Analog Integrated Circuits and Signal Processing, 30, 121–135, 2002

Analog Integrated Circuits and Signal Processing, 30, 121–135, 2002
Analog Integrated Circuits and Signal Processing, 30, 121–135, 2002
C 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.
A Retinomorphic Chip with Parallel Pathways: Encoding INCREASING,
ON, DECREASING, and OFF Visual Signals
KWABENA BOAHEN
Penn Bioengineering, 3320 Smith Walk, Philadelphia, PA 19104
Received December 12, 1999; Accepted March 14, 2000
Abstract. Retinomorphic chips may improve their spike-coding efficiency by emulating the primate retina’s parallel
pathways. To model the four predominant ganglion-cell types in the cat retina, I morphed outer and inner retina
microcircuits into a silicon chip, Visio1. It has 104 × 96 photoreceptors, 4 × 52 × 48 ganglion-cells, a die size of
9.25 × 9.67 mm2 in 1.2 µm 5 V CMOS, and consumes 11.5 mW at 5 spikes/second/ganglion-cell. Visio1 includes
novel subthreshold current-mode circuits that model horizontal-cell autofeedback, to decouple spatial filtering from
local gain control, and model amacrine-cell loop-gain modulation, to adapt temporal filtering to motion. Different
ganglion cells respond to motion in a quadrature sequence, making it possible to detect edges of one contrast or the
other moving in one direction or the other. I present results from a multichip 2-D motion system, which implements
Watson and Ahumada’s model of human visual-motion sensing.
Key Words: neuromorphic systems, analog VLSI, mixed-mode design, CMOS imager, silicon retina, silicon
neuron, spatiotemporal filtering, automatic gain control, contrast gain control, direction selectivity
1.
Parallel Pathways in the Retina
The presence of visual pathways specialized for spatial and temporal resolution—called parvocellular and
magnocellular pathways in primates—has been confirmed both physiologically and anatomically [1,2,3].
Neurons in these pathways pool signals over either
space or time to average out quantum fluctuations,
maintaining the same noise level as they trade poor
resolution in one domain for good resolution in the
other [4]. As the light intensity drops, pooling occurs
over larger distances or longer times to maintain the
signal-to-noise ratio [5].
There is a continuum of spatial and temporal resolutions within each pathway, however, due to the
variation of spatiotemporal characteristics of midget
and parasol retinal ganglion cells with eccentricity [6].
They range from small and sustained in the fovea,
where fine details of an object stabilized by tracking are resolved, to large and transient in the periphery, where sudden motion in the surroundings is captured. At a given eccentricity, parasols (also called α
cells) cover two to three times longer distances and
respond more transiently than midgets (also called
β cells) [6,7].
In terms of actual numbers and sampling densities,
midgets and parasols make up 90% of the total ganglion
cell population and occur in a ratio of about 9:1 [8].
Nine times fewer parasols are required to tile the retina
because their dendritic fields are three times larger. The
remaining 10% of the cells form a heterogeneous group
and project mainly to the midbrain [8].
Activity in each pathway is encoded by a pair
of complementary channels, served by ON- and OFFmidgets or by ON- and OFF-parasols. The ON channel
signals increases in amplitude by increasing vesiclerelease or spike-discharge rates; the OFF channel
signals decreases in amplitude in a similar fashion [9]. Complementary signaling overcomes three
shortcomings of using a single channel to transmit
both increases and decreases, measured relative to a
baseline:1
•
Elevated spike-discharge rates and vesicle-release
rates must be maintained in the quiescent
state.
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Boahen
•
Decreases are transmitted with lower fidelity, because quantum fluctuations (i.e., shot noise) decrease
only as the square root of the mean rate.
• Decreases are transmitted with lower speed, because
quanta are infrequent and membrane repolarization
and transmitter removal are passive.
Except prior to the very first synapses, found in rod
and cone terminals, complementary signaling is used
throughout the retina to transmit information efficiently
using vesicles or spikes.
In addition to reducing quiescent firing rates by
using complementary channels, I postulate that further
savings in spikes and vesicles are achieved by adapting the baseline—both at the ganglion-cell level and at
the network-level. At the ganglion-cell level, the baseline is set by calcium-dependent potassium channels,
which shunt the input current [10,11]. At the networklevel, it is set by presynaptic inhibition from amacrine
cells, which terminate vesicle release at ON and OFF
bipolar-cell terminals [12].
Behaving like leaky integrators, these baselinesetting amacrine cells follow the signal’s temporal average. To ensure signal fluctuations are not masked by
a dynamic baseline, a long time-scale average must
be computed when change is slow. And, to ensure the
signal crosses the baseline when its derivative changes
sign, a short time-scale average must be computed
when change is rapid. Thus, spikes and vesicles are
conserved, as frequent quanta produced by fast signals are discharged for short durations while infrequent
quanta produced by slow signals are discharged for
long durations.
Retinomorphic chips, which perform adaptive pixelparallel quantization [10,11], may improve their spikecoding efficiency by emulating parallel pathways in the
retina. To this end, I have recreated retinal microcircuits
serving the magnocellular and parvocellular pathways
in a chip, Visio1, that models the four predominant ganglion cell types. Visio1 performs the operations shown
in Fig. 1 at the pixel-level. Anatomically identified neural microcircuits that perform these operations and their
CMOS neuromorphs are described in the Sections 2
and 3. These current-mode circuits operate in the subthreshold region [13], where small-signal conductances
and transconductances are proportional to the current
level [14], current-spreading diffusor networks are linear [15–17], and the generalized translinear principle
holds [18]. Visio1’s design and performance are described in Section 4, and its application in a multichip,
real-time, 2-D motion-sensing system is described in
Section 5. Section 6 concludes the paper.
2.
Outer Retina Model
The outer retina performs spatiotemporal bandpass filtering and adapts its gain locally—both at the receptor level [19,20] and at the network level. Previous
attempts to make these two functions coexist in one
network produced undesirable side-effects [15,21]. In
particular, the circuit starts ringing if you attenuate
redundant low-frequency temporal and spatial signals
by increasing the negative-feedback loop’s gain. And
the receptive field expands alarmingly if you reduce
photocurrent sensitivity by increasing the cone-to-cone
conductance.
To overcome the high-gain negative-feedback outer
retina circuit model’s shortcomings, I searched the neurobiology literature for a retinal mechanism that could
decouple spatiotemporal filtering, local gain control,
and temporal stability. Horizontal-cell autofeedback,
which was demonstrated by Kamermans and Werblin a
few years ago in the tiger salamander [22], can achieve
this. Horizontal cells (HC), which are known to use
the inhibitory neurotransmitter GABA, also express
GABA-gated Cl-channels. These channels have a reversal potential of −20 mV and therefore depolarize the
cell when they are opened, forming a positive-feedback
loop. Kamermans and Werblin showed that this autofeedback loop accounted for the extremely slow dynamics of HCs, increasing their time constant from
65 ms to 500 ms. My analysis of the tradeoffs involved
in outer-retina design has yielded two new hypotheses
about the role of autofeedback [23].
HC autofeedback can improve temporal stability by
amplifying the cone signal, allowing us to decrease
the strength of the cone-to-HC synapse. Thus, we
can attenuate low-frequency signals while maintaining temporal stability. A lower cone-to-HC synaptic
transconductance extends the cone’s dynamic range as
well. Autofeedback can also make receptive-field size
independent of sensitivity by modulating the effective
strength of the cone-to-HC synapse. More HC activity
provides a larger boost to synaptic input from cones.
Therefore, if HC activity is proportional to intensity,
then the cone-to-HC synaptic strength becomes proportional to intensity as well, compensating for the
decrease in cone sensitivity with increasing intensity
when local automatic gain control is in effect. A neural
A Retinomorphic Chip with Parallel Pathways
123
Cone
Cone
Gain
Spat
1/λ Freq
Horizontal
Cell
Ampl
Ampl
0 Ampl
Amacrine
Cell
Bipolar
Cell
0 Ampl
Gain
Gain
Gain
Gain
Temp
Temp
Temp
Temp
1/τ
1/τ
Freq
Freq
1/τ
1/τ Freq
Freq
Ganglion
Cell
Freq
Ampl
On
Inc.
Off
(a)
Dec.
Ganglion
Cells
(b)
Fig. 1. Retinal circuits and operations. (a) Retinal structure: The visual signal is relayed from the photoreceptors (called cones) to the ganglion
cells (whose axons form the optic nerve) by bipolar cells, with synaptic interactions occuring within two plexiform layers. Horizontal cells
mediate lateral interactions in the first (outer) plexiform layer while amacrine cells mediate lateral interactions in the second (inner) plexiform
layer; these interneurons are inhibitory. Four types of ganglion cells, which I call ON, OFF, INCREASING, and DECREASING, encode the retina’s
output in their spike trains. (b) Retinal function: The visual signal is bandpass filtered spatially in the outer retina, then lowpass and highpass
filtered temporally in the inner retina. These analog signals are first half-wave rectified, and then later encoded as spike trains. Spatial filters adapt
to light intensity—their gain is inversely proportional. Temporal filters adapt to stimulus speed—their time-constant is inversely proportional
(i.e., τ = λ/ν, where λ is the wavelength selected by the spatial filter). And spiking neurons adapt to their input’s rate of change—their firing
rate is linearly proportional.
microcircuit for the outer retina that includes HC autofeedback is shown in Fig. 2(a).
A system-level analysis of autofeedback, with the
aid of the block diagram shown in Fig. 3(a), reveals
that
i CO
A
i HC = 2 2
B
c ρ + 1 2h ρ 2 + 1 + A/B
2 ρ 2 + 1
i CO
h 2
i CT = 2 2
B
c ρ + 1 h ρ 2 + 1 + A/B
where B is the attenuation from the cone outer segment
(CO) to the cone terminal (CT) and A is the amplification from CT to the HC. Thus, HC lowpass-filters
the CO signal while CT bandpass-filters it, as shown in
Fig. 3(b). These filters have the same corner frequency,
which is inversely proportional
√ to the closed loop
space-constant A = (B/A)1/4 c h , where c and h
are the space-constants of the cone and horizontal-cell
networks. Therefore, spatial filtering is invariant if we
make A proportional to B, which makes HC activity
track the local average intensity. Hence, CT activity
becomes proportional to contrast if we set A = B = i HC .
A novel current-mode CMOS circuit that uses
HC autofeedback to decouple spatiotemporal filtering,
local gain control, and temporal stability is shown in
Fig. 2(b). I implement CT attenuation by modulating
the conductances of both the cone’s membrane and
its gap junctions—through HC shunting inhibition—
which leaves the cone-network’s space constant unchanged. Currents represent signals instead of voltages,
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Boahen
I
Cone Outer
Segments
Vc
Vh
Cone
Terminals
Horizontal
Cells
Ic
I'
Vcq
Vc'
Vh'
Ih
Vss1
Vhh
Excitation
Conduction
Inhibition
Modulation
(a)
I c'
Vcq
I h'
Vss1
Vhh
(b)
CO
Response
Fig. 2. Morphing the outer retina. (a) Neural microcircuitry: Cone terminals (CT) receive a photocurrent I that is proportional to incident light
intensity from their outer segments (CO). To control CO to CT attenuation without changing the cone-network’s space-constant, the horizontal
cell (HC) modulates both CT gap junctions and membrane conductances. Cone-excitation modulation is realized by GABA auto-receptors in
the HC membrane, which form a positive feedback loop. (b) CMOS circuit: A pMOS transistor, with its source tied to Vc and its gate tied to
Vh , produces a current proportional to the product of the CT and HC activities, which are represented by the currents Ic and Ih . This current is
sunk from the CT node, Vc , to model HC shunting inhibition, and dumped on the HC node, Vh , to model CT excitation and HC autofeedback.
Vcq sets the mean level of the cone current Ic .
+HC
HC
1
l h ρ +1
1
l c ρ +1
2 2
HC
CT
2 2
CT
(a)
Spatial Frequency
(b)
Fig. 3. Outer retina spatial filtering. (a) System-level concept: Visual signals travel from the cone outer-segment (CO), to the cone terminal (CT),
and on to the horizontal cell (HC), which closes the negative feedback loop. To realize local automatic gain control, HC modulates the attenuation
from CO to CT. And to keep the loop-gain constant, HC also modulates the signal it receives from CT, giving rise to a positive-feedback loop. This
compensation keeps spatial filtering invariant, while HC activity tracks the local average intensity ICO and CT activity becomes proportional
to contrast ICO /ICO . (b) Frequency responses: Both HC and CT act as lowpass filters, but HC has a longer space constant (i.e., h > c ). Thus,
HC inhibition eliminates low frequency signals, resulting in bandpass response in CT. This bandpass characteristic corresponds to an impulse
response (i.e., receptive field) with a small central excitatory region and a large surrounding inhibitory region.
as this is a current-mode circuit. I use the subscripts c
and h to denote cone and horizontal-cell; a pair of letters
denotes coupling between cells or to ground, which is
denoted by 0. And I use upper case symbols (e.g., Ih )
to represent the mean (i.e., DC) signal value, while
lower case ones (e.g., i h ) represent small instantaneous
deviations from the mean.
In the continuum limit, the outer retina circuit’s
small-signal (i.e., linear) behavior can be described in
terms of the contrast signals c ≡ i c /Ic and h ≡ i h /Ih
A Retinomorphic Chip with Parallel Pathways
as follows:
i0
cc0 UT
− h + αcc ∇ 2 c =
Ih
Ih
UT
c
h0
c + αhh ∇ 2 h =
Ih
dc
+c
dt
dh
dt
where ∇ 2 ≡ ∂ 2 /∂ x 2 + ∂ 2 /∂ y 2 . The absolute signal
levels arise because the transistors’ small-signal conductances and transconductances that model membrane conductances, gap junctions, and chemical
synapses are linearly proportional to the DC current
level in the subthreshold region. αcc and αhh are determined by the relative size of the transistors coupling
the cone nodes together and the bias voltage applied
to the transistors coupling the horizontal-cell nodes together [15]. UT ≡ kT /q is the thermal voltage. Notice
that the behavior is entirely linear in the contrast signals c and h, apart from the input attenuation and the
time-constants, which are controlled by Ih . However,
the time-constants track each other, making it easy to
maintain temporal stability.
In contrast, my earlier design [15,21], which relied
on high-gain negative feedback, is described by the
equations:
i0
Ic
cc0 UT dc
− h + αcc ∇ 2 c =
+ E c
Ih
Ih
Ih dt
c + αhh
Ih 2
ch0 UT dh
∇ h=
+ E h
Ic
Ic dt
where E ≡ UT /VE is the ratio between the thermal
voltage (25 mV at room temperature) and the Early
voltage (typically about 25 V). In comparison, the
HC-to-cone synaptic gain, Ach ≡ dc/dh, is a thousand
(i.e., 1/ E ) times smaller in the new circuit, while the
Table 1. Negative versus positive feedback.
Attenuation Damping-Factor Space-Constant Sensitivity
√
Neg
cc0 Ic
cc0 Ic + ch0 Ih
Ic I h
1
E Q I Ic + Ih /Q I
L I Ih
A I Ih
Pos
0
QI
LI
A I Ic
1/4
1/4
Ic is the mean cone activity, Ih is the mean horizontal cell activity,
which is proportional to light intensity, and E ≡ UT /VE is the
ratio between the thermal voltage and the Early voltage. Ideally, the
attenuation, a measure of low-frequency signals’ relative amplitude,
√
should be zero; the damping-factor Q I = cc0 /ch0 , a measure of
temporal stability, should be less than one; the space constant L I =
(αhh αcc )1/4 , a measure of receptive field size, should be independent
of Ih ; and the sensitivity A I = (L/αcc )Ih−1 , a measure of photosignal
amplification, should be inversely proportional to Ih .
125
cone-to-HC synaptic gain, Ahc ≡ dh/dc, is infinite—
for zero temporal and spatial frequencies (i.e., DC)—
due to 100% positive feedback.2 This positive feedback
arrangement was previously used to realize a fast
current-amplifier and buffer stage [24]. For nonzero
frequencies, the cone-to-HC synaptic gain is proportional to Ih (and hence to light intensity) in the new
circuit, due to the modulatory effect of horizontal-cell
autofeedback. The intensity-dependencies of the characteristics of these two circuits are compared in Table 1.
3.
Inner Retina Model
The inner retina performs lowpass and highpass temporal filtering and adapts its dynamics locally. Midget and
parasol ganglion cells receive synaptic inputs from both
bipolar and amacrine cells, but parasol cells receive
more amacrine input (i.e., feedforward inhibition)
[25–27], which accounts for their more transient response. Parasols also have larger dendritic fields and
are driven by bipolar cells with larger dendritic and
axonal fields than those that drive the midgets [8,28],
which accounts for their larger receptive fields. Presumably, both midget and parasol bipolar cells receive
presynaptic amacrine input (i.e., feedback inhibition)
at their terminals.
I hypothesize that a change in closed-loop gain
produces temporal adaptation, and that this gain is
controlled by modulating the strength of feedback inhibition. Figure 4(a) illustrates this retinal mechanism
for adapting temporal dynamics. A wide-field amacrine
cell (WA) modulates the strength of feedback (i.e.,
presynaptic) inhibition at the bipolar terminals (BT).
WA is excited by ON and OFF bipolars and inhibited by
ON and OFF narrow-field amacrine cells (NA). All these
synaptic interactions have been found in an anatomically identified amacrine cell type, called A19 [29].
These cells have thick dendrites, a large axodendritic
field, and are coupled together by gap junctions. Hence,
they can integrate and distribute signals rapidly over a
large area.
My inner-retina circuit model, which was motivated
by temporal adaptation, also accounts for contrast-gain
control in the retina. The classic result is that ganglion
cell responses compress in amplitude and time when
they are driven with larger and larger step changes in
intensity [30,31]. Victor and Shapley accounted for
both of these nonlinear effects by modeling the inner retina with a highpass temporal filter whose
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Boahen
Vwa
Bipolar
Cell
I bt+
Amacrine
Cell
I btVtq
Vt+ Vt-
Vtq
Vtq Vtq
Vna
I bt
Ganglion
Cell
Ic
Conduction
Modulation
Excitation
Inhibition
(a)
I na
Vss1
Vss1
(b)
Fig. 4. Morphing the inner retina I. (a) Neural microcircuit: The mechanism for modulating presynaptic inhibition at the bipolar terminal (BT)
is not known—my model assigns this role to a wide-field amacrine cell. Full-wave rectification is realized by convergence of ON and OFF
pathways. For moving stimuli, the gap-junction coupled WAs obtain signal energy by spatial integration. (b) Bipolar-terminal subcircuit: Unlike
the neural circuit, complementary signaling is not used for BCs and NAs and modulation occurs before lowpass filtering. The NA signal, Ina ,
is subtracted from the unrectified cone signal, Ic , to obtain the BT signal Ibt . A four-transistor rectifier produces ON and OFF BT signals (Ibt± ).
And a four-transistor subtractor takes the difference between Ibt+ and Ibt− and supplies it to the NA node (Vna )—Vwa modulates the current
level in the subtractor.
time-constant decreases with contrast [32]. At the functional level, the model I propose here is essentially identical to theirs. My contribution is to flesh out the neural
mechanisms by which contrast is measured and the
time-constant is adjusted. In the process, I assign specific roles to anatomically identified retinal cells and
their synaptic connections.
A system-level analysis of loop-gain modulation,
with the aid of the block diagram shown in Fig. 5(a),
and the Laplace transform, reveals that
τAs + i bc , i bt =
i bc ,
τAs + 1
τAs + 1
τAs
=
i bc
τAs + 1
i na =
i gc
(1)
for NA, BT, and the parasol ganglion cell (GC),
respectively, where,
τ A ≡ τna ,
≡ 1/(1 + Iwa /Iwa0 )
(2)
τna is the time-constant of NA and Iwa /Iwa0 is the modulation of its response by WA, whose response is Iwa0 for
zero frequency (i.e., static input). Thus, NA lowpassfilters the BC signal while BT highpass-filters it—these
filters have the same corner frequency, which is inversely proportional to the closed loop time-constant
τ A . Through the dependence of τ A on the modulation
level, the corner frequency becomes proportional to
WA activity, as shown in Fig. 5(b).
Feedforward inhibition produces a purely transient
response in parasol cells, whereas midgets, which do
not receive feedforward inhibition, have a sustained
component. This residual activity, i bt , increases as the
loop gain is reduced to lower the corner frequency—
and thus the BT response asymptotically approaches
an allpass filter. However, NA’s residual grows in the
same way, and cancels out BT’s residual in the parasol
ganglion cell, irrespective of the gain setting. Thus, a
purely highpass response is achieved—this is impossible with a finite-gain negative feedback loop.
The wide-field amacrine cell centers the corner frequencies of the highpass and lowpass filters on the input
spectrum. With BT-to-WA and NA-to-WA synapses of
equal strength, WA’s activity is given by
αww ∇ 2 i wa + i bt −
Iwa
i na = 0
Iwa0
(3)
where αww is the coupling strength between WAs—
normalized by the synaptic strength—and i is the
full-wave–rectified version of i; I have neglected WA’s
leakage conductance. Notice that WA modulates the inhibition it receives from NA, forming an autofeedback
loop analogous to that found in HCs. For low spatial
+-
BT
+-+
GC
NFA
127
BT
WFA
1
τnas+1
WA
Inhbited
BC
Excited
A Retinomorphic Chip with Parallel Pathways
NA
(a)
Temporal
Frequency
(b)
Fig. 5. Inner retina temporal filtering. (a) System-level concept: Visual signals are relayed from cone terminal to ganglion cell (GC) by the
bipolar cell (BC). They are also fed to a narrow-field amacrine cell (NA), which forms both negative-feedback and negative-feedforward loops.
Feedback strength is modulated by a wide-field amacrine cell (WA) that computes the difference between full-wave rectified (double arrows)
BT and NA signals. (b) Frequency responses: NA inhibition eliminates low frequencies, resulting in a highpass response in BT that has the same
corner frequency as the lowpass NA response. For frequencies above this corner frequency, BT excitation dominates and hence WA activity
rises, and it boosts NA inhibition. For frequencies below the corner frequency, on the other hand, NA inhibition dominates and hence WA activity
falls, and it throttles NA inhibition.
frequencies (i.e., on average), the Laplacian is close to
zero, and we have
Iwa
i bt |i bt |
≈
=
=
Iwa0
i na |i na |
2 ω2
τna
+1
where i
is the local spatial average of i. Notice that
Iwa = Iwa0 when ω = 0, hence the loop-gain is unity at
DC and i bt = i na = i bc /2. Substituting this expression
into equation (2) yields:
τA =
1+
τna
2 ω2
τna
+1
≈
τna /2 ω 1/τna
1/ω
ω 1/τna
Hence, the corner frequency 1/τ A tracks the input
frequency ω if it is higher than NA’s intrinsic cut-off
frequency 1/τna .
Such temporal adaptation could account for the
variation of ganglion cells’ temporal dynamics with
eccentricity. Neurobiologists have observed that both
midgets and parasols become more transient with increasing eccentricity, and the midget’s sustained component decreases [6,7]. Given that the input spectrum
shifts to higher temporal frequencies with increasing
eccentricity [33], this variation in temporal characteristics with eccentricity can be produced by a temporal
adaptation mechanism like the one proposed here.
Temporal adaptation in my inner-retina circuit
model also results in amplitude compression, or
so-called contrast-gain control. This compression is
evident if we transform the s-domain equations for i bt
and i na (equation (1)) into the time-domain:
τna di bt
τna di bc
i bc
+ i bt =
+
1 + w dt
1 + w dt
1+w
(4)
τna di na
i bc
+ i na =
1 + w dt
1+w
(5)
where w ≡ Iwa /Iwa0 . For a uniform intensity over a
large area, i bc = I0 , i na = i bt = I0 /2 and Iwa = Iwa0 . Immediately after the intensity is stepped to I1 , we have
i na = I0 /2 and i bt = I1 − I0 /2. Substituting these values
in equation (3) yields Iwa /Iwa0 = (I1 − I0 /2)/(I0 /2),
which equals 2c + 1, where c ≡ (I1 − I0 )/I0 is the
contrast. I have assumed that the outer-retina’s temporal filtering is infinitely fast and its intensity adaptation is infinitely slow, for simplicity. Replacing i bc with
(1+c)I0 , its derivative with cI0 δ(t), and w with 2c +1,
in the equation for i bt above yields
1 τna di bt
I0
τna
+ i bt =
1+
cδ(t)
2 1 + c dt
2
1+c
It is evident from this result that the time-constant shortens and the driving force compresses as contrast increases. In my model, this effect occurs at the bipolar
terminal, which passes it on to both sustained (midgetor X-like) and transient (parasol- or Y-like) ganglion
cells. Victor and Sharpley did observe contrast-gain
control in both X and Y ganglion cells in their experiments with cats [31].
A current-mode CMOS circuit I designed to implement inner retina temporal adaptation is shown in
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Boahen
I na-
I na+
Vsq
I na
Vn-
Vn+
I na+
I na-
Vaa
Vwa
Vss1 Vss1
I cq
Vcq
I bt+
I bt-
Vt+
Vt-
Vsq
Vn- Vn+
Vss1
(a)
(b)
Fig. 6. Morphing the inner retina II. (a) Narrow-field amacrine subcircuit: A reference current Icq , which matches the cone current’s mean level,
is subtracted from a copy of Ina produced by the bipolar-terminal (BT) circuit (shown in Fig. 4(b)), and the difference is rectified to obtain ON
and OFF narrow-field amacrine (NA) signals (Ina± ). (b) Wide-field amacrine subcircuit: Copies of the ON and OFF BT (Ibt± ) and NA (Ina± )
signals, obtained from the BT and NA circuits by connecting a second transistor in parallel, are sunk from or mirrored onto the WA node (Vwa )
to excite or inhibit it, respectively. Neighboring WA nodes are connected together by transistors to model their gap junctions.
Fig. 4(b). It does not include feedforward NA inhibition onto transient GCs. Nevertheless, like the retina,
it produces a highpass response by placing a lowpass
filter in a negative feedback loop. Thus, corner frequencies of the highpass and lowpass responses are
automatically matched. To compare the energies of the
highpass- and lowpass-filtered signals, it full-wave rectifies them, takes the difference, and integrates it over
space, using additional circuitry shown in Fig. 6.
In contrast, a similar time-constant adaptation
scheme proposed by Liu uses separate highpass
and lowpass filters, integrates the difference between their peak responses over time, and adjusts
their time-constants directly by changing the amplifiers’ bias currents [34]. This scheme—implemented
with a voltage-mode circuit—requires the amplifiers’
transconductances to be matched and adapts over several cycles. Since the edge moves on after a single
response cycle, it is imperative that adaptation occur
instantaneously and this information propagate quickly
to neighboring cells. Both objectives are achieved by
my retinomorphic circuit.
My inner-retina circuit model computes signal energy rapidly by using spatial integration, since, for a
moving stimulus, all phases of the response are available at different locations at the same instant. And it
uses the same averaging network to distribute the results quickly. This collective computation also makes
the retinomorphic approach more robust, compared
to peak-detection. Unfortunately, its CMOS implementation in Visio1 has a low-frequency temporal
instability—together with other shortcomings—that
was discovered during testing.
4.
Chip Design and Testing
I designed and fabricated a 4 × 52 × 48 ganglion-cell
chip, called Visio1, in a 1.2 µm (λ = 0.6 µm) double
poly, double metal, n-well CMOS process; its die size is
9.25×9.67 mm2 . Visio1’s architecture and pixel layout
are described in Fig. 7. Each pixel includes an adaptive silicon neuron that generates spikes [11], which are
read out by an asynchronous address-event transmitter
interface [35]. Ganglion-cell type is determined by decoding the LSB’s of row and column addresses. Visio1
was used in a real-time motion processing application,
as described in Section 5.
In addition to horizontal-cell autofeedback in the
outer retina and amacrine-cell loop-gain modulation
in the inner retina, Visio1 models cone-to-bipolar convergence, which makes the receptive-field center more
Gaussian-like [36]. According to my simulations, the
steeper frequency roll-off that results produces 60 dB
attenuation at 3.75 times the peak spatial frequency—
compared to 32 times the peak without convergence.
A Retinomorphic Chip with Parallel Pathways
Photoreceptors
142λ = 85.2µm
C H
WA
Convergence
Neuron
153λ = 91.8µm
Outer Retina
Phototransistor
Bipolar
Cells
129
1/4 Inner Retina
NA
Divergence
CurrentMirror
Integrator
Ganglion Cells
(a)
(b)
Fig. 7. Visio1 chip design. (a) Imager array architecture: Bipolar cells, which connect 7 photoreceptors to 4 ganglion cells (one of each type),
subsample the image by a factor of 4. A receptor either supplies its two identical output currents to one bipolar cell or to two neighboring cells.
Starting with an N × N receptor array, we end up with 4 × N /2 × N /2 ganglion-cell arrays. (b) Pixel layout: The pixel has 39 MOS transistors:
8 in the outer retina, 6 in the inner retina, and 16 in the neuron—plus 9 transistors in three delta-structures (with a common T-shaped gate)
that connect receptor (C), horizontal-cell (H), and wide-field-amacrine cell (WA) nodes to their six nearest neighbors. Unlike the schematic in
Fig. 2(b), the phototransistor’s current is mirrored first. The inner-retina circuit is spread across four pixels, with 6 transistors in two of them and
5 in the other two, for a total of 22. The subcircuit shown here produces the on-sustained output (i.e., Ina+ in Fig. 6(a)). In two of the pixels,
a poly1-poly2 capacitor—attached to the narrow-field amacrine node (NA)—replaces the well-transistor above the current-mirror integrator.
Pixels are tiled hexagonally by flipping those in every other column vertically.
High spatial frequencies must be eliminated to preserve the signal-to-noise ratio after highpass temporal
filtering, as these components produce proportionately
high temporal frequencies when the stimulus moves.
Further signal-to-noise enhancement may be realized
by convergence at the ganglion-cell level, which I am
yet to include—it would also reproduce the parasol
cells’ larger receptive fields.
Visio1 does not include synaptic interactions at the
ganglion-cell level; these will be added in the next
version. Unlike in Fig. 1(a), its ON and OFF ganglion
cells are driven by narrow-field amacrine (NA) signals
(Ina± in Fig. 6(a)), while its INCREASING and DECREASING ganglion cells are driven by bipolar-terminal (BT)
signals (Ibt± in Fig. 4(b)). Driving all four ganglion
cell types with BT signals and adding feedforward
NA inhibition onto the transient cells, like the retina
does, will make their responses more transient. Thus,
these ganglion-cell level synaptic interactions result in
a more efficient encoding, as they remove redundant
low-frequency signals.
Visio1’s light-spot responses are shown in Fig. 8;
these measurements demonstrate the effects of
horizontal-cell (HC) and amacrine-cell inhibition. HCs
inhibit neighboring spatial locations, giving rise to
the inhibitory surround which is evident in the OFF
response. While NAs inhibit focally, but with a delay, terminating the response in the INCREASING and
DECREASING cells. However, the spot escapes this
temporal lateral inhibition when it moves, giving rise
to INCREASING and DECREASING responses at the leading and trailing edges of the excitatory center and the
130
Boahen
(a)
(b)
Fig. 8. Response of retinomorphic chip to light spot. (a) Light spot stationary (located where the single active INCREASING cell is): ON cells
pick up the increased signal at the spot’s location while OFF cells pick up the decreased signal in surrounding region, due to lateral inhibition.
Fixed-pattern noise, due to transistor mismatch, is also evident. (b) Light spot moving up and to the right: INCREASING cells pick up the increases
at the excitatory center’s leading edge and at the inhibitory surround’s trailing edge, while DECREASING cells pick up the decreases at the
inhibitory surround’s leading edge and excitatory center’s trailing edge. The mean spike rate was 5 spikes/neuron/sec.
inhibitory surround. There is considerable variability—
especially among the sustained cells—due to transistor
mismatch, which was systematic, producing striations
oriented at about 30 degrees from vertical, like those
described in [37].
A raster plot of spike trains recorded from neurons in
a single column is shown in Fig. 9(b). Unfortunately,
crosstalk tended to make all the neurons fire when a
certain activity level was exceeded, so I had to keep
their mean firing rates below 10 Hz—several time less
than in the real retina. Nevertheless, the sequence in
which the four types fire is as predicted in Fig. 9(a).
Transient cells are more synchronized than sustained
ones, indicating that their inputs are larger—temporal
adaptation does not appear to be working as expected.
Also, the second half of the response sequence is
delayed—indicating either a refractory period (unlikely) or blurring in the outer retina, which occurs
when its temporal bandwidth is exceeded.
I expected to use the variable current-gain between
the rectifier and the subtractor in my inner retina circuit (see Fig. 4(b)) to modulate the loop-gain, but
that proved futile. The currents in the subtractor are
Awa Ibt± , with Awa ≡ e(Vpn + Vtq − Vwa )/UT , where Vpn ac-
counts for unequal pFET and nFET currents when
Vtq = Vwa , due to differences in body-effect and zerobias currents. Keeping in mind that the drain conductance gd of the subtractor’s output transistors is proportional to their current levels, we find that the voltage
change vna produced at node Vna for a given current
difference i bt ≡ Ibt+ − Ibt− is:
vna =
Awa i bt
Awa i bt
=
gd
Awa (Ibt+ + Ibt− )/VE
i bt
=
VE
Ibt+ + Ibt−
It is independent of the current-gain Awa .
Surprisingly, varying Vwa does not directly influence
the relationship between the narrow-field amacrine and
bipolar terminal signals in my circuit. Infact,
i na = gm vna =
Ina
κ VE
i bt
UT Ibt+ + Ibt−
where gm = κIna /UT is the feedback device’s transconductance. Hence, to modulate the loop gain, we must
change either Ina or Ibt± ≡ Ibt+ + Ibt− . Ina , the narrowfield amcrine current’s mean level, is set by Icq , the
A Retinomorphic Chip with Parallel Pathways
131
Motion
Spike Raster
Spatial
Bandpass
Speed, ν
λ
λ
Row Number
Speed, ν
All cells in Column 25
Space
Space
Time
λ/4
20ms bins
λ/4
Space
Space
Count
Temporal
Highpass &
Lowpass
5 spks
Spike Histogram
0.3s
Halfwave
Rectification
Time
Space
Space
OFF-Sus (--)
(a)
ON-Trans (-+)
ON-Sus (++)
OFF-Trans (+-)
(b)
Fig. 9. Spike rasters and histograms for moving edges. (a) Expected responses: Bandpass spatial filtering passes a particular wavelength λ and
rejects the others. Highpass and lowpass temporal filtering translates the response in space by λ/4. Half-wave rectification produces a sequence
of four responses that peak λ/4 apart, coinciding with the INCREASING, ON, DECREASING, and OFF parts of the cycle. Reversing the direction
reverses the temporal contrast, interchanging the increasing and decreasing responses. (b) Observed responses: Spike trains produced in response
to vertical bars moving at 12◦ /s (equals 32 pixels/s) were recorded from 4 × 45 neurons in the same column. During this 2.65 s recording, each
neuron fired 13 spikes, on average. The histogram, which combines all the spike trains from this single-trial multiple-neuron recording, confirms
that the four ganglion cell types provide a quadrature representation.
mean cone current level, which is constant (set by Vcq
in Fig. 2).
However, we can increase the mean bipolar terminal signal levels, Ibt± , by increasing Vwa , and thereby
reduce the loop-gain. This dependence arises because
the rectifier’s behavior is described by the following
circuit equations [18]:
2
Ibt+ Ibt− = Ibq
Ibt+ − Ibt− = Ic − Ina
where Ibq = I0 eκ Vwa /2UT . Ibt± will have to be several hundred times larger than Ina to achieve a loopgain of unity, due to the large ratio between the subthreshold MOS transistor’s transconductance and its
drain conductance (i.e., κ VE /UT ). But, of course, the
mean currents themselves also contribute to wide-field
amacrine excitation! Hence, the ratio Ina /(Ibt+ + Ibt− )
must remain close to unity, which means that the gain
stays large.
The wide-field amacrine network cannot reach equilibrium at DC if the loop-gain is high because the
bipolar-terminal signal is attenuated by the loop gain.
According to the theory, i bt = i na = i bc /(1 + w), at
DC, where w is the modulation. But the wide-field
amacrine is excited by i bt and inhibited by wi na . Hence,
at DC, excitation and inhibition are balanced when
w = 1. When w is large, WA is inhibited whenever
the cone current deviates significantly from the mean,
since |i na | ≈ |Ic − Icq | and |i bt+ | ≈ 0. And hence
Vwa increases, reducing current levels in the subtractor,
which eventually drop below the leakage currents.
132
Boahen
Low-frequency oscillations arise when the subtractor’s current are overwhelmed by leakage currents.
Assuming leakage from Vdd to Vna dominates, it
charges the capacitor, reducing Ina . If Ina = Ic > Icq initially, inhibition decreases while excitation increases.
Consequently, Vwa eventually repolarizes, restoring
current levels in the subtractor, which discharges Vwa
and initiates another cycle. Else, if Ina = Ic < Icq , both
excitation and inhibition increase, but inhibition remains dominant. Hence, Vwa never repolarizes. Assuming leakage to ground dominates, on the other hand, Vwa
still either oscillates or is permanently inhibited—it is
just that the inequalities for Ic are reversed.
For nonstatic images, we would expect the instability to disappear—it did not show up in simulations.
This was indeed the case. To determine how the loopgain and the time-constant change, let us start with the
KCL equation for node Vna :
dvna
+ gd vna = Awa i bt
dt
Substituting vna = i na /gm and gm = κ Ina /UT gives,
C
CUT d Ina
Awa (Ibt+ + Ibt− ) UT
+
i na = Awa i bt
κ Ina dt
Ina
κ VE
As the rectifier ensures that i bt = i c − i na , we obtain
the following differential equations for i na and i bt :
τna di na
+ (1 + )i na = i c
Awa dt
τna di bt
τna di c
+ i bt =
+ i c
Awa dt
Awa dt
where τna ≡ CUT /κ Ina and ≡ (UT /κ VE )((Ibt+ +
Ibt− )/Ina ) 1. The differential equation for i bt was obtained by substituting i na = i c −i bt into the i na equation.
These circuit equations differ from the model equations (equations (4) and (5))—the circuit’s cone current
i c , which is the analog of the model’s bipolar cell current i bc , is not modulated. Only the time-constants are
modulated—due to the changing drain-conductance—
much as in Liu’s approach [34]. Setting Awa = ωτna
equalizes the driving forces for these two equations
when the temporal frequency is ω, making the amplitudes of i bt and i na the same.
5.
Detecting Motion Direction
The four ganglion-cell types respond to a moving edge
in stereotyped sequences, which make it possible to
distinguish edges of one contrast or the other moving
in one direction or the other. An example is shown in
Fig. 9—swapping off and on or increasing and decreasing produces the other three sequences. Using Visio1
as a frontend, direction-selective (DS) cells can be built
simply by wiring up these four distinct receptive fields,
using virtual connections [38], as shown in Fig. 10.
What exactly do such DS cells compute? And what is
the effect of temporal adaptation?
To compute direction of motion, we can project the
gradient in spacetime ∇ I (x, t) ≡ (∂ I /∂ x, ∂ I /∂t) onto
the vector (λ, τ ), where the x-axis is perpendicular to
the edge, which moves in the positive x direction with
velocity ν ≡ (∂ I /∂t)/(∂ I /∂ x). That is,
∂I
∂I
∂I
+τ
= (λ + τ ν)
∂x
∂t
∂x
Hence, when λ and ν have the same sign (the preferred
direction), the projection’s amplitude is large. And
when λ and ν have opposite signs (the null direction),
the projection’s amplitude is small.
We can maximize the projection by adapting either
the length constant λ or the time-constant τ to make
(λ, τ ) point along the gradient. To do this, we must
equalize the spatial and temporal components of the
projection:
∂I ∂I λ = τ ⇔ λ = ∂ I /∂t ≡ ν
∂ x ∂t τ
∂ I /∂ x (λ, τ ) · ∇ I (x, t) = λ
In so doing, we obtain a response of 2λ(∂ I /∂ x) in
the prefered direction—independent of speed—and the
response in the null-direction disappears. The timeconstant adaptation version of this strategy is accomplished by my inner retina temporal adaptation
mechanism, which acts to equalize highpass and lowpass responses (see Fig. 4(a)).
Translating the bandpass-filtered image J (x, t) by
λ/4 in the negative x direction yields the spatial
derivative—scaled by λ/2π . To obtain this approximate result, assume that the spatial filter passes the
frequency 2π/λ—and rejects all other frequencies. In
that case, the derivative is
∂J
∂
2π x
2π
2π x
=
sin
− νt =
cos
− νt
∂x
∂x
λ
λ
λ
2π
J (x − λ/4, t)
λ
Highpass temporal filtering yields an image
K hp (x, t) that is the temporal derivative of a lowpass
filtered version K lp (x, t) of the original image—scaled
=
A Retinomorphic Chip with Parallel Pathways
133
Response
(mV) 450
400
350
300
Speed
(rps)
0.5
1
1.5
2
2.5
0.5
1
1.5
2
2.5 (rps)
Response
(mV) 450
400
350
300
250
Speed
Response
(mV) vs
Orientation
160 Photoreceptors
300
200
100
-200 -100
-100
n
Motio
40
Ganglion
Cells
100 200 300
-200
1 DS Cell
Fig. 10. Direction-selective neurons. Retinal operations—bandpass spatial filtering and highpass temporal filtering—compute the gradient in
spacetime, assuming the bandpass passes only the wavelength λ and the lowpass temporal filter compensates for the highpass’ saturation above
1/τ (upper-left panel). The amplitude of the gradient’s projection onto the vector (λ, τ ) is obtained by summing signals from four types of
ganglion cells λ/4 apart—two places away in our case (lower-left). These spatial quadrature phase-shifts match the ganglion cells’ temporal
quadrature phase-shifts when a black–white edge moves in the direction shown, and hence all four responses peak simultaneously. Measurements
reveal a clear preference for contrast polarity and motion direction in a target cell with this receptive field, for speeds from 4 to 40◦ /s—equivalent
to 10.7 to 107 pixels/s (upper right). At the best speed, its direction-tuning is broad and centered around −60◦ (lower right).
by τ/2π . To obtain this approximate result, assume that
the highpass and lowpass filters have the same corner
frequency 2π/τ . In that case, making use of the Laplace
transform, the derivative is
∂ K lp
2π
L
= s Hlp (s)J (x, s) =
Hhp (s)J (x, s)
∂t
τ
2π
=
L{K hp (x, t)}
τ
since the filters’ transfer functions are related by
Hhp (s) = τ s Hlp (s)/2π , if the frequency is in Hz.
Hence, we obtain an exact temporal derivative if we
replace the original image with the lowpass filtered
one.
Therefore, to obtain the projection of the spacetime gradient ∇ I (x, t) onto (λ, τ ), pass the translated
bandpass-spatial-filtered image through a lowpass temporal filter and the untranslated image through a high-
pass temporal filter and sum their outputs together
(see Fig. 10). And maximize the projection by equalizing the output amplitudes of these two filters through
temporal adaptation. This adaptation makes the retina
exquisitely sensitive to motion by matching the inner
retina’s delay to the time-of-flight across outer-retina
receptive fields. I implemented this algorithm by wiring
up Visio1’s ganglion cells to silicon neurons on a second neuromorphic chip [11] as shown in Fig. 10. I
measured clear preferences for contrast polarity and
motion direction for speeds spanning one decade, even
though temporal adaptation was not working correctly.
This retinomorphic motion algorithm is a practical
version of Watson and Ahumada’s Hilbert-transformbased model of human visual-motion sensing [39]. In
their model, the spatially and temporally bandpass filtered image is Hilbert-transformed spatially and temporally, and summed with itself. A Hilbert transform
134
Boahen
phase-shifts each frequency component by 90◦ —its
amplitude remains unchanged. I approximate a spatial Hilbert transform by translating by λ/4—a phase
difference of exactly 90◦ for the peak frequency. And
I approximate a temporal Hilbert transform by equalizing the highpass and lowpass output amplitudes—
which have a phase difference of exactly 90◦ . EtienneCummings et al.’s implementation of Adelson and
Bergen’s [40] closely-related spatiotemporal energy
model is quite similar [41,42]—but it lacks the adaptive
temporal dynamics provided by the Hilbert transform.
6.
Conclusions
I reverse-engineered outer and inner retina microcircuits and morphed them into CMOS circuits to implement parallel visual pathways on a silicon chip. These
micropower current-mode retinomorphic circuits are
fairly compact, allowing several levels of processing
to be performed at the focal plane. By going a step
further than previous retinomorphic chips [10,11] and
including inner-retina processing, I modeled the four
predominant ganglion-cell types in the primate retina.
In addition to improving spike-coding efficiency,
these specialized visual channels provide more robust
primitives for computing optical flow than differentiation and division, which most gradient-based algorithms call for [43,44]. Adaptive inner-retina temporal
dynamics extend the dynamic range for motion—just
like adaptive outer-retina amplification extends the dynamic range for intensity. Unfortunately, my present
design failed to modulate the loop-gain; I am redesigning it to rectify this. Nevertheless, and despite extremely limited mean firing rates of 5 Hz, I demonstrated direction-selectivity over one decade of speed.
Acknowledgments
I was a doctoral student at Caltech, in Carver Mead’s
lab, when I begun this project, where it was funded by
ONR; DARPA; and NSF’s ERC Program. It is currently
funded by start-up funds from University of Pennsylvania’s Engineering and Medical Schools (through the Institute of Medicine and Engineering) and the Whitaker
Foundation. I thank Masahide Nomura, Eduardo Ros
Vidal, and Rufin VanRullen for their help in programming the projective-field processor board to implement
DS receptive fields at the 1998 Telluride Neuromorphic
Engineering Workshop.
Notes
1. The rod pathway does fine with a single channel because its mean
activity is virtually zero.
2. These synaptic gains are obtained by setting the temporal and
spatial derivatives equal to zero and differentiating the first and
second equation, respectively.
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Kwabena A. Boahen is an assistant professor in
the Bioengineering Department at the University of
Pennsylvania, Philadelphia PA, where he holds a
Skirkanich Term Junior Chair and a secondary appointment in electrical engineering. He received a Ph.D. in
computation and neural systems from the California
Institute of Technology, Pasadena, CA in 1997, where
he held a Sloan Fellowship for Theoretical Neurobiology. He earned B.S. and M.S.E. degrees in electrical and computer engineering from the Johns Hopkins
University, Baltimore MD, in the concurrent masters–
bachelors program, in 1989, where he made Tau Beta
Kappa. His current research interests include mixedmode multichip VLSI models of biological sensory
and perceptual systems, and their epigenetic development, and asynchronous digital interfaces for interchip
connectivity.
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