An Analog VLSI Model of the Fly 
Elementary Motion Detector 
Reid R. Harrison and Christof Koch 
Computation and Neural Systems Program, 139-74 
California Institute of Technology 
Pasadena, CA 91125 
[harrison, koch] @klab. caltech. edu 
Abstract 
Flies are capable of rapidly detecting and integrating visual motion in- 
formation in behaviorly-relevant ways. The first stage of visual motion 
processing in flies is a retinotopic array of functional units known as el- 
ementary motion detectors (EMDs). Several decades ago, Reichardt and 
colleagues developed a correlation-based model of motion detection that 
described the behavior of these neural circuits. We have implemented a 
variant of this model in a 2.0-/tin analog CMOS VLSI process. The re- 
sult is a low-power, continuous-time analog circuit with integrated pho- 
toreceptors that responds to motion in real time. The responses of the 
circuit to drifting sinusoidal gratings qualitatively resemble the temporal 
frequency response, spatial frequency response, and direction selectivity 
of motion-sensitive neurons observed in insects. In addition to its pos- 
sible engineering applications, the circuit could potentially be used as a 
building block for constructing hardware models of higher-level insect 
motion integration. 
1 INTRODUCTION 
Flies rely heavily on visual motion information to survive. In the fly, motion information is 
known to underlie many important behaviors including stabilization during flight, orienting 
towards small, rapidly-moving objects (Egelhaaf and Borst 1993), and estimating time-to- 
contact for safe landings (Borst and Bahde 1988). Some motion-related tasks like extending 
the legs for landing can be excecuted less than 70 milliseconds after stimulus presentation. 
The computational machinery performing this sensory processing is fast, small, low-power, 
and robust. 
There is good evidence that motion information is first extracted by local elementary mo- 
tion detectors (see Egelhaaf et al. 1988 and references therein). These EMDs are ar- 
An Analog VII Model of the Fly Elementary Motion Detector 881 
a) b) 
EMD Architecture 
photoreeeptors 
high-pass filters 
low-pass filters 
multipliers 
subtraction 
4 Aq , 
EMD output 
0.9 
0.8 
0.7 
.o.6 o 
o 
o 100 150 
50 100 150 200 250 300 350 
time [ms] 
20O 250 30O 350 
time [ms] 
Figure 1: Elementary Motion Detector. a) A simplified version of our EMD circuit ar- 
chitecture. In the actual circuit implementation, there are separate ON and OFF channels 
that operate in parallel. These two channels are summed after the muliplication. b) The 
measured response of the EMD test circuit to a drifting sinusoidal grating. Notice that the 
output is phase dependent, but has a positive mean response. If the grating was drifting in 
the opposite direction, the circuit would give a negative mean response. 
ranged retinotopically, and receive input from adjacent photoreceptors. The properties of 
these motion-sensitive units have been studied extensively during the past 30 years. Direct 
recording from individual EMDs is difficult due to the small size of the cells, but much 
work has been done recording from large tangential cells that integrate the outputs of many 
EMDs over large portions of the visual field. From these studies, the behavior of individual 
EMDs has been inferred. 
If we wish to study models of motion integration in the fly, we first need a model of the 
EMD. Since many motion integration neurons in the fly are only a few synapses away 
from muscles, it may be possible in the near future to contract models that complete the 
sensorimotor loop. If we wish to include the real world in the loop, we need a mobile 
system that works in real time. In the pursuit of such a system, we follow the neuromorphic 
engineering approach pioneered by Mead (Mead 1989) and implement a hardware model of 
the fly EMD in a commercially available 2.0-m CMOS VLSI process. All data presented 
in this paper are from one such chip. 
2 ALGORITHM AND ARCHITECTURE 
Figure 1 a shows a simplified version of the motion detector. This is an elaborated version of 
the correlation-based motion detector first proposed by Reichardt and colleagues (see Re- 
ichardt 1987 and references therein). The Reichardt motion detector works by correlating 
(by means of a multiplication) the response of one photoreceptor to the delayed response 
of an adjacent photoreceptor. Our model uses the phase lag inherent in a low-pass filter 
to supply the delay. The outputs from two mirror-symmetric correlators are subtracted to 
remove any response to full-field flicker (ws = 0, wt > 0). 
Correlation-based EMDs are not pure velocity sensors. Their response is strongly affected 
by the contrast and the spatial frequency components of the stimulating pattern. They 
can best be described as direction-selective spatiotemporal filters. The mean steady-state 
response R of the motion detector shown in Figure 1 a to a sinusoidal grating drifting in one 
direction can be expressed as a separable function of stimulus amplitude (AI), temporal 
882 tL R. Harrison and C. Koch 
a) 
positive component of Cd l 
negative component of C--ff $ 
dV 
i-- - 
b) 
dlout 
  + 10u t = Iin 
CUr 
c) 
'' lout = lref 
Figure 2: EMD Subcircuits. a) Temporal derivative circuit. In combination with the first- 
order low-pass filter inherent in the photoreceptor, this forms the high-pass filter with time 
constant rH. The feedback amplifier enforces V - V/,, and the output is the current 
needed for the nFET or pFET source follower to charge or discharge the capacitor U. 
b) Current-mode low-pass filter. The time constant r is determined by the bias current L- 
(which is set by a bias voltage supplied from off-chip), the capacitance 6', and the thermal 
voltage U, = kT/q. c) Current-mode one-quadrant multiplier. The devices shown are 
floating-gate nFETs. Two control gates capacitively couple to the floating node, forming a 
capacitive divider. 
frequency (cot = 27rft), and spatial frequency (co, = 27r f,): 
where Aq is the angular separation of the photoreceptors, r is the time constant of the 
high-pass filter, and r is the time constant of the low-pass filter (see Figure 1 a). (Note 
that this holds only for motion in a particular direction. Motion detectors are not linearly 
separable overall, but the single-direction analysis is useful for making comparisons.) 
3 CIRCUIT DESCRIPTION 
In addition to the basic Reichardt model described above, we include a high-pass filter in 
series with the photoreceptor. This amplifies transient responses and removes the DC com- 
ponent of the photoreceptor signal. We primarily use the high-pass filter as a convenient 
circuit to switch from a voltage-mode to a current-mode representation (see Figure 2a). 
For the photoreceptor, we use an adaptive circuit developed by Delbrfick (Delbrfick and 
Mead 1996) that produces an output voltage proportional to log intensity. We bias the pho- 
toreceptor very weakly to attenuate high temporal frequencies. This is directly followed by 
a temporal derivative circuit (Mead 1989) (see Figure 2a), the result being a high-pass filter 
with the dominant pole r being set by the photoreceptor cutoff frequency. The outputs 
of the temporal derivative circuit are two unidirectional currents that represent the positive 
and negative components of a high-pass filtered version of the photoreceptor output. This 
resembles the ON and OFF channels found in many biological visual systems. Some stud- 
ies suggest ON and OFF channels are present in the fly (Franceschini et al. 1989) but the 
evidence is mixed (Egelhaafand Borst 1992). This two-channel representation is useful for 
current-mode circuits, since the following translinear circuits work only with unidirectional 
An Analog VII Model of the Fly Elementary Motion Detector 883 
' 0.6 
,. 
0.2 
0.1 
silicon t. ;7 ',. , 
o ,, -..// \ ', 
..... o / ,,  ',,, ,, 
1 10 100 
Temml Fruen [Hz] 
Figure 3: Temporal Frequency Response. Circuit data was taken with fs = 0.05 cycles/deg 
and 86% contrast. Theory trace is lrt(oJt) from Equation 2, where r/-t = 360 ms and r 
= 25 ms were directly measured in separate experiments - these terms were not fit to the 
data. Insect data was taken from a wide-field motion neuron in the blowfly Calliphora 
erythrocephala (O'Carroll et al. 1996). All three curves were normalized by their peak 
response. 
currents. It should be noted that the use of ON and OFF channels introduces nonlinearities 
into the circuit that are not accounted for in the simple model described by Equation 2. 
The current-mode low-pass filter is shown in Figure 2b. The time constant rt is set by the 
bias current I-. This is a log-domain filter that takes advantage of the exponential behavior 
of field-effect transistors (FETs) in the subthreshold region of operation (Minch, personal 
communication). 
The current-mode multiplier is shown in Figure 2c. This circuit is also translinear, using a 
diode-connected FET to convert the input currents into log-encoded voltages. A weighted 
sum of the voltages is computed with a capacitive divider, and the resulting voltage is 
exponentiated by the output FET into the output current. The capacitive divider creates 
a floating node, and the charge on all these nodes must be equalized to ensure matching 
across independent multipliers. This is easily accomplished by exposing the chip to UV 
light for several minutes. This circuit represents one of a family of floating-gate MOS 
translinear circuits developed by Minch that are capable of computing arbitrary power laws 
in current mode (Minch et al. 1996). 
After the multiplication stage, the currents from the ON and OFF channels are summed, 
and the final subtraction of the left and right channels is done off-chip. There is a gain 
mismatch of approximately 2.5 between the left and right channels that is now compensated 
for manually. This mismatch must be lowered before large on-chip arrays of EMDs are 
practical. A new circuit designed to lessen this gain mismatch is currently being tested. 
It is interesting to note that there is no significant offset error in the output currents from 
each channel. This is a consequence of using translinear circuits which typically have gain 
errors due to transistor mismatch, but no fixed offset errors. 
4 EXPERIMENTS 
As we showed in Equation 2, the motion detector's response to a drifting sinusoidal grating 
of a particular direction should be a separable function of AI, temporal frequency, and 
884 R. R. Harrison and C. Koch 
'5 0.2 
0.00t 
silicon 
o 
..... ?ory 
0.01 0,1 
Spatial FrequenCYfs [cycledeg] 
Figure 4: Spatial Frequency Response. Circuit data was taken with ft = 4 Hz and 86% 
contrast. Theory trace is Rs (ws) from Equation 2 multiplied by exp (-ws 2/K 2 ) to account 
for blurting in the optics. The photoreceptor spacing Aq = 1.9  was directly measured in 
an separate experiment. Only K and the overall magnitude were varied to fit the data. 
Insect data was taken from a wide-field motion neuron in the hoverfly Volucellapelluscens 
(O'Carroll et al. 1996). Circuit and insect data were normalized by their peak response. 
spatial frequency. We tested the circuit along these axes using printed sinusoidal gratings 
mounted on a rotating dram. A lens with an 8-ram focal length was mounted over the chip. 
Each stimulus pattern had a fixed contrast AI/2 and spatial frequency rs. The temporal 
frequency was set by the pattem's angular velocity v as seen by the chip, where ft = fsv. 
The response of the circuit to a drifting sine wave grating is phase dependent (see Fig- 
ure lb). In flies, this phase dependency is removed by integrating over large numbers of 
EMDs (spatial integration). In order to evaluate the performance of our circuit, we mea- 
sured the mean response over time. 
Figure 3 shows the temporal frequency response of the circuit as compared to theory, and to 
a wide-field motion neuron in the fly. The circuit exhibits temporal frequency ming. The 
point of peak response is largely determined by rL, and can be changed by altering the low- 
pass filter bias current. The deviation of the circuit behavior from theory at low frequencies 
is thought to be a consequence of crossover distortion in the temporal derivative circuit. At 
high temporal frequencies, parasitic capacitances in current mirrors are a likely candidate 
for the discrepancy. The temporal frequency response of the blowfly Calliphora is broader 
than both the theory and circuit curves. This might be a result of time-constant adaptation 
found in blowfly motion-sensitive neurons (de Ruyter van Steveninck et aL 1986). 
Figure 4 shows the spatial frequency response of the circuit. The response goes toward zero 
as ws approaches zero, indicating that the circuit greatly attenuates full-field flicker. The 
circuit begins aliasing at ws = 1/2A, giving a response in the wrong direction. Spatial 
aliasing has also been observed in flies (G6tz 1965). The optics used in the experiment act 
as an antialiasing filter, so aliasing could be avoided by defocusing the lens slightly. 
Figure 5 shows the directional tuning of the circuit. It can be shown that as long as the 
spatial wavelength is large compared to A, the directional sensitivity of a correlation- 
based motion detector should approximate a cosine function (Zanker 1990). The circuit's 
performance matches this quite well. Motion sensitive neurons in the fly show cosine-like 
direction selectivity. 
Figure 6 shows the contrast response of the circuit. Insect EMDs show a saturating contrast 
An Analog VII Model of the Fly Elementary Motion Detector 885 
0.4 
o. 
o 
-0.4  
-0.6 
-0.8 
-150 -100 -50 0 50 100 150 
Direction of Motion [dcg] 
Figure 5: Directional Response. Circuit data was taken with ft = 6 Hz, fs = 0.05 cycles/deg 
and 86% contrast. Theory trace is cos ct, where ct is the direction of motion relative to 
the axis along the two photoreceptors. Insect data was taken from the H1 neuron in the 
blowfly Calliphora erythrocephala (van Hateren 1990). HI is a spiking neuron with a low 
spontaneous firing rate. The flattened negative responses visible in the graph are a result of 
the cell's limited dynamic range in this region. All three curves were normalized by their 
peak response. 
response curve, which can be accounted for by introducing saturating nonlinearities before 
the multiplication stage (Egelhaaf and Borst 1989). We did not attempt to model contrast 
saturation in our circuit, though it could be added in future versions. 
5 CONCLUSIONS 
We implemented and tested an analog VLSI model of the fly elementary motion detector. 
The circuit's spatiotemporal frequency response and directional selectivity is qualitatively 
similar to the responses of motion-sensitive neurons in the fly. This circuit could be a useful 
building block for constructing analog VLSI models of motion integration in flies. As an 
integrated, low-power, real-time sensory processor, the circuit may also have engineering 
applications. 
Acknowledgements 
This work was supported by the Center for Neuromorphic Systems Engineering as a part 
of NSF's Engineering Research Center program, and by ONR. Reid Harrison is supported 
by an NDSEG fellowship from ONR. We thank Bradley Minch, Holger Krapp, and Rainer 
Deutschmann for invaluable discussions. 
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o 
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02 
0 
Cont M[[%] 
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