TB, DP, US, JNE/441349, 8/10/2012
IOP PUBLISHING
JOURNAL OF NEURAL ENGINEERING
J. Neural Eng. 9 (2012) 000000 (13pp)
UNCORRECTED PROOF
Artificial retina : the multichannel
processing of the mammalian retina
achieved with a neuromorphic
asynchronous light acquisition device
Henri Lorach 1,2,3 , Ryad Benosman 1,2,3 , Olivier Marre 1,2,3 ,
Sio-Hoi Ieng 1,2,3 , José A Sahel 1,2,3,4,5,6 and Serge Picaud 1,2,3,6,7
1
INSERM, U968, Institut de la Vision, 17 rue Moreau, Paris, F-75012, France
UPMC Univ Paris 06, UMR_S968, Institut de la Vision, 17 rue Moreau, Paris, F-75012, France
3
CNRS, UMR 7210, Institut de la Vision, 17 rue Moreau, Paris, F-75012, France
4
Centre Hospitalier National d’Ophtalmologie des Quinze-Vingts, 28 rue Charenton, Paris, F-75012,
France
5
Institute of Ophthalmology, University College of London, London, UK
6
Fondation Ophtalmologique Adolphe de Rothschild, 25 rue Manin, Paris, F-75019, France
2
E-mail: [email protected]
Received 1 August 2012
Accepted for publication 25 September 2012
Published DD MM 2012
Online at stacks.iop.org/JNE/9/000000
Abstract
Objective. Accurate modeling of retinal information processing remains a major challenge in
retinal physiology with applications in visual rehabilitation and prosthetics. Most of the
current artificial retinas are fed with static frame-based information, loosing thereby the
fundamental asynchronous features of biological vision. The objective of this work is to
reproduce the spatial and temporal properties of the majority of ganglion cell (GC) types in the
mammalian retina.
Approach. Here, we combined an asynchronous event-based light sensor with a model pulling
nonlinear subunits to reproduce the parallel filtering and temporal coding occurring in the
retina. We fitted our model to physiological data and were able to reconstruct the
spatio-temporal responses of the majority of GC types previously described in the mammalian
retina (Roska et al 2006 J. Neurophysiol. 95 3810–22).
Main results. Fitting of the temporal and spatial components of the response was achieved
with high coefficients of determination (median R2 = 0.972 and R2 = 0.903, respectively).
Our model provides an accurate temporal precision with a reliability of only few
milliseconds—peak of the distribution at 5 ms—similar to biological retinas (Berry et al 1997
Proc. Natl Acad. Sci. USA 94 5411–16; Gollisch and Meister 2008 Science 319 1108–11). The
spiking statistics of the model also followed physiological measurements (Fano factor : 0.331).
Significance. This new asynchronous retinal model therefore opens new perspectives in the
development of artificial visual systems and visual prosthetic devices.
Q1 (Some figures may appear in colour only in the online journal)
7
Author to whom any correspondence should be addressed.
1741-2560/12/000000+13$33.00
1
© 2012 IOP Publishing Ltd
Printed in the UK & the USA
J. Neural Eng. 9 (2012) 000000
H Lorach et al
Introduction
to temporal contrasts could be partially reproduced. However,
they still lacked the temporal precision of biological GCs and
did not respond to temporal frequencies higher than 10 Hz as
opposed to mammalian retinas. Moreover, this artificial retina
did not perform the complex feature extractions of the other
cell types.
The advantage in using neuromorphic technology is
straightforward. First, the entire computation is performed in
situ and does not need any dedicated processor, meaning a
more compact device. Secondly, the hardware implementation
of processing makes it low power consuming. And lastly,
visual information can be sampled and processed in parallel
over the entire field of view, matching thereby the retinal
temporal resolution. However, implementing the entire retinal
network in silico would require the integration of some 50
different cell types of interneuron and GCs [10]. In this
context, there is no existing acquisition device able to output
the majority of GC responses with the necessary temporal
precision.
Here, we have implemented an intermediate strategy
based on an asynchronous dynamic vision sensor (DVS) [25]
also called ‘silicon retina’ by the inventors. This sensor detects
local temporal contrasts but does not introduce temporal
and spatial integrations occurring in biological retinas. It
provides information about local light increments (ON) and
decrements (OFF). The purpose of this work was to produce a
computational model accounting for these integrations thereby
matching temporal and spatial properties of different retinal
GC types of the mammalian retina described in the literature
[1]. The novelty in this study is to use this new asynchronous
sensor instead of a classic frame-based camera to feed
a computational model of retinal information processing
keeping thereby the asynchronous properties of biological
vision.
The mammalian retina samples and compresses visual
information before sending it to the brain through the optic
nerve. Complex features are already extracted by the retinal
neural network such as movements in horizontal and vertical
directions by direction selective cells and even expanding
patterns [4, 5]. These feature extractions are not only very
precise in the spatial domain but also in the temporal domain.
Indeed, light responses to random patterns were found to
be reproducible with a millisecond precision [2, 3]. Moreover,
the ganglion cell (GC) response latencies can reach 30 ms in the
primate retina [6] allowing thereby fast behavioral responses.
For instance, static visual stimuli were shown to allow motor
decision and the resulting motor response as early as 160 ms in
monkeys and around 220 ms in human subjects [7–9]. Visual
prosthetic strategies should match retinal processing speed and
temporal precision. While some 20 different types of retinal
GCs have been morphologically identified in mammals [10],
more than half were individually recorded [11] such that the
responses to a given visual stimulation could be reconstructed
in different populations of retinal GCs [1].
To further understand biological vision, various
computational models of the retina were developed. Some
have intended to implement each biophysical step from
phototransduction at the level of photoreceptors (PRs) to
spike initiation in GCs [12, 13]. These models involve a
series of nonlinear differential equations ruling the biophysical
processes involved in retinal signaling. Although they reach
a high level of detail, these models are not suited for
large-scale simulations of retinal responses. Other models
are more functional and combine a linear filtering of the
light signal followed by a static nonlinearity and spike
generation models [3, 2, 14, 15]. The spike generation
mechanism can be either deterministic or probabilistic
[15–17]. These models are qualified as linear–nonlinear (LN)
and are computationally inexpensive because they involve
linear convolution operations. However, they do not reproduce
responses to natural stimuli for the vast majority of GC types
[5] because retinal GCs are often selective to multiple visual
features at the same time. For example, ON–OFF direction
selective cells cannot be modeled by the LN approach because
both ON (light increase) and OFF (light decrease) information
are summed nonlinearly. Moreover, their implementation often
relies on visual scene acquisition based on conventional
synchronous cameras [18, 19]—as found in retinal implant
devices [20].
An alternative approach is offered by recent developments
in the field of neuromorphic devices. The principle of
neuromorphic engineering is to build electronic circuits that
mimic a neural processing [21] such as visual cortical
functions: orientation detection and saliency mapping [22].
Synapses and electrical coupling are replaced by transistors
and cell membranes by capacitors. Neuromorphic retinas, in
particular, have been developed for mapping retinal network
in silico and were able to output four GC types—ON and OFF
transient and sustained cells [23, 24]. Their spatio-temporal
filtering properties as well as light adaptation and responses
Methods
Event-based sensor
The temporal contrast DVS [25] that will be used in the rest
of the paper is an array of 128 × 128 autonomous pixels, each
of them asynchronously generating ‘spike’ events that encode
relative changes in pixel illumination, discarding the absolute
light value. The DVS does not deliver classical image data in
the form of static pictures with absolute intensity information.
Rather, the device senses the temporal contrast information
present in natural scenes at temporal resolutions much higher
than what can be achieved with most conventional sensors. In
addition, temporal redundancy that is common to all framebased image acquisition techniques is largely suppressed. The
digital event addresses containing the position of the pixel and
the polarity of the events are asynchronously and losslessly
transmitted using a four-phase handshake. The event ek is
defined by its spatial position (xk , yk ), polarity pk and time
of occurrence tk :
ek = (xk , yk , pk , tk ).
(1)
The analogue visual information is therefore encoded in the
relative timing of the pulses. For a detailed description of the
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H Lorach et al
(a)
(b)
(c)
(d)
Figure 1. Principle and output signals from an asynchronous dynamic vision sensor (DVS). (a) Sampling of light intensity into positive and
negative events by an individual pixel. The logarithm of the intensity log(I) reaching the pixel (top trace) drives the pixel voltage. As soon as
the voltage is changed by ±θ , since the last event from this pixel, an event is emitted (middle) and the pixel becomes blind during a given
refractory period. Events generated by the sensor convey the timing of the threshold crossing and the polarity of the event (bottom). Positive
events are plotted in red, negative events in blue. (b) 3D plot of the recorded signal from the dynamic vision sensor viewing a translating
black disc. The position (x, y) and time t of the events are plotted along with the plan of motion. Positive events appear in red and negative
events in blue, together drawing a tubular surface. (c) Experimental design to assess the temporal resolution of the dynamic vision sensor
with respect to that of a classic frame-based camera. Both devices were placed in front of a blinking LED. From the DVS signal, the
blinking duration could be measured as the time difference between first positive events and first negative events (τDVS ). The duration
measured by the camera was the time difference between the time of the frame with light on and first frame with light off τframe .
(d) Performances of the sensors. The frame-based camera (red triangles) was not able to measure a blinking duration below 40 ms. It was
limited by the sampling period of 33 ms. This behavior explains the horizontal asymptote for short durations of τLED . For higher values,
τframe follows linearly the blinking duration. In contrast, the DVS (black squares) can measure blinking durations as low as 2 ms and follows
the ideal linear behavior from 2 ms to 1 s.
light sources are indeed driven by alternating current, thus
generating artifactual events. Adjusting the biases of the DVS
could remove this effect by increasing the refractory period of
the pixels. However, it would lower the temporal reliability of
the sensor. To avoid flickering effects, we only used continuous
illumination conditions in our experiments.
To give a graphic representation of the sensors output,
a spacetime plot of the events can be drawn (figure 1(b)).
Here, the stimulus consisted in a translating black disc. Moving
edges generated either positive (red in figure 1(b)) or negative
(blue in figure 1(b)) events with a sub-millisecond temporal
resolution. Thermal noise inside the pixels generated diffuse
events occurring randomly over the array. In this work, we
sensor, see [25]. Briefly, it generates positive and negative
events whenever the light intensity reaches a positive or
negative threshold. This threshold is adaptive and follows a
logarithmic function thus mimicking PRs adaptation. This
sampling strategy for each pixel is summarized in figure 1(a).
The light intensity I reaching the pixel is scaled by a log
function (top). Every time log(I) is increased by θ from the last
event, a positive event is emitted (middle). When it decreases
by θ , a negative event is generated. A refractory period during
which the pixel is blind limits the transmission rate of the
sensor. This period is of the order of tens of microseconds.
Therefore, very fast temporal variations of the light input
can be sampled accurately and particular attention had to be
paid to avoid flickering induced by artificial ac light. Some
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J. Neural Eng. 9 (2012) 000000
H Lorach et al
used the DVS (#SN128-V1-104) with a lens Computar (16 mm
1:1.4) at nominal biases.
Temporal precision assessment
To assess the timing resolution of the DVS compared to a
conventional camera, an LED was controlled with a microcontroller (Arduino UNO) to deliver light flashes of duration
τLED ranging between 1 ms and 1 s; we examined the minimum
timing for detecting a flash with either a conventional 30 Hz
R
C500) or the dynamic vision sensor. From
camera (Logitech
the DVS signal, the blinking duration could be measured as
the time difference between the first positive events and the
first negative events (τDVS ), while it was the time difference
between the time of the frame with light on and the first
frame with light off (τframe ) for the frame-based camera.
Figure 2. Implementation principle. The DVS generates events (x, y,
p, t) encoded by their position, polarity and time of occurrence (1).
These events are transmitted to a computer (2) through a USB
connection. The timing t of the incoming event is binned at a
millisecond precision t . The state of the current (I) of 128×128
cells is updated every millisecond (3). The new events contributes to
the evolution of I by the addition of the spatial kernel (4). From this
updated value of the state I, spikes are emitted according to a
threshold mechanism (5). The resulting spikes are encoded by their
position and their millisecond timing (x , y , t ).
Electrophysiological data
occurrence (x, y, p, t) are transmitted to the computer through a
USB connection. The events are contributing to the calculation
of the current I(t) of the 128×128 cells. The timing of the event
(t) is approximated at the millisecond precision by the time (t ).
The matrix I is therefore calculated every millisecond and a
threshold detection generates output spikes (x , y t ,).
The alpha-functions that we chose to describe the
temporal evolution of the currents and the independence of
the spatial and temporal components allowed us to compute the
output of the filters iteratively. The filter output was calculated
with a 1 ms time step, thus providing a millisecond timing
resolution regardless of the
event sequence. Let
fi and gi be
−t
−t
defined as fi (t ) = βit e τi and gi (t ) = βi e τi and the event
e = (x, y, p, t ). The evolution of the alpha-function fi was
calculated as
Patch clamp recordings from [1] were used to build the retinal
model. Briefly, inhibitory currents, excitatory currents and
spiking activity were recorded in response to a 600 μm square
of light flashed for 1 s at different positions around the cell. Ten
different cell types were described and characterized both on
electrophysiological responses and morphological parameters.
Excitatory and inhibitory currents were recorded by holding
the membrane potential at −60 and 0 mV, respectively. This
protocol allowed us to segregate GC responses into four
different components: ON-driven excitation and inhibition and
OFF-driven excitation and inhibition.
Parameter fitting
We fitted the spatial and temporal parameters by nonlinear
least-squares method (Matlab, Levenberg–Marquardt algorithm). In the model, spatial and temporal components of the
response were separated and fitted independently. The temporal parameters were fitted on the average temporal profile
along the spatial dimension. The spatial parameters were fitted
on the average spatial receptive field over the first 200 ms after
stimulus onset and offset. Alpha functions classically describe
excitatory post-synaptic currents. Here, the temporal profiles
were fitted with a sum of two alpha-functions. The spatial component of the filter was fitted using a 3-Gaussian combination:
hspatial (x, y) =
n
(x−xi0 )2 +(y−y0i )2
ri2
(2)
−(t−ti0 )
βi t − ti0 e τi
(3)
−
αi e
− dt
τ
fi (t + dt ) = dt.e
− dt
τ
gi (t + dt ) = e
htemporal (t ) =
i
− dt
τ
g(t ) + e
i
f (t )
gi (t ) + hspatial,i .
(4)
(5)
The contribution of the new event e was introduced
by adding the corresponding spatial kernel hspatial,i =
−
αi e
2
(x−xk+1 −xi0 )2 +(y−yk+1 −y0
i)
ri2
to the function gi .
Spike generation mechanism
From this input signal, an output spike was generated as soon as
the difference between the excitatory and inhibitory currents
crossed a threshold k : k ∈ Z. This threshold was set to
obtain a maximum firing rate of 200 Hz in the modeled cells.
i=1
m
i
Uniform light stimulation
i=1
with n = 3 and m = 2, introducing 15 free parameters. Four
different sets of parameters were fitted over the excitatory
currents from ON and OFF for both inhibition and excitation.
The uniform random light stimulus was designed using Matlab
(Psychtoolbox) and presented on an LED backlit display (iMac
screen, maximum luminance: 300 cdm−2 ). The intensity was
chosen from a Gaussian distribution with 10% variance at
mean light intensity of the monitor (∼150 cdm−2 ). The refresh
rate was 60 Hz and the stimulus duration was 5 s. The same
stimulus was repeated 50 times over the entire field of the DVS
sensor and these conditions did not saturate the sensor.
Iterative implementation
Figure 2 presents the system diagram. The events from
the camera encoded by their position, polarity and time of
4
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J. Neural Eng. 9 (2012) 000000
H Lorach et al
The time constants of the LED screen pixels may have an
influence on the timing reliability of the model. Therefore, we
assessed the effect of rise-time and fall-time of the screen by
computing the autocorrelation of the DVS events of a single
pixel. The autocorrelation of the positive events accounted
for the rise-time of the screen, whereas the autocorrelation
between negative events reflected the fall-time of the screen. In
both cases, the autocorrelation displayed a sharp peak around
1.5 ms.
a blinking duration below these 33 ms corresponding to the
acquisition of two successive frames. This behavior explains
the horizontal asymptote for short LED blinking durations
(below 33 ms), whereas the curve τframe follows linearly the
blinking duration for higher values. In contrast, the DVS (black
squares) can measure blinking durations as low as 2 ms with
great reliability. The DVS behavior was linear from 2 ms to 1 s.
This DVS sensor can thus detect changes in light intensities
with a higher temporal resolution than conventional cameras.
The ability of the sensor to follow high-frequency stimuli
and increase temporal precision depended on illumination
conditions and bias settings. Increasing light intensity reduced
both event latencies and jitter down to 15μs ± 3.3% [25].
Although mammalian cone PRs do not emit spikes, they
continuously release neurotransmitter and respond over seven
log-units of background illumination [27] and providing three
log-units dynamic range for a given background illumination.
This adaptive feature is shared by the DVS. Moreover, cone
PRs display fast light responses. Although the PR peak
photocurrent is reached after 30 ms, a few picoampere change
can be obtained a few milliseconds only after stimulation
onset [28, 29]. Such small current changes were shown to
be sufficient to change the cell potential and generate spike in
retinal GCs [30]. These results are consistent with the 20 ms
response latency of the fastest retinal GCs [31]. Therefore, the
dynamic vision sensor with its low latency appears sufficient
to match the PR response kinetics to model the retinal GC
responses.
Statistical analysis of spiking activity
Spike time variability of the modeled cells was assessed as the
standard deviation of reliable spike timings occurring across
trials when presenting the same stimulus. The repetition of
the same stimulus evoked firing periods separated from each
other by periods of inactivity clearly appearing as peaks in the
peristimulus time histogram (PSTH). However, peaks in the
PSTH can be either due to high firing rate in one trial, or timelocked firing in many trials. We can discriminate these two
situations by quantifying the variability of the spike rate across
trials. If this variability exceeds a given threshold, it means that
the firing period is not reliable. To estimate the reliability of the
responses, we applied the technique used in [2] to analyze
biological recordings. First, the timescale of modulation of
the firing rate of a cell was assessed by cross-correlation of
spiking activity across different trials and fitting this crosscorrelation with a Gaussian function (variance usually around
20 ms). We used a smaller time bin (5 ms) to compute the PSTH
allowing us to discriminate distinct periods of activity. From
the PSTH, reliable activity period boundaries were defined if
the minimum ν between
two surrounding maxima (m1 , m2 )
√
m m
was lower than 1.51 2 with 95% confidence. This criterion
rejects peaks in the PSTH that would be due to a few bursting
cells only.
For each of these reliable firing periods, the standard
deviation of the first spike time across trials was computed to
assess timing reliability. This standard deviation was computed
without binning, allowing us thereby to reach variabilities
lower than the 5 ms time bin. The variability in the number of
spikes was assessed by computing its variance in 20 ms time
bins across trials. The Fano factor was calculated as the slope
of the linear fitting of the number of spikes per time bin against
its variance.
Structure of the retinal model
To determine if the DVS sensor could provide a useful
visual information for a retinal model, we implemented
a computational model of retinal information processing.
At the retinal output, each GC type extracts a particular
feature of visual information based on its underlying network.
Figure 3(a) illustrates the general structure of the neural
network allowing this information processing although the
respective operation by each neuronal step is not identical
for all GC types. Phototransduction is performed by PRs
with an adaptive behavior. They contact horizontal cells (HC)
that provide lateral feedback inhibition. Bipolar cells (BC)
are either excited (OFF-BC) or inhibited (ON-BC) by PRs
glutamate release. In turn, they excite amacrine cells (AC) and
GCs. AC can potentially receive inputs from both ON and OFF
BC and provide inhibitory inputs to GCs. The different GC
types behave as threshold detectors integrating inputs from BC
and AC generating action potentials as soon as their membrane
potential reaches a particular threshold.
The DVS events may appear similar to the spiking
activity of transient retinal GCs. However, they lack the
biological temporal and spatial integration properties, such as
surround inhibition. Inspired by this biological architecture,
we implemented a model similar to [32, 33], segregating ON
and OFF inputs to different channels and applying different
filters to these components. This phenomenological model
does not reproduce the behavior of each interneuron but their
global equivalent inputs to the GCs. We applied temporal
and spatial filtering stages to the DVS events (figure 3(b)).
Results
Temporal precision of the sensor
Spike timing is critical in retinal coding [2, 3, 26]. We therefore
started by checking the timing accuracy of our light acquisition
system. If a millisecond precision is to be achieved in retinal
coding, our light sensor must at least reach this precision.
To quantify this accuracy, we assessed the minimal duration
of a blinking LED that could be measured with the DVS.
Figure 1(c) shows how the dynamic vision sensor performs as
compared to a conventional frame-based camera. As expected,
the conventional camera (figure 1(d) red triangles) was limited
by the sampling period of 30 Hz. It was not able to measure
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J. Neural Eng. 9 (2012) 000000
H Lorach et al
(a)
(b)
PR
HC
ON-BC
OFF-BC
AC
excitation
inhibition
Θ
GC
Figure 3. Architecture of the computational model. (a) Architecture of the biological retina. (b) The different filtering stages of the model.
ON events from the sensor provide inputs to ON bipolar cells and ON-driven amacrine cells and OFF events provide inputs to OFF bipolar
cells and OFF-driven amacrine cells. These four filtering stages are further combined by the ganglion cell that emits a spike whenever this
input signal varies from a threshold .
ON and OFF events ek = (xk , yk , pk , tk ) were segregated and
convolved with different filters (see section ‘Methods’), passed
through a static nonlinearity (N) and summed to provide GC
input current. An output spike was emitted as soon as the input
current I varied up to a threshold . This threshold was chosen
to obtain a maximum output firing rate of 200 Hz. The model
was implemented in Matlab as follows:
exc
inh
exc
inh
I(x, y, t ) = ION
− ION
+ IOFF
− IOFF
(6)
exc,inh
(x, y, t )
ION,OFF
⎛
⎞
⎠
=N⎝
hexc,inh
ON,OFF (x − xk , y − yk , t − tk , pk )
retina [1]. In these experiments, retinal GCs were recorded
with the patch-clamp technique during light stimulations with a
white square presented for 1 s successively at regular positions
in the cell receptive field. Excitatory and inhibitory currents
were recorded by voltage-clamping the cell at −60 and 0 mV,
respectively, whereas spiking activity was recorded with a
loose cell-attached electrode. These responses lead to the
classification of the recorded cells into ten functional types.
They were used to fit our model parameters to model each
individual cell type. Figure 4 illustrates one type of GC
excitatory currents in response to the flashed stimulus. Each
row of the color plot accounts for the temporal response
current at a respective position of the light stimulation. Based
on the ten cell types previously described, we fitted the
model to reproduce their spatial and temporal features for
both excitatory and inhibitory inputs (see Methods). Figures 5
and 6 present the measured temporal and spatial components
of the responses and the fitted curves. The coefficients of
determination for the fitting were close to unity in the
majority of cell types (median R2 = 0.972 and R2 = 0.903
respectively for temporal and spatial fitting). The full set of
model parameters is presented in table 1. From these excitatory
and inhibitory currents, a spike was generated as soon as the
sum of the excitation and inhibition reaches increases by a
(7)
k:tk <t
with hexc,inh
ON,OFF being the four respective filters for ON and OFF
excitation and inhibition. The nonlinearity N was chosen as
the positive part of the signal corresponding to the nonlinear
transmission from BC and AC to GCs. The temporal profiles
of the filters hexc,inh
ON,OFF are described by two time constants (see
section ‘Methods’), reflecting the temporal integration of BC,
HC, AC and GCs.
Response to a flashed stimulus
In order to fit our model parameters, we used the results
obtained in physiological experiments performed on the rabbit
6
ON BETA
7
τ1
(ms)
α2
t20
(pA ms−1 ) (ms)
τ2
(ms)
β1
(pA)
r1
x10
(μm) (μm)
β2
(pA)
r2
x20
β3
(μm) (μm) (pA)
r3
x30
(μm) (μm)
292
87.8
43.3
41.4
141
23.9
168
31.7
104
142
30.5
81.1
30.7
14.8
96.9
39.7
58.4
423
36.7
324
74.2
66.4
44.6
21.4
556
71.2
71
77.2
8.46
45
5.81
27.2
29.4
124
21.1
130
16.5
18.9
0.000 233
32.4
44.6
63.5
63.8
26
52.9
56
168
46.5
28
46.9
1e+03
81.2
36
604
41.2
45.5
723
61.7
2.21
137
97.5
340
156
32.5
52.7
213
30
51
70.2
47.4
12.5
2.86
299
139
123
29.1
561
22.3
13.4
44.7
72.4
130
43.2
79.6
89.5
23.9
57.1
13.9
242
15.5
30.5
64.1
17.6
66.4
32.3
37.6
91.5
11
25.4
59.9
27.4
114
44.6
113
40.4
67.8
52.7
64.9
6.05
39.6
7.33
0.002 45
48.6
87.1
21.1
82.7
73.7
10.6
0.000 233
31.9
277
608
63.8
25.1
59
56
1e+03
390
122
403
1e+03
23.2
167
61
223
41
148
309
2.08
1e+03
386
51.4
156
32
935
37
29.6
245
369
590
8.82
3.33
105
21.9
123
122
128
29.4
13.4
514
−395
1.59
7.07
6.1
10.4
−2.6
18.7
0.382
−7.41
−2.9
3.76
−222
−1.23
0.936
1.55
1.67
−1.63
3.13
−3.17
−7.62
−139
2.02
76
2.68
71.7
0.929
−7.07
3.22
0.331
−0.958
50.8
0.122
−33.4
3.03
22.2
26
−4.09
5.04
0.431
−3.45
74.3
371
324
87
22.5
218
55.1
950
25
211
271
49
43.3
104
214
74.8
38.8
589
301
240
0.746
582
28.2
658
92.7
966
207
16.4
13
520
58.9
347
266
299
188
334
56.7
47.8
39.7
90.8
398
−1.41
−6.75
31.5
−19.5
3.69
−69.8
−0.721
23.9
1.96
−6.67
225
−2.57
−8.89
−14.6
−3.84
2
8.9
1.16
9.15
−4.87
1.36
−76.3
−3.36
−58.5
−3.87
5.93
2.56
0.0903
1.09
1.38
0.163
−3.63
4.23
−42.6
5.55
43.8
16.8
−0.487
23
75.6
97.6
302
249
0.698
449
106
12
170
895
106
49.5
165
1.56
92.9
693
19.8
82.7
378
447
31.8
136
28.5
465
95.7
43.4
269
64.5
845
829
78.9
1e+03
31.4
244
212
55.6
361
74.1
92.7
240
2.27
1.56
46.3
234
75.2
277
84.8
35.6
122
0.823
70.2
1e+03
395
511
88
1e+03
227
29.6
247
62.8
443
49.2
438
97.9
343
193
24.5
1e+03
125
136
59.5
106
274
135
236
320
354
89.7
491
220
76.7
69.2
147
85.5
275
93.1
94
67.3
89.9
71.1
92.9
106
88
4.8e−05
72.5
65.3
44.1
64.8
13.8
83.6
76.2
30.8
72.3
1.15
68.8
106
211
94.9
154
89.5
61.6
1.14
58.4
71.4
72.5
99
4.92e−06
94.9
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100
8.03e−07
0.809
147
112
208
93
61.7
83.2
62.3
7.2e−06
92.9
184
67.1
69.1
42.1
108
57.9
6.54
16
176
20.6
102
72.3
116
7.32e−06
82.4
145
126
146
33.9
80.5
237
90.2
132
72.5
113
123
54.2
0.000 739
148
74.4
41.4
−4.82
−0.0886
146
169
134
−44.1
44.3
−22.5
18.9
39.3
115
−38.5
87.2
188
−15.4
30.8
−7.11
24.3
91
−163
21.7
−200
12
45.5
45.8
131
36.9
168
30.7
−200
36.8
−200
14.3
−53.1
1.17
−9.85
107
−127
71.7
180
−5.61
−9.78
72.3
−42.7
57
96.4
114
−85.2
−7.85
38.8
−16.5
83.4
168
178
93.4
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7.9
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200
21.5
−104
17.6
174
45
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200
24.9
183
35.4
168
17.4
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175
76.4
47.6
86.8
125
839
−2.33
−34.1
5.5
−2.91
76.9
−2.34
−23.3
5.27e+03
−2.48
0.594
1.7
0.467
13.3
3.47
2.19
−15.5
2.23
−5.57
1.38
−13.5
0.645
4.79
3.51
−1.4
0.82
0.276
−0.276
0.872
−52
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33.9
−6.01
21
−25.7
−42.7
−16.2
0.123
−23
52.4
2.9
17.3
−7.81
−170
−200
39.9
34.4
161
52.1
184
−174
−13.2
−200
168
170
−4.77
94
−0.717
78.3
81.8
43.2
81
18.3
20.5
−113
144
139
−17.2
−24.1
30.6
22
37.1
51.7
20.4
−52.4
183
65
−24.4
102
H Lorach et al
ONexc
ONinh
OFFexc
OFFinh
OFF BETA
ONexc
ONinh
OFFexc
OFFinh
ON-PARASOL ONexc
ONinh
OFFexc
OFFinh
OFF PARASOL ONexc
ONinh
OFFexc
OFFinh
ON DELTA
ONexc
ONinh
OFFexc
OFFinh
OFF DELTA
ONexc
ONinh
OFFexc
OFFinh
ON BISTRAT
ONexc
ONinh
OFFexc
OFFinh
OFF COUPLED ONexc
ONinh
OFFexc
OFFinh
LED
ONexc
ONinh
OFFexc
OFFinh
ON−OFF DS
ONexc
ONinh
OFFexc
OFFinh
α1
t10
(pA ms−1 ) (ms)
J. Neural Eng. 9 (2012) 000000
Table 1. Parameters list. Each current (ON-excitation, ON-inhibition, OFF-excitation, OFF-inhibition) is described by a set of 15 parameters including 6 parameters for the temporal component
and 9 parameters for the spatial profiles. LED: local edge detector.
J. Neural Eng. 9 (2012) 000000
H Lorach et al
Figure 4. Reconstruction of an ON-Beta ganglion cell excitatory currents in response of a square of light. Experimental data from [1] were
obtained by recording excitatory currents (holding the membrane potential at −60 mV) in response to a square of light flashed at different
positions. The stimulus consisted in a 600 μm square of light flashed for 1s across the ganglion cell with 60 μm steps. Each row of the color
plot represents the temporal response current at the respective position of the light square. Model parameters were fitted on the spatial (top)
and temporal (bottom) averages of the currents for both ON phase and OFF phase.
threshold . This threshold was set to achieve a maximum
firing rate of 200 Hz in the modeled cells.
as the standard deviation of the first spike in an activity
window occurring across trials when presenting the same
stimulus. Indeed, the repetition of the same stimulus evoked
firing events separated from each other by periods of inactivity
(figure 7(a)). Although these activity periods occur clearly as
vertical bands in the raster plots, we provide a mathematical
criterion for separating spiking periods from one another (see
section ‘Methods’). In trials where no spike appeared within
an activity window, no contribution was made to the standard
deviation calculation [2]. The variability was calculated as the
standard deviation of the timing of the first spike in the activity
period across trials. Similar measures have been often used and
allow comparisons with existing data. The timing variability
histogram for all cells is presented in figure 7(b). Some cells
displayed timing reliability as low as few milliseconds with
a maximum value of the histogram at 5 ms. This result is
in agreement with physiological findings in mammalian GCs
[2, 26].
The variability in the number of spikes across trials
was illustrated by expressing the mean number of spikes
Spike timing and count variability
Variability in GC responses has been characterized in vitro
and is thought to play an important role in retinal coding [2].
In order to quantify the variability in our artificial retina, we
used a random stimulation protocol. Spatially uniform random
light stimulations are often used to probe retinal function
[2, 26, 36]. Here, we assessed the bursting behavior of the
modeled cells. Figure 7(a) presents the reliable activity of the
GCs. The stimulus consisted in a spatially uniform Gaussian
distributed intensity with 10% variance in contrast refreshed
at 60 Hz. It evoked typical bursting activity shown by the
raster plots for 50 repetitions of the same stimulus. Each cell
responds with a particular temporal signature in its activity
periods underlining the importance of temporal coding.
The timing reliability of the modeled cells was analyzed as
previously described in [2]. Spike time variability was assessed
8
J. Neural Eng. 9 (2012) 000000
H Lorach et al
Figure 5. Fitting of temporal parameters. Temporal response profiles were split into four different components. The ON-driven excitation
and inhibition corresponding to the stimulus onset and the OFF-driven excitation and inhibition generated by the stimulus offset. Recorded
−(t−t 0 )
data (black curves) were fitted by a sum of two alpha-functions (red curves) 2i=1 βi (t − ti0 ) exp( τi i ) and provided good coefficient of
determination for all cells (median R2 = 0.972).
mimic retinal processing. Despite the transient nature of the
DVS signal, both transient and more sustained cells could be
modeled by introducing different time constants in the alphafunctions—ranging from 22 ms to 1 s (see table 1). However,
longer time constant or dc components of the light signal were
not taken into account.
Moreover, the event-based nature of the DVS does not
reproduce the analogue nature of the PR signal. The conversion
from spikes to analogue signal and to spikes back again in our
implementation may seem puzzling and we agree that it does
not faithfully reproduce retinal physiology itself. The retina
indeed remains analogous until spike generation in GCs—
and in some AC. However, the asynchronous nature of the
DVS signal and its low latency are critical advantages for
the temporal precision of the model. Moreover, the general
nature of the DVS output signal allows flexible processing to
reproduce multiple different cell types from the same signal.
Conventional retinal models include linear ones where
spike rate is linearly dependent on light intensity, LN,
stochastic or not [15, 17] and integrative models where each
ion channel of each cell is accounted for [12]. However,
practical use of these models always relies on an acquisition
device. For the purpose of implementing an artificial retina,
a millisecond timing precision seems critical. Therefore, the
in a 20 ms time bin against its variance over the 50 trials
(figure 7(c)). As expected, this spiking variability was much
lower than predicted from Poisson statistics (following the
linear relationship plotted). The linear fitting of the meanto-variance relationship gave a Fano factor of 0.331, to be
compared to the 0.277 found in primate GCs [26]. This
low variability means that a significant amount of visual
information is represented by the number of spikes at the 20 ms
timescale [35].
Discussion
Taking advantage of a fast asynchronous sensor with a wide
dynamic range, we showed that our artificial retina could
reproduce the temporal precision of the mammalian retina
for different visual information channels. The main advantage
relies in the high temporal resolution of the sensor and
the event-based representation of the visual information. The
dynamic vision sensor mimics the adaptive and asynchronous
characteristics of phototransduction. Its wide dynamic range
(120 dB) quantitatively matches the sensitivity of the human
retina. It is able to respond to illuminance ranging from 1 to
105 lux [25]. By responding to logarithmic temporal contrasts,
it provides a compact signal that can be further processed to
9
J. Neural Eng. 9 (2012) 000000
H Lorach et al
Figure 6. Fitting of spatial parameters. Spatial response profiles were split into the four components: ON-driven excitation and inhibition
and OFF-driven excitation and inhibition. The recorded spatial profiles (black curves) were fitted using a sum of three Gaussian functions
3
(x−xi0 )2
) (red curves). This fitting was performed by nonlinear least-squares method and provided a good coefficient of
i=1 αi exp(− r2
i
determination for the vast majority of cells (median R2 = 0.903).
solution. Alternatively, reaching a similar precision with the
frame-based camera would require a high computational cost.
As pointed out earlier, high frame rate cameras already
reaching the kHz-sampling frequency are usually well suited
for slow motion analysis in industry and research and would
theoretically be fast enough to compute accurate spike trains.
However, these devices are power consuming and inefficient.
First, they produce data regardless of the changes in a scene
so that a 1000 × 1000 pixel array at 1 kHz with a 12-bits
precision transfers 1.5 GB per second. Moreover, due to their
short exposure times, they need high illumination levels as well
as heavy cooling system to reduce thermal noise and improve
signal to noise ratio. For all these reasons, fast cameras using
frames are expensive, heavy and large, high energy consuming
and thus not suited for embedded applications where light
conditions are not necessarily controlled and where efficiency
in power and data production is a key challenge. Asynchronous
sensors offer promising results for these kinds of applications.
As opposed to the frame-based cameras, data are produced
exclusively when motion occurs, thus compressing visual
information prior to any processing. Moreover, the continuous
exposure of the pixels and the adaptive threshold provide a
high sensitivity in a wide dynamic range (120 dB) without
any cooling system. Finally, the event-based nature of the
accuracy of the sensor itself is an important limiting factor.
Here, we circumvented this problem by using the dynamic
vision sensor and were able to match the millisecond timing
accuracy of retinal coding. We showed that the use of an
asynchronous neuromorphic sensor is well suited for artificial
retina implementation.
We based our work on physiological experiments in the
literature. We fitted our parameters on responses from rabbit
GCs obtained with a relatively simple stimulus. Therefore we
did not account here for more complex behaviors. However,
we provided evidence that timing precision and reliability as
well as spiking statistics in response to a flickering random
stimulus were achieved by our artificial retina. A parameter
fitting on stimuli with natural statistics would improve the
accuracy of the model and would unravel more complex
behaviors. Moreover, multiple sources of noise such as photon
noise, synaptic noise and channel noise are not included in our
implementation in which noise comes from thermal noise in
the pixel and photon absorption noise.
In theory, the DVS and AER are not essential to reproduce
the GC responses and their temporal precision. This can indeed
be done by a simple model like, for example, the one in
[36]. However, implementing this model in a device raises
several challenges, to which the DVS provides an elegant
10
J. Neural Eng. 9 (2012) 000000
H Lorach et al
(a)
(b)
(c)
Figure 7. Response reproducibility in the modeled retinal ganglion cell. (a) Cell responses to a spatially uniform random flicker. The
stimulus consisted in a spatially uniform random illumination (red trace) from a Gaussian distribution with 10% variance updated at 60 Hz.
Raster plots of the cell response to the 50 consecutive trials are represented. Reliable firing events for individual cells appear as vertical bars
in the raster plot. Each cell display a specific time coding for the same stimulus. (b) Histogram of the spike timing variability. The variability
is computed for each reliable spiking period as the standard deviation in the millisecond timing of the first spike across trials (taken without
binning). This variability can be as low as 2 ms for some spiking periods. The histogram maximum for all cells is 5 ms in good agreement
with biological results [2]. (c) Spike count variability. The mean number of spikes per event across trials is plotted against its variance. The
straight line represents equality between mean and variance. This relationship is valid if the spiking probability follows a Poisson law
depending on the stimulus strength. Here, the variability is lower than expected from a Poisson process meaning that the number of spikes
per reliable spiking periods is reproducible across trials. The Fano factor obtained by linear fitting of the mean/variance relationship (blue
dotted line) is lower than unity (0.331).
in our model—up to 1 s—would be difficult to implement in
purely analogue circuits because this would require very large
capacitances or very low currents, leading to prohibitively
large area and/or mismatch of the circuits. Mixed analogue-todigital circuits could however be used to implement large time
constants. Such an implementation would constitute a key step
to reach real time processing in embedded devices.
Another application of such embedded vision device could
be for medical purposes. Indeed, patients suffering from retinal
degeneration can lose part of their visual field. This loss
that may be either central or peripheral can be compensated
by visual aids for visually impaired patients providing the
missing information in an augmented reality fashion. An
external camera is used to extract relevant information to
provide to the patient. Therefore, the use of an efficient sensor
and a biomimetic model can greatly improve these kinds
of embedded systems. In the case of complete blindness,
functional vision rehabilitation can be achieved by retinal
or cortical prostheses stimulating remaining retinal cells or
DVS signal would allow us to use event-based strategies for
simulating neural networks [37].
Here, as a first step, we implemented the model in Matlab
to fit the spatial and temporal parameters. Using computer
simulations, we were not able to achieve real time simulation
of the retinal GCs. The computational cost of the model scales
with the number of events and the size of the spatial filter. Here,
typical filter sizes were 10 × 10 allowing us to process around
104 events per second with a conventional processor under
Matlab. Natural scenes generate around 105 events per second
on the DVS; therefore our implementation method is 10 times
slower than real time. This lack of efficiency was mainly due to
the synchronization step when calculating the evolution of the
input currents iteratively at a millisecond resolution. However,
once the model parameters are set, it is possible to increase
computation speed using C, GPU or FPGA programming.
Asynchronous convolution chips are also under development
[38, 39] so that a hardware implementation of this retinal model
could be performed. However, the long time constants present
11
J. Neural Eng. 9 (2012) 000000
H Lorach et al
are considered for retinal prostheses, either at the level of the
degenerated PRs in the subretinal space or at an epiretinal
position to directly activate retinal GCs. In these epiretinal
implants as well as in cortical prostheses, an important
visual information processing is required to provide adequate
stimulations to the cells. Since single cell stimulation starts
to emerge [41, 42], our model provides different information
channels that could be sequentially tested in patients in order to
select the most efficient one because each information channel
in the retina might be devoted to specific task. In the field of
visual implants, the main goal for the patients is to achieve
face recognition task or reading tasks. In this context, our
model can be used to evaluate which one of the different
information channels is more appropriate to achieve such tasks.
Figure 8 illustrates the encoding of a moving face through
the ten information channels underlining different features
of the image. For cortical implants, our model needs to be
completed by higher order computational processes occurring
between the retina and the targeted brain area in order to
provide time accurate and meaningful visual information. In
all cases, the asynchronous nature of the generated signal could
provide information to the stimulating device, thus reducing
the power required for existing conventional image conversion
systems. This point will be critical in a near future as pixel
numbers is likely to increase exponentially requiring more
powerful image analyzers connected to conventional framebased cameras. DVS sensors may thus reduce the need for
powerful image processors for retinal modeling and prosthetic
applications.
Acknowledgments
We thank Dr Posch, Dr Frégnac and Dr Guiraud for helpful
discussions on the project. We also thank the reviewers for their
constructive remarks. This work was supported by INSERM,
Université Pierre et Marie Curie (Paris VI), Fondation
Ophtalmologique A de Rothschild (Paris), Agence Nationale
pour la Recherche (ANR RETINE), ITMO Technologie pour
la santé, the Fédération des Aveugles de France, IRRP, the city
of Paris, the Regional Council of Ile-de-France. HL received
a doctoral fellowship from the Ecole Polytechnique.
Author contributions. All authors contributed extensively to
the work presented in this paper.
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Figure 8. Parallel coding of a complex stimulus. The person is
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by the sensor over 20 ms. The next images represent the scaled
colormaps of input currents to different populations of retinal
ganglion cells allowing us to define visual information sent to the
brain by the different parallel channels during complex stimulations.
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