JPRS ID: 10211 TRANSLATION ARTIFICIAL SENSE ORGANS PROBLEMS OF MODELING SENSORY ORGANS BY S.V. FOMIN, YE. SOKOLOV AND G.G. VAYTKYAVICHYUS

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JPRS LI10211 �
23 [~ecember 1981
Translation
ARTIFICIAL SEN~E O~RGANS
~RCBLEMS O~F M~GDELING SENSORY SYSTEMS
_ By
= S.V. Fomin, Y~. N. Sokolov and ~.G. V~ytleyavichyus
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~ JPRS L/10211
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~ 23 December 1981
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ARTIFICIAL SEP~SE ORGANS ~
; PROBLEMS OF MODELING SENSORY SYSTEM~ ~
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,i Moscow ISKUSSTVENNYYE ORGANY CHUVSTV. PRCBLEMY MODELIROVANIYA
i SENSORNYKH SISTEM in Russian 1979 (signed to press 15 Jun 79)
I
[Book by Sergey Vasil'ye~rich Fomin, Yevgeniy Nikolayevich Soko~.ov and
Genrikh Genrikhovich Vaytkyavichyus, Izdatel'stvo "Nauka", UDC 519.9~]
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~ .CONTENTS
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~ Annotation
_i Foreword 2
~ Chapter 1. Construction of Arti'licial Sense Organs 4
' Chapter 2. Model of Channel Number Coding 10
~ 38
~ Chapter 3. Intensity Analyzer
Chapter 4. Color Analyzer 47
~ Chapter 5. Line Slant Analyzer 59
Chapter 6. Visual Analyzer of Direction and Speed ~f M~tion 75
Chapter 7. Stereo Analyzer g5
Chapter 8. Gravity Analyzer 99
Chapter 9. Construction of Analyzers~to Order 102
, Appenlice5:
i i. C~ner~~ Theury 109
~ ~ 123
L. Intensity A?ialyzer ....................................o..............
' 3. Culor Analyzer 127
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~ 4. Lir~ Slant Analyzer 131_
~ i 141
~ 5. Analyzer of llirection and Speed of Motion
~i ` 143
i 6. Stereo Analyzer .........................e............................
~ 7. Po.larized Lig}it An~l.yzer 148
~ Bibliograpliy 150
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PUBLICATION DATA
English ti~le : Artificial Sensory Systems. Problems
~ of Modeling..Sensory Systems
~ Russian title . Iskusstvennyye organy chuvstv. Problemy
- modelirovaniya sensornykh sistem
Authors ~ : S. V. Fomin, Ye. N. a~okolov and
G. G. Vaytkyavichyus
Ed3_tor : Yu. P. Leonov, candidate of
engineering sciences
Publishing house : "Nauka"
Place of publication : Moscow ~
Signed to press : 15 June 19~y
Copies . 1200
- COYYRIGHT : Izdatel'stvo "Nauka", 1979
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~ ANNOTATION
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This book deals with construction of artificial human and animal sense organs. The
analyzer systems, in which there is a mechanism for enhancing differential sensi-
r tivity, codes the stimulus.with the number of the most stimulated cha.~nel. Ana-
lyzers of intsnsity, color, orientation, line. of direction and speed of movement
of an object, its position in space are described.
1 This book is intended for neurophysiolooists, biophysjcists and specialists in
I sensitizing robots.
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There are 74 figures; bibliography lists 111 items.
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FOREWO1tD
This book is the result of 15 years of work using methods of psychophysics, neuro-
physiology and cybernetics. The r~search was conducted in a man-neuron-model system.
Investigation of a concrete sensory function on the psychophysical level, in experi-
ments on man, developed in the direction of demonstrating its neuronal mechanisms in
animaY experiments. The final stage of the study was a model, for which rather rigid
requirements were imposed; the entire model reproduced the psychophysical charac-
, terisCics of the function under study, while each neuron-like element of the model
reproduced the characteristics of the corresponding real neuron.
Construct~on of the models was based on the neurophysiologically validated principle
of cod~ng a signal by the number of the detector channel. This principle provided
for combining data transmission and processing in a large number of parallel
channels.
The study of concrete analyzers of color, intensity, motion, orientation and depth
made it possible to formulate general principles 4f construction of artificial sense
organs out of neuron-like el enents. Expressly these general principles of construc-
tion of artificial sense organs, with the features of natural neuronal analyzers,
constitute the main content of this book.
Adhering to the principle of coding by ch~nnel number in artif icial sensory systems,
it is necessary to settle the question of using information presented in this manner
in problems of control. Electrophysiological studies of command neurons, which
generate "chords" of motioils by means of their systems of oommunication ;~izn moto-
neurons, made it po,sible to conclude that control problems are solved by connecting
or disconnecting detectors from command neurons. The results of this analysis were
.formulated in the description of the conceptual reflex arc.
'Z'he aggregate of receptors, primary detectorg and selective secondary detectors
forms the neuronal analyzer. This analyzer is an expreasion of the biological
analyzer discovered by I. P. Yavlov. An exogenous f~ignaZ, which elicits a seti ~~f
~excitations in indep~ndent primary detectors, generates an excitation vector. The
exc�ltation vector, which acts upon the "fan" of communication [or connection] vectors
that cannect primary and secondary detectors, creates single maximum excitation on
~ one of the elements of the population of secondary detectors, coding the signal
with the localization site of the excitation maximum. ~
According to the principle of coding a signal by channel numher, a set of stimuli
i~ reflected in an rc-dimensional sphere, which is formed by the detector neurons.
With a change in sibnal, the excitati~n maxim~am reflecting the signal chang~ shifts
over the quasireceptive surface represented by a set [or many] secondary detectors.
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~ Reflection of the signal on the sphere.leads to a new apprcach in human psychophysics
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' and metrics of robot perceptive space. The sub~ective difference between stimuli
~ in man and a robot equipped with neuronal analyzers is measure3 by the amall arc of
the large cixcle of the n-dimensional sphere. This arc connects points at which
I� are localized the secondary detectors reprPsenting the corresponding stimuli.
j The precision of function of the human and animal neuronal analyzer is enhaaced as
_i a result of operation of adaptation mechanisms of primary detectors and lateral
; inhibition of homologous primary detectors referable to differeat local analyzers�.
; The emphasis of differences between signals is manifested by successive and concu'r-
j rent contrasts. Introduction of adaptation and lateral inhibitiion into artificial
sense organs providing for enhancement of discritninant sensitivity generates illu-
' sions in them that are analogous to man's p~rceptive illusions.
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~ Thus, artificial sense organs consisting of neuron-like elements reproduce very
; completely the structure and function o� hiunan sense orgar.s. The general principles
~ of construction of artificial sense organs from neuron-like elements map find prac-
~ tical applications in two different fields: development of sensory prostheses.
i directly coordinated with the net.~ronal structures of thP human brain and design of
; sense organs for robots with elements of artificial intellisence~
'j Regrettably, Sergey Vasil'yevich Fomin, whose ideas served as the basis of this
~ book, passed away at the final stage of preparing the manuscript and could not
-j see it published.
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CHAPTER 1. CONS1'RUCTION OF ARTIEICZAL SENSE ORGANS
Robot's artificial sense organs. Development oi modern technolog~ is largely
related to advances in creating integral robots with alements of artificisl intell:i-
gence. xhe ability to functi.on in a complex environment is a c~istinctive feature
of such robots. ~or this, not only must they have'a sophisticated system of
actuating elements, but a well-developed system of artificial sense organs capabl~
of processing a large volume of sensory data for analysis of scenes and complex ~
- acoustical signals.
There must be provisions for man's communication.with robots for effective control
- thereof. We refer not only to development of an effective language for communica-
tion, but obtaining a similarity of internal conceptions of man and robot. In
other words, it is necessary for ob3ects distinguished in t~e environment by robot
and :aan to�coincide as fully as possible. .Only then will the intexaction of man
and r~bot be effe~tive. Finally, all deviations of interual conceptions of the
robot from the internal conceptions of man should have a simple and graphic inter-
p~etation in terms of human perception. .
All these considerations compel us to search for the means of creating artificial
- sense organs, the operating principles of which would�be similar to the operating
principles of human and animal analyzers. Since human and animal analyzers are ,
capable of rapidly processing large arrays of input data, we can expect to find
ne:a effective means of information processing on this route. ,
Computex's perception organs. The area of refinement of systems of man's
communication with a comt?,ster is an important area of application of artificial
sense organs. Although all of the procedures of recognizing speech sounds and
analyzing visual scenes can be imp].emented by computers, this would require a
large memory and signi'ficant time for conversion of such complex signals. A
better way would be to develop specialized parallel-action processors that would
_ permit rapid processing of complex acoustical signals and visual scenes. Thus,
- the problem of creating artificial 5ense organs for a robot ties in with the prob-
lem of creating perception organs for a computer. It is also desirable to have
- the internal representations of acoustical and visual signals in the computer:agree
with the internal. conceptions of man, so that the language of communication between
man and computer would be based on the similarity of conceptions.
Prostheses of human sesne organs. In order to perform the task of creating
s~ousti~~~ and visual prasthesis directly~related to neuronal mechanisms of the ~
brain, it is necessary for the principles of aignal coding in the prosthesis
to conform with the principles of signal coding in the brain. Work on artificial
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sense organs based on biological principles enables us to come close to such
agreement, since the reactions at the output of technol~gical neuron-like elements
_ ar~e analosues of reactions of real neurons. Thus, development of artificial sense
organs based on the functional principles of human and animal sense organs would
also serve~ a~ the basis for developing new types of prosthetics of human sensory
system~.
Man--neuron--model. Development of general theory of artificial sense organs
providing for ,~i:milarity of internal conceptions of man and robot is based on psycho-
physiology, whi:.f~ emerged on the borderline of psychology, physiology of higher
n~rvous activity, neurophysiology and cybernetics. Psychophysialogy is the discip-
line that deals,with neuro:ial mechanisms of psychological processes; it is based on
the man--neuron--.~udel grinciple. As they analyze functions on the level of human
behavior and verbal reactions, psychophysiologists turn to analysis of neuronal
m~chanisms implementing this function. The work ends with construction of a model
of the function under study. The model is created with neuron-like elements.
Rigid requirements aLe imposed on the model: the model as a~;hole must recreate
the function under. study on the behavioral l~vel, while its neuron-like e].ements
m ust conform in cliaracteristics to real neurons involved in the mode]-ed function.
From the standpoint of development of artificial sensory systems where internal
. conceptions of man and robot would coincide, such a model of a sensory funetion is
also a technical solution of the problem.
� A comparison of concrete models of sensa:y systems makes it possible to construct
a single scheme--generalized model of sensory funcCions. It is possible to construct
artificial sensory systems that have no direct biological prototypes on the basis
of such a generalized model. ~
Information coding in the nervous system. The ner~io~s system performs
functions of control, transmission and processing of in.coming information. Inci-
dentally, it should be borne in mind that the above separation is quite arbitrary,
since cantrol always includes some information processes, whereas the organs
that transmit and process information serve as objects of control (for example,
perception of visual information depends appreciably on control of eye movements).
Moreover, there are many general principles, such as multilevel organization and
learning ability, ar.e inl~erent in processes of contr.ol and information processing.
The same flow of :;igiials transmitr_ed over a communication line can deliver differ-
ent information, dependin~; on expressly what the corresponding receiver reacts to.
For example, when we receive a letter ~e arP usually interested only in its text.
. However, it is coiiceivable that two individuals who are corresponding a.greed to
attribute meaning to, for example, the color of the paper or lettering, rather
than the text of the letter. One can selpct such "informative signs" arbitrarily;
but the receiver must have the physical properties to perceive them (the color of
the paper would mean nothing to a blind person) and to retain thpm in the course
of transmitting tlie message (how the letters are written cannot serve as the code
if we use telegraphy, rather than the mails).
Tt~ese obvious considerations are quite applicable to transmission of infcrmation
in ttie nervous system also. Our perception of the world around us is multi-
faceted. We perceive bright colors, diverse sounds, odors and peculiar shapes in
it. In the nervous system, all relevant information is coded by a specific dis-
tribution of excitations in numerous neurons. The question of expressly how
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this coding is done is one of the basic ones in n~urophysiology and biophysic$ of
com~plex systems.~ Let us consider two problems, na~mely, coding information by a
series of impulses within a single (unbranched) nerve fiber and coding in a complex
multichannel system.
Coding .information in a nerve fiber. It is a known fact that the inter-
spike intervals serve as information carriers when a series of impu'les extends over
a nerve fiber, since spikes themselves are rather ~ctandard. But what precisely is
significant: the length of different intervals, their mean length over a certain .
segment, grouping of impulses in a bundle or something else? This is far from
~lear, and one could hardly offer a single answer that would be suitable for all
cases.
At first glance, it appears best to code information by the lengths of different
Interimpulse intervals, similar to the dots and dashes of the Morse r_ode. This
method could provide for a high throughput of the communication channel and high
. speed of system operation. Coding information with the average frequency of impu~-
sation or �ome other statistical characteristics of a series of impulses cannot
pr.ovide such rapid action. However, there are several factors that limit the
possibility of coding information by the lengths of different interspike intervals.
These factors include, among others, the following.~
Mathematical modeling of processes of dissemination of excitation in a nerve fiber
(1] and direct physiologic~l experiments have shown that the impulse sequence, which
has a complex structure, does not retain this structure as it ~ravels over a long
ner~e fiber if the impulse frequency in a train is high enough. This effect is
attributable to the depend~ence of velocity of impulse propagation over the nerve
f:Lber on duration of the refractory phase, i.e., time tha~ has elapsed after the
preceding impulse. By virtue of this dependence, there is gradual equalization af
interspike intervals in a train of spikes, and only information about the mean
impulse frequency is retained a.*. ttie output. Of course, this does not happen when
impulses follow one another at long enough inte~rvals, since none falls into the
phase of relative refraetoriness of the fiber. But then the information is trans-
mitted slowly, and the main advantage of coding by individual intervals, high
' throughput, is lost.
Thc~se considerations apply mainly to long fibers. Similarly to exponential extinc-
tion of potential in a cable, there is exponential leveling down of infc.~rmation
about the duration of individual interspike intervals in a long fiber. Tn short
fibers, the shape oE the impulse train doee not have time to level down, even
wtien f recluency is h igh .
It ~t?ould be borne in mind that dissemination of impulses over a fiber in a
rela~ively refrar_tory state cannot be construed as a purely laboratory phenomenon
observed with unnaturalty high stimulation frequencies. The phase of relative
- refractoriness lasts abaut 100 ms and the interpulse interval constitutes only
6-lU ms in the motor axons of the locust. In the internuncial neurons of th~
- spinal cord~of mammals, in the neurons of certain ascending tracts and acoustic
nerve fibers freyuencies of up to 100 imp s'1, and in fibers innervating the
electrical argans of fish the frequencie.s are even higher, up to 1500 imp s'1.
Ttius, the propagation of impulses over a fiber in a relatively refractory state
is certainly encountered under natural conditions.
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j Smoathing of interpulse intervals is one of the reasons that limit coding by the
~ lengths uf different intervals. Another reason is referable to the distinctions
i of the decoding system. Secretion of inediator in synapses in re$ponse to an impulse
! is atochastic in a nwnber of instances. There is a probability of only 1/2 th.at
i
; an impulse going to motoneurons over group I fiberf will elicit secretion of inediator.
~ It is obvious that in such a case it becomes unredlistic to consider the possibility
of coding infot~nation by individual interimpulse intervals.
These circumstances limit the possibilities of cod~ng information in a nerve fiber
i with individual impulses. However, such cod:tng is by no means ruled out, particu-
; larly in short fibers. Thus, as far back as the early 1960's, in several well-
~ known studies conducted with neurons of the Aplysia mollusk, it was demonstrated
! that one can obtain difFerent responses from artificial stimulation of these neurons
~ with pulse trains of the same average frequency but different configuration. For
I example, the neuronal reaction may change if this pulse train is de~ivered in re-
i verse order. Evidently, in this and other similar cases, the neuron rQacts to the
~ temporal pattern of the pulse train as a certain whole [2, 3].
~ Coding informa.tion by channel number. Recent experimental and theoretical
' studies indicate that there is widespread so-called coding of information by the
j channel number, or locus [site] cnding in a living organism, particularly its
i sensory systems. According to i:his conception, the sensory system has a set of
i detector neurons, one of which is stimulated mora than its neighbors bp a speci~ic
stimulus. The number of the detector neu~on that is maximally excited determines
~ the sensation that is elicited by the coded signal parameter (brightness, color,..
! direction of movement). If two stimuli elicit maximal excitation of the same
~ detector, they are not distinguished according to a given parameter.
I It wss demonstrated experimentally that the reaction of individual sensory neurons
~ presents distinct specificity for the value of .the parameter of the stimulus deli-
vered [4-6]. In particular, some of the neurons of tha visual ans~lyzer do not
react at all to diffuse illuminatiori of the retina [7~. One must del.iner an appro-
priately organized image to a specific part of the retina to elicit a reaction in
such a neuron. The mechanism of lateral inhibition [8] provides for the high
i sensitivity of detector systems. However, ln the opinion Qf the critics of the
detector conception, detectors are temporary combinations of neurons that reflect
~ only the process of "running" a certain program ~for pattern recognition throug~
~ the neuronal network. After running this program, the "detector functions" of the
I cell may disappear and it could take on other functions. ~
i Current experiments on stability of detector properties of nEUrons revpaled that in
~ individual neurons these properties are either genetically determined or formed
j in early ontogenesis, ~and then persist for the entire lifetime of an animal.
~ Coding by channe'1 number as a process of parallel information processing by no means
~ rules out successive analysis. If a etimulus is complex enough and the animal
' does not have to deal with it often, perception may proceed step by step, by
~ isolating the impurtant and simple features of the analyzed image. This is asso-
; ciated with successive acCivation of different detector neurons, which reflects
E the process of successive assembly of the "internal. image" of an exogenous
i sttmulus from simE~le ta~s [9, 10]. Such is the function, for example, of eye
! movements in percE~ption of a complex image [11]. It should also be stressed that
~ coding by channel number provides for concurrent transmission and processing of ~
~
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information. Concurrent ["parallel"~ information processing enables living organ- .
isms to effectively.solve identification problems.
" is also
A property of living systems, which we could call "functional stability,
related to coding by channel number. We use functional stability to refer to
viability, the capacity of a living system to perform its main functions, even if
in a somewhat.reduced form (for example, a doincthe resencetoffsomerinjury,teven
legs, whereas a car missing a wheel cannot), P
rather significant. The concept of functional stability is related, to some
extent, to the concept of reliability in the meaning of von Neumann, but does not
c:oincide with i+t. In his well-known wqrk, von Neumann [12] discussed the reliabi-
lity of a system which, like an electric switch, has two states--on and off. A
different situation is inherent in living systems, in that along with the two ex-
treme states--complete work capacity and camplete breakdown--there are also various
intermediate states of partial work capacity. It is logical to intxoduce the con-
cept of functional stability in the presence of injury for such systems. Evidently,
the principles of constructing functionally stable.systems must be other than
Neumann's principles of reliability.
The combination of coding by channel number and appropriately organized lateral
inhibitory connections could serve as the basis for constructing neuronal systems
that are quite perfect in functional stability, although some elements of these
structures do not have such perfection [13].
In conclusion, it should be indicated that informatiAn processing in neural networks
is often described as follows: all processing occurs in neurons, while ~he nerve
fibers that connect them play merely a passive, transmitting role. However, there
is every reason to be~ieve that this conception, is not entirely,correct. Let us
~ consider the process of propagation of excitation over a branching fiber in the
belief that this process is described by the well-known equations of Hodgkin-Huxley.
As shown b;� estimates, the branching node of such a fiber could P1aY and pand of �
logic element, implementing certain basic logic functions of "or," "
"inhibition,"~depending on the conditiona (proportion of diameters of fibers forming
the"ramification, difference in times of input signal in the unit via different
fibers). ~ . ~ .
By combining the main logic functions one can obtain others. Here it is suggested
that there are natural analogies with so called homogeneous environments--technical
equipment similar in properties to branching neural networks, which have recently
gained rath~�r wide popularity as the basis for construction of various computer
systems.
Thus, even a single branching unit of a nerve fibdetector.peThe possibility ofex
_ physiological functions, for example, serve as a
complex logical information processing in branching structures siiggests that, per-
haps, the role of dendrite arborizat~.ons in information processing is much greater
than usually believed. With reference to neuronal nets, we are apparently over-
simplifyin~; the individual cell. Stating that "the brain is a computer," we
relcgate the modest role of a single elemsnrloser tonthe truth. Perhaps the
formula that "the neuron is a computer i
- f detector cotild be performed by parts
- According to the�furegoing,:the function c,
of a neuron, rather than the neuron as a whole. The material submitted below is
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, not in contradictic,n with this conclusion, although the term "detector" implies a
single element of the corresponding neuronal net. The cambination of numerous
; independent detectors in a single element does not introduce any appreciahle
difficulty in considering the function of the entire analyzer.
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CHAPTER 2. MODEL OF CHANNEL NUMBER CODING . ~
Spherical model. The function of signal discrimination in a model of coding
by channel number is provided by the fact that a specific value of parameter of
an exogenous signal generates a solitary maximum of excitation on one of the spe-
cialized detector neurons.. Detector refers to a neuron that is selectively
. adjusted for a specific value of the signal parameter. This selective adjustment
of the detector is obtained by a specific system of communications, by which the
detector is connected to neurons of the 'underlying level or receptors. Each de-
tector forms one of the parallel channels for information processing. With a
change in th.e exogenous signal, the maximum excitation shif ts from one detector to
another. If two signals elicit maximum excitation of the same detector, they
are not distinguished. Schematically, a detector can be described as a formal
- neuron with several inputs through which signals come from underlying neurons--
_ primary detectors or receptors. Each c~f the inputs should provide independent
information to ttie detector (Figure 1). The independence of the inputs means that
one cannot predict the activity of one input on the basis of knowledge about the
activity of any other input.
The diagram illustrates a secondary detector. The arrow shows the direction of the
signal at the detector output. The lines converging on the detector illustrate
arrival of signals that converge on the detector (f2--excitation coming over the ith
channel). The small circles at the point of contact between the input and detector
represent the coefficients of synaptic transmission; e~2--coeff icient of synaptic
transmission of the ith channel on the ~jth detector. The dotted line refers to
part of the inputs not shown on the diagram. The detector adds the paired products
of eacti input signal multiplied by the corresponding coefficient of synaptic
- transmission:
~ n
~ ~l~ = c~ i1~~ + . + c~ifi + . + e~nfn � ~ ~~jifi~
_ i=1
where d~ is magnitude of excitation of the ~jth detector. The set of delivered
stimuli forms excitation vector F={fl, fi~ fn}� The set of communica-
tion coefficients forms the communication vector C~j ={e~l, e~j2, e~jn}.
Ttie reaction at the detector output equals the scalar product of excitation vector
multiplied by communication vector d~j =(F, C~). When the input signal changes,
so does the i. ronal react3on, and it reaches a maximum when the excitation vector
is collinear with the communication vector. The modulus of the communication vector
- is constant (C~~ = con~t. . If ~F~ = l,~d~jmax = ~os ~F~ I~~IIFI - - 1'
m).
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~
1
+ FnR (1M1~1('IA1. II~M: nN1.Y
~
i .
.
~
i
~ j
- ~ .r
f ~i. ~ Jk ~ ~
~ ' ~ d~ j' . �
; ~ X ~
f' f 0).
A maximum increase in sensitivity is obtained when the adaptive stimulus corres�-
, ponds to the following values for the argument of the cosine curve that describe
the sensitfvity of primary detectora: ,
f (~)=0~ 90~ l80, 270� . . (1.23) .
and differential sensitivity does not change under the influence of adaptation if:
, f (~)-45, i35~ 225. 3i5�. (1.23a)
,
- Such an increase in analyzer sensitivity is useful from the functional point of
view: during prolonged viewing of the eame stimulus there is an increase in the
system's capacity to detect minor deviations from the adapting stimulus.
It should be noted that if the sensitivity of primary detectors increases during
adaptation, the differential senaitivity of the analyzer to stimuli clase to
the adapti~~e one, on the contrary, diminishes ~~
~If the density of the detectors is not constanC, ~ will be a certain function of I. '
If this function is known one can determine Weber's ratio, with consideration of
the changing threshold.
- Adaptation in the intensity analyzer. Adaptation at the inp'ut of primary
detectors: Let adaptive stimulus SI be delivered to the input of the system.
A signal is delivered to the input o~ horizontal cells which equals.:
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where Pp(I~ is the receptor's reaction to the adaptive stimulus, RB is the seC of
receptors of the main field. If the adaptive stimu3us is followed by delivery of
stimulus SI whose intensity is I units, the signal at the input of the primary de-
tectors can be calculated as follows:
- sinau(1), if u~j)=~p~~j~-~~1'r~l.)~a~ , . (2.11)
. f~ _ if u(1) ~ 0; '
- ~ . cos au (l), if u (1) ~ 0, ~ . . _ .
' ' 0, if u(~ G0. ~ .
~ Adaptation of primary detectors: Let adaptive stimulua SIa, which excites primary
detectors to level (2.11) be delivered to the input of the system. Quantities
(2.11) are components of ex citation vector ~(I~ generated by stimulus SIa. Under
the influence of prolonged excitation, the sensitivity of primary detectors dimini-
shes proportionally to the level of their excitation by the adaptive stimulus. As
- a result, stimulus SI delivered right after the adaptive one generates the follow-
ing~.excitaZion vector: ' _ _
^ F(Ill.)=~~1.~ . ~ (2.12)
where.A(Ia, t) is the adaption operator (Appendix I) and t is the time of delivery
, of the adaptive stimulus.
~ Knowing the corresponding excitation vectors (2.12) and zero vector of "gray proper,"
one can calculate the angle between them: ~
, ; (I ) = I~' (l - 0)~ F ~111.)~� (2.13)
- ~
~
Overall level of activity of intensity analyzer. We shall call the sum
, of a~tivity of all secondary detectors the overall level of analyzer activity.
The excitation profile on the set of secondary detectors (aee Appendix 1) is des-
. cribed by the function cos [f(I) - f(I~)], where I~ is the intensity of the optimum
stimulus for the ~jth detector. In this case, overall activity of all detectors
will be: ~ ~
�rs ~ ~ ' � :
- S (1) - j cos [f ~1~ - i di ~J~), .
o �
i.e., . �
s~n~~~ f cn+d~n ~~n. cz. ~4>
Expression (2.14) assumes a maximum value when cos f(I) = sin f(I), i.e., when the
components of the excitation vector equal one another. Thus, total illumination of
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the entire retina from zero to a certain intensity I first leads to an increase in _
overall analyzer activity, which reaches a maximum with intensities that generate ~
an excitation vector with = 45�, after which further increase in intensity leads ~
to decrease in overall analyzer activity. `
1
Overall activity of primary detectors behaves analogously: SP(I) = cos f(I) + sin f(I). '
With increase in stimulus intensity Sp(I) increases, reaching a maximum at th.e point `
where cos f(I) = sin f(I), and further increase in intensity leads to decrease in
Sp (I) .
An analogous function of intensity was described in a study of the magnitude of
evoked potential or mean level of activity derived from the optic nerve [18].
In the foregoing, photosensitive elements with characteristics of the (2.3) and
(2.4) types were used as photoreceptors. However, the dynamic range of such charac-
teristics does not exceed two logarithmic units. We obtain even closer coincidence
of the model's characteristics with the analogous ones of man if we use as photo-~
receptors elements with characteristics of the following appearance:
.
" 2.15)
r(1)=Na.: ~
where R~X is the maximum response of the receptor, c7 is intensity of light at which
the response of photoreceptors equals half its maximum value and n is a cons tant that
determines the steepness of responses. For example, with n= 0.5, the range over
which Weber's ratio is constant, ~I/I = const, equals about four logarithmic units,
while the indicator of xhe law of Steveneon is about~0.4. Expression (2.15) des-
cribes receptor responses better than a hyperbolic tangent.
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~
I
' ' .
;
~
`
` . �
~
Y- .
~
I
APPENDIX 3. COLOR ANALYZER
I Sensitivity characteristics of cones and primary color detectors.
~ Color perception is possible only when there is sufficient illumination, when the
outside world is perceived by the conea. In twilight condifions, when only the
; rods are functional, man cannot perceive colors, and the world around him is
~ perceived as being black and white.
~ There are three types of cones, R, G and B. If the sensitivity characteristics
of cones were to be described as functions of frequency of monochromatic radiation,
these characteristics would have the same appearance for all three types of cones,
~ . although their characteristics are shifted in relation to one another. The
general characteristic thus obtained coincides, with accuracy to a constant factor,
with the so-called Dartnall nomogram [34].
Hereafter, it is assumed that the cone charseteristics are Dartnall functions.
The question arises: Are Dartnall functions optimal from the standpoint of integral
sensitivity of the entire analyzer? For this, let us rewrite functional
- rf _ _ .
~ ~ (f~) = ~ ~a IF Ur (f~ -1- T)~I~ (3.
4~
(~o determine the cosin, see Appendix 1, expression 1.2), using smallness T, i.e.~,
~ f2(~I-T~ = f2(~~ + TfZ(~), in a somewhat different form: ~
f p, . .
, ~1 ~ir ~~P)) = J cos {F (fr I~ ~fr ~FT ~fi ~ (3.2)
v. .
where F' is a vector with components of the {dfy(~)ld~} type.
Functional (3.2) does not overtly contain variable d. Consequently, for Dartnall
' functions {fi(~)}, i= 1, 2, 3, to describe the extremal, the corresponding
Hamiltonian [104] along these extremal must be constant:
II - -4~ ~b~~/, conat, ' � (3.3)
. , �
where @ is a.subintegral function of expres~sion (3.2) and ~f2 is its partial deri-
vative ~/a; fi.
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In determining functional (3.2), it must be borne in mind that Dartnall functions
are not orthogonal. Condition (3.3) with symmetrical position of Dartnall func-
tions on the frequency axis was dirsctly checked in [103, 106]. It was found that
condition (3.3) is satisfied over the entire range of the visible spectrum.
Thus, there are grounds to m~aintain that Dartnall functions are close,to optimal.
However, it is not desirable to make direct use of cones with Dartnall functions of
sens~tivity as primary detectiors determining the componeats of the color excitation
vector. The fact�of the matter is that, in this case, the sub~ective distance be-
tween colors would be small and the excitation vector would not exceed the range
of one octant. ~
For this reason, detectors whose responses were obtained as a linear combination of
responses of individual cones are used as primary detectors. Also, the direction
of the excitation vector should change as much as possible with change in spectral
composition of illumination. In the ideal case, the sensitivity characteristics of
primary detectors should be described by the corresponding directing cosine curves.
Let us now consider the construction of secondary detectors, without determining
- the characteristics of primary detectors. As we know, the reaction of the ~th se-
condary detector c~;n be found from the expression
d ~1~ R) _ F (3.4)
Let us now stipulate that, with frequency of light radiation the ~th detec-
tor is excited more than any other detector. This condition is met if, at a given
- value of the reaction of the ~th detector reaches a maximum, and the maximum
reaction of any detector equals a certain constant value B. In other words,
dd tl, ~l ( aF (avllf ~ ~ . (3.5)
' ~ (r-r~ `C~' ~ / Ir-~?f ~ � .
provided that ' (3.6)
d (f ~ ~p f)=B~
where ~j = 1, . , ?n.
In this case, let us first consider condition (3.5), and use (3.6) to�fiMd:unknown
constants that determine the modulus of communication vector. From (3.5) we get
ad a~, r1(~~ = I I( a~~ I co8 ~C~, a~ ~I _ p~ . ( 3. 7 i
~ r-p~ .
i.e., ~
. 1 ap l~) I .
r-.f.
Communication vector C~j must be orthogonal to vector dF(~)~d~l~ a~~j, tangential to
spatial ~:urve {fk(~)}, k= 1, 2, 3, and ~CL is the interval of frequencies of
visibl~ monochramatic radiation. The sought vector C~ is in a plane that is ortho-
gonal vector dF(~)Ic~I~ There may be many such vectors. Let us choose
one of them so that the angle between it and excitation vector F(~~) would be as ~
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, small as possible. To find such a vector, let us pro3ect on the plane of communica-
tion vectors {C~j} excitation vector F(~~) and we shall get vector F~(~~):~ ~eught
vector C~ coincides in direction with vector F~(~~), i.e.,
.
_ _T-.._ .
~ ~~=YF~c~,~: c~:s~.
where Y is a certain constant.
In view of the fact that vector F~(~) is orthogonal to vector F~(~~)--pro3ection
of vector F(~ ) on the plane of communication vectors {C~}, we can submit vector
F(~~) as the ~ollowing sum:
r = F~ (~f) + ~F; (~)1~=a, .
or .
rr f) = F ~~P~) - ~FY ~v=ri, ~ 3 . 9 ) ,
' where S is a certain constant. ~
Since vector F~(~~) is orthogonal to vector F'~(~)I~a~~, with consideration of ~
(3.9) we get:
~F~ f)� F~~~)) ~r=~ f = (F F, I4=4~ . .
. Y ~ p~~~ IT-4 f- O .
or '
p t~)~ F* (~11 I (3.10)
1' 9 Fp t'=4~ ~ �
Moreover, considering condition (3.6), we can obtain the value of the other
unknown constant: ~
D
7 ~F ~9'~~ - ~F9 F Ii=4J ~ . ' ~3.11~
Knowing curve {fk(~)}, (~~L, k= 1, 2, 3), we can calculate comm4unication vector
C� (3.8), where coefficients Y and ~ can be found from conditions (3.10) and
(~.11). The communication vector enables us to calculate the characteristics of
output detectors (3.4). Figure 40 illustrates the respones of different output
det ectors calculated by the method described in [105]. If we were to choose any
thr ee independent orthogonal functions out of the existing set of responses,
these functions could be used as the characteristica of primary detectors.
Tw o-dimensional invariant spaces of color adaptation operator. Let
' a certain adaptive stisnulus S o be given, to which corresponds excitation vector
F(~o) with components {fi(~o)~. Let the vector be transformed under the influence
of prolonged viewing of stimulus S~o as follows:
~~Po~~o) = e9~ ~~o~ F ~~o)~ ~ ~3.12)
where.~ (~o, t) is the adaptation operator. ~(~p, t) is a diagonal operator,
with the following coefficients on the main diagonal:
aii =1- T ~~)I ~3.13)
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In the general case, vector F(~o/~o) is not collinear to vector F(~o). The question ~
arises: In what cases is the trajectory of the vector flat in the course of a~ap- !
tation and, in addition, does it contain the vector of white color2 In other words, ~
in what cases does adaptation have no effect on the perceived color of the stj~nulus?
Let there be the three following vectors: purely monochromatic vector in the absence
of adaptation F(~), white vector F(8) with components fZ(d) and vector dF(~o/~o)
tangential to the tra3ectory of adaptation. The components of the last vector equal
Y~~t~~ {f~(~Q)}, 1, 2, 3. If all these vectors are in the same plane at any
point in time t, the tra~ectory of vector F(~o/~o) W~11 be flat. In this case, all
three vectors should be linked with a linear function. Then the determinant plotted
on these vectors should equal 0: ~
-i i i
~~~1i� f~) _ -7~ ~t) f ~a) ~fi ~~o) f~ ~~o) ~'Po) =0. (3.14)
~ ~~o) ~ ~~o~ ~ ~T~)
Since we are dealing with an alternant [Vandermond determinant], condition (3.14)
can be replaced with condition: !
v~-i,~u~-i,iv,-~a=o� c3. ~5~
Thus, for ust exciteutonan equalaextentgathleastitwoyofuthegthreetprimarytdetectors. ;
stimulus m
i
. i
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l .
: AppENDIX 4. LINE SLANT ANALYZER
T~rimary detectors of line slanof illiumination byfineanssofion orloffnreceptive
gradient: Distinction of the range
fields has a substantial flaw: in order to distinguiah a black line on a white
background and white line on a black background, different systems of receptive
fields must be used: off-on in the first case and on-off in the second. St~ch a sys-
~ tem is cumbersome and unreliable.
Let us consider another method that is suitable for distinguishing both a white out-
Figure 74 illustrates a
line on a black background and a black outline on white.
system that will function only if its receptor layer makes small random ~umps all
of the time. Let the image of a black-white border be projected on the receptive
field. Two groups of receptors can be distinguished. On some receptors, the
level of illuaiination changes constantly since the range of change in illuminThe
tions shifts from one receptor to another in the presence of random~trem~esult,
illumination level remains constant on the rest of the receptors.
~ a variable signal arises a_t the output of the first group of receptors and a con-
stant one at the output of the second group of receptore. The signal passes from
' the receptor to the ionuof~the signalrviantheeinhibitory channelalags in relatiouion
channel. Transmiss
to the excitatory channel.
When there is an unchanging image on tthe retina, signals from the constantly illu-
minated group of receptors passing via the inhibitory and excitatory channels com-
pensate one another. As a result, the output signal of these neurons is found to
- � equal zero soon after turning the stimulus on. If the signal at the output of
~ ~ the receptors changes in time, excitation and inhibition passing to the input of
the second neuron are unable to compensate one another. As a result, th~s signal
passes only from the receptors, on which the limit of illumination is projected
in the presence of tremor. This method makes it poasible to single out a white
- outline on a~black background and a black outline on a white background.
This method can also be well-used in the visual analyzer, since the eye has the
- required random tremor. Thus, frequency of tremor in man constitutes 150 Hz and
amplitude is about 18 s of the visual angaewithin therrangenof 1-3sconesn[11].~
an image in the centra~ part of the retin
Interaction betweenvariable~component,ageneratingnphasic reactiona8innganglionr
distinction of the
cells [22]. '
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In the following, it is assumed that
- ~n to construct primary detectors of
~ ~ff orientation use is made of signals taken
� from neurons, on which there is preli-
~ minary distinction of image outline.
Organization of receptive field of
primary detectors: Let a segment of
+ image outline be pro3ected in the re-
~ ~ ~ e� ceptive f ield of a 1oca1 analyzer.
t Under the influence of light at the out-
- put of receptors or neurons distinguish-
- ing the outline, there is appearance of
~ signal r2(I), i= 1, s, where i is
receptor number,.s is the number of
` f- photoelements in the receptive field �
~ on and I is intensity of receptor illumina-
~ tion. The set of signals {rZ(I)}(i = 1,
: -~-d - ~
f . . . , s) is a discrete approximation
~ ~ . of the image delivered to the receptive
~ II ~ 1 R field o.f the local image analyzer. We .
shall consider set {r2(I) } (i = 1, ,
8) as components of s-dimensional~
_ f-~--~ A n �jf vector The orientation of a local
Fibure 74. line segment is given by the number ~
Distinguishing outline of an image by (angle of tilt in a given system of
menas of tremor coordinates), which takes on.any yalue
in the interval [0, ~r]. It is assumed
that the value of the parameter is coded unambiguously by the direction of exeita-
. tion vector F(~) or number i~[0, 2~r].
' Vector F(~) ~must be at least two-dimensional, and hereafter we assume that dimen-
- sionality equals two. Consequently, ~ae must have two independent primary detectors
whose responses are described by the functions:
_ f' (~p) ` sin 2~ x f~(~) = cas 2~. (4.1)
Thus, the image on the retina generates s-dimensional vector o~. Then, by means
of a certain degenerate operator oBl, vector-~ is transformed into the second
excitation vector The appearance of operator ~1(~ is determined ~
by the contacts between receptors aad primary detectors. Apparently, there are
many [or a set] such transformations, with which the following equation applies:
- We shall discuss below two methods of determining operator ~1: Let the receptive _
field of primary detectors be divided into two interaecting connected zones. We
shall call the zone, illumination of which elicits inhibition of a primary detector,
the inhibitory zone, and the one illumination of which excites the primary
detector;, the excitatory zone. Let the influence of each point of the illuminated
receptive~ field,on detector activity be conatant and independent of the position
of the point in the receptive field. The pro~ection of the line on the receptive
field elicits a reaction by the primary detector, formed by the sum of signals from
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the inhibitory RT and excitatory Rg areas. These sigr._.is equal the cosine and sine
of the dual angle of inclination of line In or.der to determine the form of re-
ceptive field of the corresponding pximary detector, let us transform (4.1) into
the following expressions:
fa = si~~ 2~ = cos~ -I- 45~ - sin' 45~~ (4 . 2)
, f, = cos 2~ = cos' ~ - sin' (4 . 3)
Thus, according to (4.2) and (4.3), the overall signal from excitatory regions should
equal cos2 ~ and cos2 (~+45�) and the itthibitory one should equal sin2~ and.sin2
(~+45�), respectively. Consequently, the length of the presented line lying in the
excited part of the receptive field is pB = cos2~ or cos2 (~+45�), and for the line
segment in the inhibitory zone, sin2 ~ or sin2 (~+45�). The overall length of the
vector-radius for the entire receptive field is sin2 cos2 1. Thus, the
vector-radius of the receptive field is constant--thQ receptive field is in the
I form of a circle.
The f law of such organization of the receptive field is that, in this case, the re-
action of primary detectors depends on the presence of noise contained in the image.
- Indeed, let the receptive field of the analyzer be illuminated by random spats. The
spots are small, but their density is rather high. If the density of noi~e is high
enough, the overall output signal of the primary detec~or from both zones of the
receptive field separately is pr~portional to the area of these regions. The ~rea
of the excitatory region in the previously proposed case is:
. ZR tR
.Se = i f p'~ _ ~ ~ cos~ ~ - .
o u
_ lo;-}- 8 sin 2~p Io` ~h sIn 4~ lo r:. ~ (4 . 4)
The area of the inhibitory region is found as the difference between areas of the
circle and excitatory region, i.e.,
sr=,~~~,~= g,~� (4.5)
From these results we see that with noisy illumination of the receptive field the
signal at the output of primary detectors does not equal zero:
fi Se Sr = -a14~ = SB - Sr = --n/4, ( 4 . 6 )
which is equivalent to excitation vector ~ 112�30') with~equal negati�ve com-
ponent3. Thus, in the presence at the input of only noisy illumination, there
is the il?usion of perception of a line tilted at 112�30'.
In order to eliminate this flaw, let us consider a dif�erent structure of organiza-
tion of the primary detector receptive field.
- Each p~int on the receptive field has the samP effect on activity of a primary
detector. When an outline is projected in the detector's receptive field, the
absolute value of its reaction equals the length of the line in the receptive field.
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_ The overall reaction of the primary detector should equal fl(~) = ain 2~ and
f2(~) = cos 2~, respectively. Cansequently, the receutive field in polar coordinates
has the following appearance:
p~ _ ~ sin ~ ( N P~ _ ~ cos 2~ . _ (4 . 7 )
Figure 49 illustrates the form of recepti~~e field thus obtained. In constructing
~ a primary detector, it must be borne in mind that a"plus" refers to regions that
have an excitatory effect on the activity of the primary detector and "minus" t~
those that have an inhibitory effect.
With such organization of the receptive field, the reaction of primary detectors
does not depend on presence of random uniform noise in illumination. Indeed, in
this case the areas of~the inhibitory and excitatory zones are equal, so that the
signals from both zones balanre one another.
Finally, there can also be a third form of receptive field. Let there be a center
given in the receptive field, through which a line is drawn. The tilt of this line
equals zero. The orientation of the arbitrary line is determined by angle which
it forms with the line that ha~ zero tilt. The magnitude o~ contact between the
receptor and primarq detector is proportional to cos 2~ (or sin 2~).
Mixture effects in orientation analyzer: Let there be two centered lines, L~1 and
L~2, pro,jected on the receptive field, which correspond to excitation vectors:
c~ (~p~) _(cos 2~p1, aiM 2cp1) H~' (~s) _{cos 2cps, sjn 2~p,). (4.8)
As a result of joint excitation of primary detectors, their excitation level is:
- , _ ~ - - _
f, (~pi, = sln 2~1-}- sIn 2~, - 2 aln (~1-{- ~os (~pl - .
~ (4.9)
f~ 'PS) = 2 cos ~~i -3- ~g ~~i - ' '
The vector with components (4.9) corresponds in direction with the excitation
vector generated by line tilt (~1-I~2)/2. Thus, with simultaneous delivery to
the receptive field of two lines, there is generation of a vector that corresponds
to a line, which is the bissectrix of the small angle between these lines.
Adaptation effects in orientation analyzer. Normalization effect: During
prolonged viewing of a line, its slan*_ does not change when this line corresponds
to one of the eigen vectors of the adaptation operator, i.~., the vector in which
either all not~-zero components equal one another, or else only one c.omponent does
not equal zero (Appendix 1). The former case corresponds to lines with tilt: ~
=1E+~18, (k= 9, 3~ 5, 7), . ~ (4.10)
and the latter, with tilt:
~k=ku/8, (k=0~ 2, /f, 6). ~ . , (4.11)
Let us consider the adaptation properties under the influence of lines with tilts
of the (4.10) and (4.11) type. For this, let us determine how the angle between
the arbitrary line and closest line with tilt (4.11) changes with adaptation,
i.e.,
~ ~ ~ 134
FOR OFF[C[AL USE ONLY .
APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500010009-6

APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500014449-6
FOR OFF(CIAL USE ONLY
a coe F d E ti -'r I 1~ (~?p l~ (~~)1~
_ a~ [ (~PI c~ ('P~)l = .
a~
, ~ (E - Y (t) I 1r q' 1~
(~)-1
~ ~ .
Putting ai=!-Y (t)~/i (~p)~, we have ~ ;
~S - a eos ~ ~~k)~ - d Ear1t ( sk)1t~(Yl ~ (4.12)
- dt ~ dt [En3~r ~T~1
Let cpk =0 or ~pk= a/2, �
f 1\~k~ = Cn9 ~k 1 {1 9~~k~ - 9~R 2~~ ~ i ~ 4� 13 ~
Considering (4.13), expression (4.12) assumes the following appear-
ance: d R~1~ (~1 fl Tk =
~ ~ - dt ~
~a~~ ~ ~ .
- _ Ri/i ~~l ~ail~- a~l~Ea~ail~ , (4.14)
_ IBa~~~'/. f~~~~t)~
Since the denominator of (4.14) is positive, the sign of the entire expression is
determined by the sign of the numerator, After reducing in the numerator dl(t)
- we have
S~ (t) = r~~ [aia, - ala=1 fi fi ~~k)� _ ~ (4 .15 )
Since a2>0, a2f2>0 also, and the sign of (4.15) is determined by the sign of
the expression: .
s9 _ ~ai~i - aia:) ft ~~P) ~i ~~k)� ~ (4.16)
; After substituting in (4.16) the values a2 = 1- Y(t) ~ f2(~) I and ai ='Y~ ~t~ ~,fi�~ ~
, we get - -
, Sa (t) =t~ f~ (~k) f~ (~)I - I t~ (~)I) ~r' ~4. i~>
- Since �Y' (t) ~ 0, the sign is determined by the sign of
- a~ (t) = t~ l, (~k) (I t~ (~)I - I f~ (~)I . ~ ` (4. is> .
Let us first consider the case ~k = 0, i.e., fl(~k) = 1 in the interval of 0f2~~)� Thus, with ~C[0, 45�], expression (4.18) is negative.
In other words, during adaptation the angle of F(~/~), o~(~k), (c~J~ = 0; 0-45� , then ~ f l($) f 2(~) t, f i�)>~ ~ f l~~k) = l, consequently
- da(t)~f 2(~) ~ and, consequently, d4 (t) 0, ~f2(~)~>Ifl(~)~ and, consequently,
expre~sion (4.19) is negative.
Let then = 135� (f2(~k) _-1), ~Cf112�30', 157�30') and 135�, i.e., f2(~)