Plasticity of Center-Surround Opponent 
Receptive Fields in Real and Artificial 
Neural Systems of Vision 
S. Yasui 
Kyushu Institute of Technology 
Iizuka 820, Japan 
T. Furukawa 
Kyushu Institute of Technology 
Iizuka 820, Japan 
M. Yamada 
Electrotechnical Laboratory 
Tsukuba 305, Japan 
T. Saito 
Tsukuba University 
Tsukuba 305, Japan 
Abstract 
Despite the phylogenic and structural differences, the visual sys- 
tems of different species, whether vertebrate or invertebrate, share 
certain functional properties. The center-surround opponent recep- 
tive field (CSRF) mechanism represents one such example. Here, 
analogous CSRFs are shown to be formed in an artificial neural 
network which learns to localize contours (edges) of the luminance 
difference. Furthermore, when the input pattern is corrupted by 
a background noise, the CSRFs of the hidden units becomes shal- 
lower and broader with decrease of the signal-to-noise ratio (SNR). 
The same kind of SNR-dependent plasticity is present in the CSRF 
of real visual neurons; in bipolar cells of the carp retina as is shown 
here experimentally, as well as in large monopolar cells of the fly 
compound eye as was described by others. Also, analogous SNR- 
dependent plasticity is shown to be present in the biphasic flash 
responses (BPFR) of these artificial and biological visual systems. 
Thus, the spatial (CSRF) and temporal (BPFR) filtering proper- 
ties with which a wide variety of creatures see the world appear to 
be optimized for detectability of changes in space and time. 
I INTRODUCTION 
A number of learning algorithms have been developed to make synthetic neural 
machines be trainable to function in certain optimal ways. If the brain and nervous 
systems that we see in nature are best answers of the evolutionary process, then 
one might be able to find some common 'softwares' in real and artificial neural 
systems. This possibility is examined in this paper, with respect to a basic visual 
160 S. YASUI, T. FURUKAWA, M. YAMADA, T. SAITO 
mechanism relevant to detection of brightness contours (edges). In most visual 
systems of vertebrate and invertebrate, one finds interneurons which possess center- 
surround opponent receptive fields (CSRFs). CSRFs underlie the mechanism of 
lateral inhibition which produces edge enhancement effects such as Mach band. It 
has also been shown in the fly compound eye that the CSRF of large monopolar cells 
(LMCs) changes its shape in accordance with SNR; the CSRF becomes wider with 
increase of the noise level in the sensory environment. Furthermore, whereas CSRFs 
describe a filtering function in space, an analogous observation has been made 
in LMCs as regards the filtering property in the time domain; the biphasic flash 
response (BPFR) lasts longer as the noise level increases (Dubs, 1982; Laughlin, 
1982). 
A question that arises is whether similar SNR-dependent spatio-temporal filtering 
properties might be present in vertebrate visual cells. To investigate this, we made 
an intracellular recording experiment to measure the CSRF and BPFR profiles of 
bipolar cells in the carp retina under appropriate conditions, and the results are 
described in the first part of this paper. In the second part, we ask the same 
question in a 3-layer feedforward artificial neural network (ANN) trained to detect 
and localize spatial and temporal changes in simulated visual inputs corrupted by 
noise. In this case, the ANN wiring structure evolves from an initial random state so 
as to minimize the detection error, and we look into the internal ANN organization 
that emerges as a result of training. The findings made in the real and artificial 
neural systems are compared and discussed in the final section. 
In this study, the backpropagation learning algorithm was applied to update the 
synaptic parameters of the ANN. This algorithm was used as a means for the com- 
putational optimization. Accordingly, the present choice is not necessarily relevant 
to the question of whether the error backpropagation pathway actually might exist 
in real neural systems(cf. Stork & Hall, 1989). 
2 
THE CASE OF A REAL NEURAL SYSTEM: 
RETINAL BIPOLAR CELL 
Bipolar cells occur as a second order neuron in the vertebrate retina, and they have 
a good example of CSRF Here we are interested in the possibility that the CSRF 
and BPFR of bipolar cells might change their size and shape as a function of the 
visual environment, particularly as regards the dark- versus light-adapted retinal 
states which correspond to low versus high SNR conditions as explained later. Thus, 
the following intracellular recording experiment was carried out. 
2.1 MATERIAL AND METHOD 
The retina was isolated from the carp which had been kept in complete darkness 
for 2 hrs before being pithed for sacrifice. The specimen was then mounted on 
a chamber with the receptor side up, and it was continuously superfused with a 
Ringer solution composed of (in mM) 102 NaCl, 28 NaHCO3, 2.6 KCI, i CaC12, 1 
MgC12 and 5 glucose, maintained at pH=7.6 and aerated with a gas mixture of 95% 
O2 and 5% CO2. Glass micropipettes filled with 3M KC1 and having tip resistances 
of about 150 MR were used to record the membrane potential. Identification of 
bipolar cell units was made on the basis of presence or absence of CSRF. For this 
preliminary test, the center and peripheral responses were examined by using flashes 
of a small centered spot and a narrow annular ring. To map their receptive field 
profile, the stimulus was given as flashes of a narrow slit presented at discrete 
positions 60 pm apart on the retina. The slit of white light was 4 mm long and 0.17 
mm wide, and its flash had intensity of 7.24 pW/cm 2 and duration of 250 msec. 
The CSRF measurement was made under dark- and light- adapted conditions. A 
Plasticity of Center-Surround Opponent Receptive Fields 161 
(a) 
Light )center 
I 
5111V 
Dark 
GOltm 
(b) 1.0 
-1.0 
(c) 
I I 
-1.0 0 
n Light 
Dtrk 
[ 
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1sec 
Figure 1: (a) Intracellular recordings from an ON-center bipolar cell of the carp 
retina with moving slit stimuli under light and dark adapted condition. (b) The 
receptive field profiles plotted from the recordings. (c) The response recorded when 
the slit was positioned at the receptive field center. 
steady background light of 0.29/W/cm 2 was provided for light adaptation. 
2.2 RESULTS 
Fig. la shows a typical set of records obtained from a bipolar cell. The response 
to each flash of slit was biphasic (i.e., BPFR), consisting of a depolarization (ON) 
followed by a hyperpolarization(OFF). The ON response was the major component 
when the slit was positioned centrally on the receptive field, whereas the OFF 
response was dominant at peripheral locations and somewhat sluggish. The CSRF 
pattern was portrayed by plotting the response membrane potential measured at 
the time just prior to the cessation of each test flash. The result compiled from 
the data of Fig.la is presented in Fig. lb, showing that the CSRF of the dark- 
adapted state was shallow and broad as opposed to the sharp profile produced during 
light adaptation. The records with the slit positioned at the receptive field center 
are enlarged in Fig.lc, indicating that the OFF part of the BPFR waveform was 
shallower and broader when the retina was dark adapted than when light adapted. 
3 THE CASE OF ARTIFICIAL NEURAL NETWORKS 
Visual pattern recognition and imagery data processing have been a traditional 
application area of ANNs. There are also ANNs that deal with time series signals. 
These both types of ANNs are considered here, and they are trained to detect and 
localize spatial or temporal changes of the input signal corrupted by noise. 
162 S. YASUI, T. FURUKAWA, M. YAMADA, T. SAITO 
3.1 PARADIGMS AND METHODS 
The ANN models we used are illustrated in Figs.2. The model of Fig.2a deals 
with one-dimensional spatial signals. It consists of three layers (input, hidden, 
output), each having the same number of 12 or 20 neuronal units. The pattern 
given to the input layer represents the brightness distribution of light. The network 
was trained by means of the standard backpropagation algorithm, to detect and 
localize step-wise changes (edges) which were distributed on each training pattern 
in a random fashion with respect to the number, position and height. The mean 
level of the whole pattern was varied randomly as well. In addition, there was 
a background noise (not illustrated in Figs.2); independent noise signals of the 
same statistics were given to the all input units, and the maximum noise amplitude 
(NL: noise level) remained constant throughout each training session. The teacher 
signal was the "true" edge positions which were subject to obscuration due to the 
background noise; the learning was supervised such that each output unit would 
respond with 1 when a step-wise change not due to the background noise occurred 
at the corresponding position, and respond with -1 otherwise. The value of each 
synaptic weight parameter was given randomly at the outset and updated by using 
the backpropagation algorithm after presentation of each training pattern. The 
training session was terminated when the mean square error stopped decreasing. 
To process time series inputs, the ANN model of Fig.2b was constructed with the 
backpropagation learning algorithm. This temporal model also has three layers, 
but the meaning of this is quite different from the spatial network model of Fig.2a. 
That is, whereas each unit of each layer in the spatial model is an anatomical 
entity, this is not the case with respect to the temporal model. Thus, each layer 
represents a single neuron so that there are actually only three neuronal elements, 
i.e., a receptor, an interneuron, and an output cell. And, the units in the same 
layer represent activity states of one neuron at different time slices; the rightmost 
unit for the present time, the next one for one time unit ago, and so on. As is 
apparent from Fig.2b, therefore, there is no convergence from the future (right) to 
the past (left). Each cell has memory of T-units time. Accordingly, the network 
requires 2T- 1 units in the input layer, T units in the hidden layer and i units in 
the output layer to calculate the output at present time. The input was a discrete 
time series in which step-wise changes took place randomly in a manner analogous 
to the spatial input of Fig.2a. As in the spatial case, there was a background noise 
(a) 
/ :.position lut / : : % 
Input : :  (b) /,ern _ I tLrne 
lyer .  . 
lyer 
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Figure 2' The neural network architectures. Spatial (a) and temporal model (b). 
Plasticity of Center-Surround Opponent Receptive Fields 163 
(a) (b) 
f.O 0.3 
Output umts 
2000 4000 10000 30000 
0.2 
0.0 -r? 8 0 x10d 
0.0 4.0 . 
Iterations 
Figure 3: Development of receptive fields. Synaptic weights (a) and mean square 
error (b), both as a function of the number of iterations. 
added to the input. The network was trained to respond with +1/-1 when the 
original input signal increased/decreased, and to respond with 0 otherwise. 
3.2 RESULTS 
Spatial case: Emergence of CSRFs with SNR-dependent plasticity 
As regards the edge detection learning by the 
ANN model of Fig.2a, the results without 
the background noise are described first (Fu- 
rukawa & Yasui, 1990; Joshi & Lee, 1993). 
Fig.3a illustrates how the synaptic connec- 
tions developed from the initial random state. 
If the final distribution of synaptic weight pa- 
rameters is examined from input units to any 
hidden unit and also from hidden units to 
any output unit, then it can be seen in ei- 
ther case that the central and peripheral con- 
nections are opposite in the polarity of their 
weight parameters; the central group had ei- 
ther positive (ON-center) or negative (OFF- 
center) values, but the reversed profiles are 
Hidden Layer 
Output Layer 
Figure 4: A Sample of activity 
pattern of each layer 
shown in the drawing of Fig.3a for the OFF-center case. In any event, CSRFs were 
formed inside the network as a result of the edge detection learning. Fig.3b shows 
the performance improvement during a learning session. Fig.4 shows the activation 
pattern of each layer in response to a sample input, and edge enhancement like 
the Mach band effect can be observed in the hidden layer. Fig.5a presents sample 
input patterns corrupted by the background noise of various NL values, and Fig.5b 
shows how a hidden unit was connected to the input layer at the end of training. 
CSRFs were still formed when the environment suffered from the noise. However, 
the structure of the center-surround antagonism changed as a function of NL; the 
CSRFs became shallow and broad as NL increased, i.e., as the SNR decreased. 
Temporal case: Emergence of BPFRs with SNR-dependent plasticity 
With reference to the learning paradigm of Fig.2b, Fig.5c reveals how a represen- 
tative hidden unit made synaptic connections with the input units as a function of 
NL; the weight parameters are plotted against the elapsed time. Each trace would 
correspond to the response of the hidden unit to a flash of light, and it consists of 
164 S. YASUI, T. FURUKAWA, M. YAMADA, T. SAITO 
two phases of ON and OFF, i.e., BPFRs (biphasic flash responses) emerged in this 
ANN as a result of learning, and the biphasic time course changed depending on 
NL; the negative-going phase became shallower and longer with decrease of SNR. 
4 
DISCUSSION: Common Receptive Field Properties in 
Vertebrate, Invertebrate and Artificial Systems 
A CSRF profile emerges after differentiating twice in space a small patch of light, 
and CSRF is a kind of point spreading function. Accordingly, the response to any 
input distribution can be obtained by convolving the input pattern with CSRF. 
The double differentiation of this spatial filtering acts to locate edge positions. On 
the other hand, the waveform of BPFR appears by differentiating once in time a 
short flash of light. Thus, the BPFR is an impulse response function with which 
to convolve the given input time series to obtain the response waveform. This is 
a derivative filtering, which subserves detection of temporal changes in the input 
visual signal. While both CSRF and BPFR occur in visual neurons of a wide variety 
of vertebrates and invertebrates, the first part of the present study shows that these 
spatial and temporal filtering functions can develop autonomously in our ANNs. 
The neural system of visual signal processing encounters various kinds of noise. 
There are non-biological ones such as a background noise in the visual input itself 
and the photon noise which cannot be ignored when the light intensity is low. En- 
dogenous sources of noise include spontaneous photoisomerization in photoreceptor 
cells, quantal transmitter release at synaptic sites, open/close activities of ion chan- 
nels and so on. Generally speaking, therefore, since the surroundings are dim when 
the retina is dark adapted, SNR in the neuronal environment tends to be low during 
dark adaptation. According to the present experiment on the carp retina, the CSRF 
of bipolar cells widens in space and the BPFR is prolonged in time when the retina 
is dark adapted, that is, when SNR is presumably low. Interestingly, the same 
SNR-dependent properties have also been described in connection with the CSRF 
and BPFR of large monopolar cells in the fly compound eye. These spatial and 
temporal observations are both in accord with a notion that a method to remove 
noise is smoothing which requires averaging for a sufficiently long interval. In other 
words, when SNR is low, the signal averaging takes place over a large portion of 
the spario-temporal domain comprised of CSRF and BPFR. Smoothing and differ- 
entiation are entirely opposite in the signal processing role. The SNR dependency 
of the CSRF and BPFR profiles can be viewed as a compromise between these two 
operations, for the need to detect signal changes in the presence of noise. These 
0 10 20 
(! .... (c) __ 
Figure 5: (a) A sample set of training patterns with different background noise 
levels (NLs). The NLs are 0.0, 0.4, 1.0 from bottom to top. The receptive field 
profiles (b) and dash responses (c) after training with each NL. The ordinate scale 
is linear but in arbitrary unit, with the zero level indicated by dotted lines. 
Plasticity of Center-Surround Opponent Receptive Fields 165 
points parallel the results of information-theoretic analysis by Atick and RedItch 
(1992) and by Laughlin (1982). 
5 CONCLUDING REMARKS 
We have learnt from this study that the same software is at work for the SNR- 
dependent control of the spatio-temporal visual receptive field in entirely different 
hardwares; namely, vertebrate, invertebrate and artificial neural systems. In other 
words, the plasticity scheme represents nature's optimum answer to the visual func- 
tional demand, not a result of compromise with other factors such as metabolism 
or morphology. Some mention needs to be made of the standard regularization 
theory. If the theory is applied to the edge detection problem, then one obtains 
the Laplacian-Gaussian filter which is a well-known CSRF example(Torre & Pog- 
gio, 1980). And, the shape of this spatial filter can be made wide or narrow by 
manipulating the value of a constant usually referred to as the regularization pa- 
rameter. This parameter choice corresponds to the compromise that our ANN finds 
autonomously between smoothing and differentiation. The present type of research 
aided by trainable artificial neural networks seems to be a useful top-down approach 
to gain insight into the brain and neural mechanisms. Earlier, Lehky and Sejnowski 
(1988) were able to create neuron-like units similar to the complex cells of the visual 
cortex by using the backpropagation algorithm, however, the CSRF mechanism was 
given a priori to an early stage in their ANN processor. It should also be noted that 
Linsker (1986) succeeded in self-organization of CSRFs in an ANN model that op- 
erates under the learning law of Hebb. Perhaps, it remains to be examined whether 
the CSRFs formed in such an unsupervised learning paradigm might also possess 
an SNR-dependent plasticity similar to that described in this paper. 
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PART III 
THEORY 
