitory chemical synapses, respectively. The 
grey regions between adjacent cells are electrical gap junctions. 
766 
Boahen and Andreou 
2 THE RETINA 
The outer plexiform layer of the retina produces the well-known antagonistic cen- 
ter/surround receptive field organization first described in detail by Kuttter in the 
cat [11]. The functional neurocircuitry, based on the red cone system in the tur- 
tle [10, 8, 6], is shown in Figure 1. Cones and horizontal cells are coupled by gap 
junctions, forming two syncytia within which signals diffuse freely. The gap junc- 
tions between horizontal cells are larger in area (larger number of elementary pores), 
so signals diffuse relatively far in the horizontal cell syncytium. On the other hand, 
signals diffuse poorly in the cone syncytium and therefore remain relatively strong 
locally. When light falls on a cone, its activity increases and it excites adjacent hor- 
izontal cells which reciprocate with inhibition. Due to the way signals spread, the 
excitation received by nearby cones is stronger than the inhibition from horizontal 
cells, producing net excitation in the center. Beyond a certain distance, however, 
the reverse is true and so there is net inhibition in the surround. 
The inhibition from horizontal cells is of the shunting kind and this gives rise to 
to contrast sensitivity. Horizontal cells depolarize the cones by closing chloride 
channels while light hyperpolarizes them by closing sodium channels [9, 1]. The 
cone's membrane potential is given by 
V = gv,,Ev,, + gDV. 
gv,, + gc + gD 
(1) 
where the conductances are proportional to the number of channels that are open 
and voltages are referred to the reversal potential for chloride. gD and V, et describe 
the effect of gap junctions to neighboring cones. Since the horizontal cells pool 
signals over a relatively large area, got will depend on the background intensity. 
Therefore, the membrane voltage will be proportional to the ratio between the 
input, which determines gN,, and the background. 
Vf Vf 
':I' I Mail '> 'I 
(a) (b) 
Figure 2: (a) Diffusor circuit. (b) Resistor circuit. The diffusor circuit simu- 
lates the currents in this linear resistive network. 
3 
A Contrast Sensitive Silicon Retina with Reciprocal Synapses 
SILIOON MODELS 
767 
In the subthreshold region of operation, a MOS transistor mimics the behavior of a 
gap junction. Current flows by diffusion: the current through the channel is linearly 
proportional to the difference in carrier concentrations across it [2]. Therefore, the 
channel is directly analogous to a porous membrane and carrier concentration is the 
analog of ionic species concentration. In conformity with the underlying physics, we 
call transistors in this novel mode of operation diffusors. The gate modulates the 
carrier concentrations at the drain and the source multiplicatively and therefore sets 
the diffusivity. In addition to offering a compact gap junction with electronically 
adjustable 'area,' the diffusor has a large dynamic range--at least five decades. 
A current-mode diffusor circuit is shown in Figure 2a. The currents through the 
diode-connected well devices M1 and M2 are proportional to the carrier concen- 
trations at either end of the diffusor Ma. Consequently, the diffusor current is pro- 
portional to the current difference between M1 and M2. Starting with the equation 
describing subthreshold conduction [2, p. 36], we obtain an expression for the cur- 
rent IpQ in terms of the currents Ip and IQ, the reference voltage Vre! and the bias 
voltage V/: 
For simplicity, voltages and currents are in units of V- = kT/q, and I0, the zero 
bias current, respectively; all devices are assumed to have the same  and I0. The 
ineffectiveness of the gate in controlling the channel potential, measured by   0.?5, 
introduces a small nonideality. There is a direct analogy between this circuit and 
the resistive circuit shown in Figure 2b for which leo = (ff,/ffl)(IQ- Is,). The 
currents in these circuits are identical if G=/G1 = exp(Vz - Vrel) and  = 1. 
Increasing Vz or reducing Ve! has the same effect as increasing G= or reducing 
Chemical synapses are also modeled using a single MOS transistor. Synaptic inputs 
to the turtle cone have a much higher resistance, typically 0.6Gf or more [1], 
than the input conductance of a cone in the network which is 50M or less [8]. 
Thus the synaptic inputs are essentially current sources. This also holds true for 
horizontal cells which are even more tightly coupled. Accordingly, chemical synapses 
are modeled by a MOS transistor in saturation. In this regime, it behaves like 
current source driving the postsynapse controlled by a voltage in the presynapse. 
The same applies to the light-sensitive input supplied by the cone outer-segment; 
its peak conductance is about 0.4GF in the tiger salamander [9]. Therefore, the 
cone outer-segment is modeled by a bipolar phototransistor, also in saturation, 
which produces a current proportional to incident light intensity. 
Shunting inhibition is not readily realized in silicon because the 'synapses' are cur- 
rent sources. However, to first order, we achieve the same effect by modulating the 
gap junction diffusitivity gD (see Equation 1). In the silicon retina circuit, we set 
VL globally for a given diffusitivity and control V,,e! locally to implement shunting 
inhibition. 
A one-dimensional version of the current-mode silicon retina circuit is shown in 
Figure 3. This is a direct mapping of the neurocircuitry of the outer-plexiform 
layer (shown in Figure 1) onto silicon using one transistor per chemical synapse/gap 
junction. Devices M1 and M2 model the reciprocal synapses. M4 and Ms model 
768 Boahen and Andreou 
T 
I 
I I 
M4 
Figure 3: Current-mode Outer-Plexiform Circuit. 
the gap junctions; their diffusitivities are set globally by the bias voltages V6 and 
Vr. The phototransistor M6 models the light-sensitive input from the cone outer 
segment. The transistor Ms, with a fixed gate bias Vu, is analogous to a leak in 
the horizontal cell membrane that counterbalances synaptic input from the cone. 
The circuit operation is as follows. The currents Ic and IH represent the responses 
of the cone and the horizontal cell, respectively. These signals are actually in 
the post-synaptic circuit--the nodes with voltage Vc and VH correspond to the 
presynaptic signals but they encode the logarithm of the response. Increasing the 
photocurrent will cause V to drop, turning on M2 and increasing its current Ic; 
this is excitation. Ic pulls VH down, turning on M1 and increasing its current IH; 
another excitatory effect. IH, in turn, pulls Vc up, turning off M2 and reducing its 
current I; this is inhibition. 
The diffusors in this circuit behave just like those in Figure 2 although the well 
devices are not diode-connected. The relationship between the currents given by 
Equation 2 still holds because the voltages across the diffusor are determined by the 
currents through the well devices. However, the reference voltage for the diffusors 
between 'cones' (M4) is not fixed but depends on the 'horizontal cell' response. Since 
IH = exp(VDD -- VH), the diffusitivity in the cone network will be proportional to 
the horizontal cell response. This produces shunting inhibition. 
3.1 RELATION TO LINEAR MODELS 
Assuming the horizontal cell activities are locally very similar due to strong cou- 
pling, we can replace the cone network diffusitivity by  = (IHIg, where (IHI is the 
local average. Now we treat the diffusors between the 'cones' as if they had a fixed 
A Contrast Sensitive Silicon Retina with Reciprocal Synapses 769 
diffusitivity ; the diffusitivity in the 'horizontal cell' network is denoted by h. Then 
the equations describing the full two-dimensional circuit on a square grid are: 
;,(x,,,yn) = ;(xm,Yn) + 0  {;cO',,Yj) - ;c(m,Yn)) (a) 
j=n-}-I 
Ic(xm, y.) = Itr + h  {In(xm,yn) -- In(xi, yj)} (4) 
i= m-}-I 
j = n-i-1 
This system is a special case of the dual layer outer plexiform model proposed by 
Yagi [19]--we have the membrane admittances set to zero and the synaptic strengths 
set to unity. Using the second-difference approximation for the laplacian, we obtain 
the continuous versions of these equations 
= + 
= - (6) 
with the internode distance normalized to unity. Solving for In(x, y), we find 
y) + nx,y) = 
(7) 
This is the biharmonic equation used in computer vision to find an optimally smooth 
interpolating function 'In(x,y)' for the noisy, discrete data 'I(x,y)' [13]. The co- 
efficient X = h is called the regularizing parameter; it determines the trade-off 
between smoothing and fitting the data. In this context, the function of the hori- 
zontal cells is to compute a smoothed version of the image while the cones perform 
edge detection by taking the laplacian of the smoothed image as given by Equation 6. 
The space constant of the solutions is )1/4 [13]. This predicts that the receptive 
field size of our retina circuit will be weakly dependent on the input intensity since 
 is proportional to the horizontal cell activity. 
4 CHIP PERFORMANCE 
Data from the one-dimensional chip showing receptive field organization is in Fig- 
ure 4. As the 'cone' coupling increases, the gain decreases and the excitatory and 
inhibitory subregions of the receptive field become larger. Increasing the 'horizontal 
cell' coupling also enlarges the receptive field but in this case the gain increases. This 
is because stronger diffusion results in weaker signals locally and so the inhibition 
decreases. Figure 5(a) shows the variation of receptive field size with intensity-- 
roughly doubling in size for each decade. This indicates a one-third power depen- 
dence which is close to the theoretical prediction of one-fourth for the linear model. 
The discrepancy is due to the body effect on transistor M2 (see Figure 3) which 
makes the diffusor strength increase with a power of 1/n 2. 
Contrast sensitivity measurements are shown in Figure 5(b). The S-shaped curves 
are plots of the Michaelis-Menten equation used by physiologists to fit responses of 
cones [6]: 
I" 
v = + (s) 
770 Boahen and Andreou 
5O 
45 
,,_. 40- 
35- 
30- 
25- 
20- 
lO 
50 I I I I I 
5 10 15 20 25 
(a) Node Position 
50- 
45' 
40' 
35' 
30' 
9.5- 
15' 
10' 
5 I I I I I 
0 5 10 15 20 25 
(b) Node Position 
Figure 4: Receptive fields measured for 25 x I pixel chip; arrows indicate 
increasing diffuser gate voltages. The inputs were 50nA at the center and 
10nA elsewhere, and the output current Iv was set to 20nA. (a) Increasing 
inter-receptor diffuser voltages in 15mV steps. (b) Increasing inter-horizontal 
cell diffuser voltages in 50mV steps. 
50- 
40- 
30- 
20- 
10- 
0- 
-10 0      
5 10 15 20 25 
(a) Node Position 
50- 
40' 
-- 30- 
9.0- 
10- 
0 
: '-o ..... 1"::: ': i' '-s 
10 -' 10 0 
(b) Input (A) 
10-? 
Figure 5: (a) Dependence of receptive field on intensity; arrows indicate in- 
creasing intensity. Center inputs were 500pA, 5hA, 15hA, 50hA, and 500hA. 
The background input was always one-fifth of the center input. (b) Contrast 
sensitivity measurements at two background intensity levels. Lines are fits of 
the Michaelis-Menten equation. 
A Contrast Sensitive Silicon Retina with Reciprocal Synapses 771 
Figure 6: Video images from 90 x 92 pixel chip with and without cone coupling. 
The vertical lines between pixels are artifacts of the scanning circuitry. 
where tr is the background intensity and the exponent n determines the slope of the 
S-curve. A vertical offset is included to account for the dependence of transistor 
mismatch on the intensity level. The circuit deviates at high intensities due to 
increasing inter-receptor coupling strength. For these fits, n is 1.2 in both cases, 
compared to the physiologically observed value of 1.0 for cones [6], and tr is 1.5nA 
and 3.0nA; the actual background intensities were 0.56nA and 1.SnA. Thus the 
responses are centered at a higher intensity and did not shift horizontally as much 
as expected with intensity. This is due to the difference in gain for inputs above 
and below the background level. As the inputs decrease the cone coupling reduces 
and so the gain increases. Hence there is a smaller range of operation below the 
background level. 
Figure 6 shows video images of a face produced by the two-dimensional silicon retina 
chip. The chip includes scanning circuitry which rasterizes the image and generates 
all the signals required to drive a multiscan monitor [14]. The image on the left 
shows a considerable amount of spatial noise due to transistor mismatch. The face is 
hardly recognizable. In the other image the inter-cone diffusors have been turned on 
and greatly enhance the signal-to-noise. The center-surround processing highlights 
edges, producing the 'halo' around her head, and regions with high curvature, like 
the cheeks. 
5 CONCLUSIONS 
Using a current-mode approach, we have built a dense, robust, contrast-sensitive 
silicon retina modeled closely after the vertebrate retina. Our single-transistor 
gap junctions and chemical synapses yield very efficient implementations of neural 
networks. Unfortunately, the implementation of shunting inhibition used here makes 
the receptive fields enlarge with increasing intensity. We are presently developing 
new circuits that address this problem. 
772 Boahen and Andreou 
Acknowledgements 
We are very grateful to Carver Mead for his support and encouragement. KB 
is supported by a graduate fellowship from Caltech. AA is supported by a Re- 
search Initiation Award from NSF (MIP-9010364). KB thanks Tobi Delbriick, Andy 
Moore, Lloyd Watts, Misha Mahowald, and Xavier Arreguit for their help. Chip 
fabrication was provided by MOSIS and computing facilities in the Mead Lab by 
Hewlett-Packard. 
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