0362-1197/03/2904- $25.00 © 2003

MAIK “

Nauka /Interperiodica”0408

Human Physiology, Vol. 29, No. 4, 2003, pp. 408–414. Translated from Fiziologiya Cheloveka, Vol. 29, No. 4, 2003, pp. 22–29.Original Russian Text Copyright © 2003 by Krasilnikov, Krasilnikova, Shelepin.

There is a considerable body of data on the effi-ciency of the visual system in recognition of images ofstatic objects in the presence of static additive spatialnoise [1–10], and only a few papers describe similarmeasurements taken in the presence of dynamic noise[11, 12]. No data are available to estimate visual systemefficiency in identifying images of moving objects inthe presence of dynamic noise. However, this mode ofoperation of the visual system is of special interest.This study stems from our previous study [12] and cen-ters on the analysis of the efficiency of the visual sys-tem in identifying images of moving test objects in thepresence of dynamic additive Gaussian spatial noise.

As in the previous study, the performance of a visualsystem is compared with that of the so-called idealobserver and the efficiency, as it was defined by HoraceBarlow, is used as a measure of comparison. It is knownthat the efficiency is determined as the ratio of the thresh-old image contrast energy for the ideal observer

E

id

tothat for a human observer

E

h

at which images of testobjects with a priori known parameters are correctlydetected (or identified) with a present probability

P

:

The objective of this paper was to study the relation-ship between the efficiency of the human visual systemand the duration of presentation of a moving test objectin the presence of dynamic additive quasi-white Gaus-sian spatial noise, with the a priori information on thetest objects being varied.

METHODS

The following method of comparative measure-ments was used. Briefly, the same images of movingtest objects were presented for identification to humanobservers and a computer model of an ideal observer in

k Eid/Eh.=

the presence of dynamic additive quasi-white Gaussianspatial noise. The efficiency was calculated from the prob-abilities of the human observer and the model correctlyidentifying the test objects. Let us consider in detail howthis method was implemented in our experiments.

First, dynamic images of moving test objects in thepresence of dynamic additive quasi-white Gaussianspatial noise were presented in the form of short digitalvideos. Each video consisted of a sequence of noisystatic images of a test object, to each of which a differ-ent sample of noise was added. The test objects werelocated at the center of the images, which were muchlarger than the test objects (Fig. 1a). In this manner, vid-eos with different noise levels were produced for testimages. In a video film, a test object was perceived asmoving across the field of the dynamic image, because,from frame to frame, images were regularly shifted rel-ative to each other, and their sequence was observedthrough a fixed mask with a window size smaller thanthe image size. When observing the images shifting rel-ative to the fixed mask, an observer could see the noisydynamic image, across the field of which a test objectmoved. A mask with a window through which the frag-ment of the noisy image with a test object is seen isshown in Fig. 1b along with a dashed line indicating theedges of the hidden part of this image.

Experimentally, dynamic images (video) were pre-sented in random order for a specified period of time toboth an observer and the computer model. The probabili-ties of correct identification were recorded. In this manner,we performed measurements for images with differentlevels of noise superimposed during video production.

The second particular is the calculation of the effi-ciency. In the general case, the conditions of image rec-ognition were different for a human observer and forthe ideal observer (or, in our experiments the computermodel of an ideal observer). The ideal observer is fur-

Efficiency of the Human Visual System in Recognitionof Moving Objects

N. N. Krasilnikov*, O. I. Krasilnikova*, and Yu. E. Shelepin**

* St. Petersburg State University of Aerospace Instrumentation, ul. Bol’shaya Morskaya 67, St. Petersburg, 190000 Russia** Pavlov Institute of Physiology, Russian Academy of Sciences, nab. Makarova 6, St. Petersburg, 199034 Russia

Received July 5, 2002

Abstract

—The relationships studied between the efficiency of the human visual system for recognition ofmoving objects in the presence of dynamic additive quasi-white Gaussian noise and the duration of object pre-sentation are studied. Different conditions of observation and the parameters of moving objects were analyzed.The efficiency-presentation duration relationship was shown to be a function with two extrema (a minimum anda maximum, at 120 and 400 ms, respectively). The study offers an interpretation of the findings and a functionalmodel to explain this phenomenon.

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EFFICIENCY OF THE HUMAN VISUAL SYSTEM 409

nished, by definition, with full a priori information onthe test objects, i.e., their initial position, velocity,direction of movement, etc. A human observer in ourexperiments, as a rule, had no such information. Conse-quently, his lower efficiency is accounted for not onlyby the fact that his visual system is imperfect, but alsoby the lack of a priori information on the test objects tobe identified. In other words, the reciprocal of the effi-ciency shows how many times higher the energy of theimages has to be for a human observer than for the idealobserver in order for the human observer to match theideal observer in the probability of correct identifica-tion (detection) of the images.

On this basis, the efficiency was calculated in the fol-lowing way. The experimentally determined probabili-ties of correct identification of test objects

P

by a humanobserver and by the model of the ideal observer wereused to calculate the signal-to-noise ratios

ψ

correspond-ing to these probabilities. These signal-to-noise ratiosresult from filtering taking place in the visual system ofthe human observer and in the computer model, respec-tively. They can be calculated using the values of theprobabilities of correct identification obtained.

(1)

where

î

(–1)

(

y

)

is the inverse function of the probabilityintegral:

The efficiency

k

was calculated using the signal-to-noise ratios found:

(2)

where

ψ

h

and

ψ

id

are the signal-to-noise ratios calcu-lated from the experimentally obtained probabilities ofcorrect identification of test objects by the humanobservers and the ideal observer model, respectively.

ψ î 1–( ) 2P 1–( ) 0.68+0.57

--------------------------------------------------,=

î y( ) 2

2π---------- e

x2

2-----–

0

y

∫ dx.=

kψh

ψid

-------2

,=

RESULTS

The study involved two trained observers and12 implementations of the noisy dynamic images of themoving test objects. Stylized Landolt-C were used astest objects. The observation distance was 500 mm, andthe test object size was

5.9

×

5.9

mm. Experimentally,we determined the probabilities of correct identificationof the images of moving test objects in the presence ofdynamic noise by a human observer and the idealobserver model, which were then used to calculate theefficiency. Different levels of dynamic additive quasi-white Gaussian spatial noise superimposed on theimages of moving test objects and different durations oftest object presentation were used. Five series of exper-iments were performed.

In the first series of experiments

, we analyzed therelationship between the efficiency

k

and the durationof test object presentation, expressed in the number offrames

N

at the root-mean-square (RMS) level ofdynamic Gaussian noise

σ

= 62.5. The duration offrame presentation was 40 ms. In this series of experi-ments, all the parameters of the test object images wereknown a priori. The test object images were demon-strated to the human observers and the ideal observermodel within a square window that coincided with thetest objects in size. The efficiency was calculated byformulas (1) and (2) using the obtained probabilities ofcorrect identification of the test objects by the humanobserver and the computer model for different dura-tions of presentation of test objects in combination withdynamic noise. The relationship between the efficiencyand the duration of test object presentation expressed inthe number of frames is given in Fig. 2 (curve

1

). Thisrelationship has several interesting properties.

As can be seen from Fig. 2, as the duration of pre-sentation of the noisy images of the static test objectsincreases, the efficiency first rises, then passes througha maximum, and then decreases monotonically. Wepropose the following explanation. When observing theimages of the static test objects in the presence ofdynamic noise, both the visual system and the idealobserver accumulate these images. Noise averaging

V

12345

(a) (b)

Fig. 1.

Illustration explaining the way of presentation of images of moving objects.

410

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during accumulation increases the signal-to-noise ratio andthereby raises the probability of correct identification of thetest objects by the visual system and the ideal observer.However, these processes follow different laws because ofthe different properties of the dynamic memories of thevisual system and the ideal observer and because of thepresence of internal noise in the visual system.

The first difference is that the time of signal accu-mulation is limited in the human visual system, unlikefor the ideal observer, in whom it is unlimited by defi-nition. Two opposite processes take place simulta-neously in the visual system: accumulation (memoriz-ing) of a newly presented signal and loss (forgetting) ofthe accumulated signal. It is this property of the visualsystem that makes it possible to clearly see both mov-ing objects and the background against which they areobserved. However, it is the same property that causesthe signal-to-noise ratio in the visual system to tend toa certain limit when the observation period tends toinfinity. In case of the ideal observer, only accumulationof the newly presented signal takes place. Therefore thesignal-to-noise ratio increases unlimitedly when theperiod of presentation of the noisy images goes to infinity.This difference in the signal-accumulation properties mayaccount for the monotonic decrease in efficiency whennoisy images are presented for more than 200 ms. Wedescribed this relationship previously [12]; in this paper, itis given for comparison with the other relationships.

The second structural difference between the humanvisual system and the ideal observer is that the visualsystem has a source of internal noise, while the ideal

observer has no such source. Therefore, the probabilityof correct identification of the test objects by the idealobserver depends solely on the signal-to-noise ratio andthe duration of test object presentation, whereas theprobability of correct identification by the visual sys-tem also depends on the level of its internal noise. If theperiod of observation is rather long, internal noise maybe neglected. If the period of observation is short and theaccumulated signal is small, the internal noise of thevisual system becomes an important factor, especially forimages with low-level dynamic noise. In this range, adecrease in the presentation duration causes the signal–to–resulting noise ratio to decline to a greater extent in thevisual system than in the ideal observer. As a result, theefficiency falls as the duration of presentation decreasesbelow 200 ms. It is likely that the dynamic processesassociated with decision-making during image identifica-tion by the visual system are of some importance.

In the second series of experiments

, we found thatthe relationship between the efficiency

k

and the dura-tion of presentation of the moving test objects had twoobvious extrema.

In this series, the RMS level of dynamic Gaussiannoise

σ

was equal to 62.5 and the test object velocityand the direction of movement were known a priori.The experiments were performed with two velocities oftest objects. Their velocity was set by the extent, towhich these objects were shifted from one frame toframe (by one-twentieth and or one-fourth of the testobject size). With the above-mentioned test objectsizes, observation distance, and frame rate, the angularvelocities were as follows:

V

= 0.85 deg/s and

V

=4.33 deg/s. The test object images were presented toboth the ideal observer model and the human observerwithin a square window. Its size was chosen so that thetest object could be observed within the windowthroughout the period of its presentation; i.e., the win-dow size exceeded the test object size. The duration ofpresentation of moving test objects was expressed in thenumber of frames

N

. The demonstration started with thetest objects appearing at the center of the window. Theexperimentally obtained probabilities of correct identifi-cation of the test objects by the human observers and thecomputer model allowed us to calculate the relationshipbetween the efficiency and the duration of test object pre-sentation, using equations (1) and (2).

As can be seen from the curve in Fig. 2, even a slowmovement of the object significantly changes the effi-ciency-duration relationship. Thus, as the duration of pre-sentation of a moving test object increased, the efficiencyinitially decreased, passed through a minimum at 120 ms(

N

= 3), and then increased and reached a maximum at400 ms (

N

= 10); a further increase in the duration of pre-sentation caused a monotonic decrease in the efficiency.

These data can be explained by the fact that (1) theobject image in the second and subsequent frames isshifted relative to its initial position and (2) no in-phaseaccumulation of the signal occurs in the visual system

0.1

0 5

k

10 15

N

0.2

0.3

0.4

1

2

34

5

Fig. 2.

Relationship between the efficiency

k

and the dura-tion of test object presentation expressed in the number offrames

N

under the following conditions: (

1

) test objects arestatic; (

2

) the velocity and the direction of movement of thetest object are known a priori (

V

= 0.85 deg/s); (

3

) the veloc-ity of the test object is random and the direction of move-ment is known a priori (

V

= 4.33 deg/s); (

4

) the velocity andthe direction of movement of the test object are random (

V

=4.33 deg/s); (

5

) the velocity and the direction of movementof the test object are known a priori (

V

= 4.33 deg/s).

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until the latter determines the displacement of theobject from frame to frame and starts to follow this dis-placement. Moreover, the signal from the first frame,which is subject to decay with time due to “forgetting”,is corrupted by the noise from the second and subse-quent frames. The decaying signal is also corrupted bythe internal noise of the visual system. Therefore, thesignal-to-noise ratio in the visual system decreases,thus causing a decrease in the probability of correctidentification of the test objects. Because in-phaseaccumulation takes place in case of the ideal observer,an increase in the observation period for the idealobserver results in an increase in the signal-to-noiseratio, thus causing an increase in the probability of cor-rect identification of the test objects by the idealobserver. The above processes cause a decrease in effi-ciency, which can be seen in Fig. 2. As soon as thevisual system determines the displacement of the testobject from frame to frame (usually at frame 3 or 4), thesituation changes. From this point onwards, the visualsystem keeps track of the moving test object, whichprovides for in-phase signal accumulation. In this case,the accumulated signal-to-noise ratio increases, thusincreasing the efficiency. As mentioned above, this isthe case until the signal accumulation prevails over thesignal loss. Thereafter, the efficiency decreases mono-tonically.

As can be seen from the curve, an increase in thevelocity of a test object for which the initial position isknown a priori results in a decrease in the efficiency.

In the third series of experiments

, we analyzed therelationship between the efficiency

k

and the durationof presentation of moving test objects expressed in thenumber of frames

N

for two cases. In the first case, thetest objects moved upwards and their velocities wereunknown a priori. In the second case, both the velocityand direction of movement were unknown a priori. Inboth cases, the observers knew only the maximumvalue of the velocity

V

, which was distributed uniformlyover the range [0,

V

]. The RMS level of dynamic Gaus-sian noise was set to 62.5. As in the previous series ofexperiments, test object images were presented to boththe ideal observer model and the human observerswithin a square window. Its size chosen so that the testobject was observed within the window throughout theperiod of test object presentation. In the first frame, atest object appeared at the center of the window as inthe previous series of experiments; i.e., the initial posi-tions of the test objects were known a priori. The exper-imentally obtained probabilities of correct identifica-tion of the test objects by the human observers and thecomputer model allowed us to calculate the relationshipbetween the efficiency and the duration of test objectpresentation using equations (1) and (2). These resultsare shown in Fig. 2. The relationships were similar tothose obtained in the previous series of experiments.However, they allowed us to make several new interest-ing conclusions, as follows. (1) All other factors beingthe same, the lack of a priori information on the direc-

tion of movement of test objects caused a decrease inthe efficiency. (2) At a given maximum velocity of thetest object, the lack of a priori information on its veloc-ity manifested itself in an increase in the efficiency. Atfirst glance, the result is paradoxical. However, in thiscase, the average velocity was half the maximum veloc-ity. Given that an increase in the velocity causes adecrease in the efficiency, there is no contradiction inthese results. (3) As in the previous series of experi-ments, an increase in the test object velocity causes adecrease in the efficiency if the initial position of thisobject is known a priori.

In the fourth series of experiments

, we analyzed thesame relationship as in the previous three series, with theonly difference being that the initial positions of the testobjects were unknown a priori. Experimentally, the effi-ciency was calculated for different durations of test objectpresentation. Analysis of these relationships led us to thefollowing conclusions. (1) If the test object is presented fora short period, the lack of a priori information on the initialpositions of moving test objects causes a decrease in effi-ciency. (2) If the test object is presented for a long period,the lack of a priori information on the initial positions ofmoving test objects affects the efficiency only slightly. Inother words, if the test object is presented for a sufficientlylong period, the probability of correct identification of thetest object is higher. (3) The lack of a priori information onthe initial positions of the test objects is always associatedwith a decrease in efficiency.

Functional Model of the Visual System

On the basis of the results described above, a func-tional model of the visual system was developed (Fig. 3).The model consists of four modules: a module describ-ing adaptation of the visual system to light; a moduledescribing the dynamic memory, in which a noisydynamic image projected on the retina is accumulated; amodule simulating the internal noise of the visual sys-tem; and a module of image identification. The latter isbased on the modified Siegert–Kotelnikov algorithmdescribed in [5]. This module includes a unit for compar-ing the image presented with the reference image (i.e., asubtraction unit); a unit for squaring the differenceobtained in the previous unit; an integration unit; and adecision-making unit, where it is decided to which of thereference images the image being identified is closest.

Let us discuss how this functional model works.When a noisy dynamic image is projected onto the ret-ina, the light distribution is transformed into the con-trast distribution, usually called the neuron image, dueto visual information processing by triads, each ofwhich consists of a receptor, a system of horizontalcells, and a bipolar cell. Thereafter, the neuron image istransferred to the input of the dynamic memory riddenby inertia of the visual system, in which two processestake place simultaneously: accumulation of input sig-nals and their forgetting with time. These processes aredescribed by introducing the impulse characteristic,

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which is approximated by an exponential function

h

(

t

) =

e

–

α

t

, where

1/

α

is the time constant of the visualsystem and

t

is time. Then, the neuron image accumu-lated in the dynamic memory is transferred to the inputof the identification module, in which it is comparedwith each of the set (alphabet) of reference images.Specifically, the input image is subtracted from each ofthe reference images on a point-by-point basis; the dif-ferences are squared and accumulated in the integrator;and, finally, in the decision-making unit, the accumu-lated results are compared with each other and on thisbasis the decision on identification of the input imagewith one of the reference images is made. This modeldiffers from those reported previously in that it includesa dynamic memory module to describe the processestaking place in the visual system during observation ofdynamic images. Let us consider how this moduleworks in greater detail.

When a video consisting of a sequence of images of atest object moving in the presence of dynamic noise is pre-sented to a human observer, a signal component

s

accumu-lates in the visual system following the equation:

(3)

where

T

is the duration of one frame presentation;

N

isthe number of frames presented for identificationwithin the observation period (

TN

);

k

is the frame num-ber;

K

is the image contrast of the test object;

a

0

is thedimension factor; and e–αT(N – k) are the multipliers of thesignal component from the kth frame. The longer thetime elapsed since the presentation of the kth frame, thelesser is the contribution of this frame to the total. Thecoefficients Ck are used in equation (3) to determine theeffect of the motion of the test object on the result ofsignal component accumulation in the dynamic mem-ory. The fact is that the projection of the moving objectonto the retina is shifted from frame to frame. Thus, theaccumulation of the useful signal is disturbed, becausethe informative parts of the object (the breaks in thestylized Landolt-C) are superimposed on each other

s a0K CkeαT N k–( )–

k 1=

N

∑= ,

with a shift or are not superimposed at all if shifts fromframe to frame are large.

When calculating the noisy component accumulated inthe dynamic memory, note that (1) the noise is summed bythe square law because it is not mutually correlated in dif-ferent frames and (2) the variance of the resultant accumu-

lated noise contains the variance of the internal noise

of the visual system as a summand. Therefore,

(4)

and the signal-to-noise ratio reads

(5)

Because there is no internal noise in the ideal observer,and signal and noise are accumulated in an ideal man-ner, the signal-to-noise ratio can be written as

(6)

Substituting Ψh and Ψid given by equations (5) and(6) into equation (2), we arrive at the equation for theefficiency predicted by the model:

(7)

Using this formula, we calculated the relationshipsbetween the efficiency and the duration of test objectpresentation expressed in the number of frames N.These relationships are depicted by the curves in Fig. 4.

σΣ2

σin2

σΣ2 a0

2σ02 e 2αT N k–( )– σin

2 ,+k 1=

N

∑=

Ψh s/σΣ

K CkeαT N k–( )–

k 1=

N

∑

σ02 e 2αT N k–( )– σin/a0( )2+

k 1=

N

∑----------------------------------------------------------------------.= =

ΨidKσ0----- N .=

kΨh

Ψid

--------

2Cke

αT N k–( )–

k 1=

N

∑2

N e 2αT N k–( )– σin/a0σ0( )2+k 1=

N

∑----------------------------------------------------------------------------.= =

Dynamicimage Module

of adaptationto light

Dynamicmemorymodule

Internalnoise

+ –

Identification module

Decision-makingmodule

Decision[ ]2 ∫

Visual memoryinvariant

to shift, size, contrast, rotation, etc.

Fig. 3. Functional model of the visual system.

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EFFICIENCY OF THE HUMAN VISUAL SYSTEM 413

The experimental points, which agree well with the the-oretical curves, are also given in Fig. 4. The time con-stant of the visual system and the coefficients Ck werecalculated by fitting the calculated data to our experi-mental data. The time constant of the visual system wasestimated at 150 ms. The coefficient values are given inthe table.

Analysis of the curves shows that the theoreticalrelationships agree rather closely with the experimentalpoints; i.e. the model adequately describes signal accu-mulation during observation of both static and movingobjects.

Analysis of the table allows us to make some inter-esting conclusions. Thus, presented as a sequence offrames, the images of a static test object equally effi-ciently accumulated in the visual system because all thecoefficients Ck are equal to unity. The situation is differ-ent when the object to be identified is moving. In thiscase, 1 ≥ C2 ≥ C3 because of the shift in the object posi-tion from frame to frame. As a result, the images of theobject are superimposed on one another in the dynamicmemory with a shift as well. This causes either adecrease in signal accumulation if the shift is small, asin the case of curve 2 in Fig. 4, or its disruption if theshift is large, as in curves 3–5 in Fig. 4. This is the caseuntil the visual system determines the velocity of thetest object and begins to track this object, thus provid-ing for a correct superposition of the images in the sub-sequent frames. As can be seen from the curves inFig. 4, tracking starts after 150–200 ms, i.e., from thefourth or fifth frame after the onset of observation.

CONCLUSIONS

Experimentally, we found the extrema of the rela-tionship between the efficiency and the presentationduration, which allowed us to understand the mecha-nism of signal accumulation in the dynamic memory ofa human observer observing static or moving objects innoisy images. On this basis, we developed a model ofthe visual system that takes into account signal accu-mulation.

Interestingly, the time required to start tracking ascalculated from the relationship between the efficiencyand the presentation duration of moving test objectscoincides with that determined experimentally in [13].

ACKNOWLEDGMENTS

This work was supported by the Russian Foundationfor Basic Research, project nos. 98-06-80001, 01-06-80297, and 02-04-48685.

0.125

0 5

k

10 15 N

0.250

0.3751

2

34

5

Fig. 4. Relationship between the efficiency k and the dura-tion of test object presentation expressed in the number offrames N under the following conditions: (1) test objects arestatic; (2) the velocity and the direction of movement of thetest object are known a priori (V = 0.85 deg/s); (3) the veloc-ity of the test object is random and the direction of move-ment is known a priori (V = 4.33 deg/s); (4) the velocity andthe direction of movement of the test object are random (V =4.33 deg/s); (5) the velocity and the direction of movementof the test object are known a priori (V = 4.33 deg/s). Solidlines show the results simulated in the model; experimentaldata are given in the form of separate points.

Table

Curve number C1 C2 C3 C4 C5, C6, C7, C8, C9, …

1 1.0 1.0 1.0 1.0 1.0

2 1.0 0.199 0.157 0.647 0.882

3 1.0 0.260 0 0.436 0.764

4 1.0 0 0 0.375 0.692

5 1.0 0 0 0.100 0.689

414

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