The informational difference concept in analyzing target recognition issues

D. Sheffer and D. Ingman Vol. 14, No. 7 /July 1997 /J. Opt. Soc. Am. A 1431

The informational difference concept in analyzingtarget recognition issues

Dan Sheffer and Dov Ingman

Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel

Received November 27, 1995; revised manuscript received January 2, 1997; accepted January 15, 1997

A model for analyzing issues involving monospectral target recognition is presented. These issues includemodeling target detection, recognition and identification thresholds, and predicting the functional parametricdependencies of the results of observation experiments with human observers. The model makes extensiveuse of concepts used in information theory. An image of a scene is treated as a sample of an entire set ofimages of that scene. A difference measure, called the informational difference (InDif ) between two imagesets is defined. The main assertion is that accomplishing target recognition tasks is equivalent to settingthresholds for the InDif. The applicability of the InDif to the performance of the human visual system (HVS)is shown both analytically, in very simple situations, and in computer calculations involving noisy images. Fi-nally, a single framework for dealing with the HVS and artificial intelligence systems in target recognitionapplications is shown to result naturally from the InDif formalism. © 1997 Optical Society of America[S0740-3232(97)02506-4]

1. INTRODUCTIONModeling target recognition by human observers has beenthe focus of a large amount of work by many researchersin the past. Perhaps the most well-known work in thisarea is that of Johnson,1 who laid the foundations for sub-sequent research in this field. Johnson introduced themethod of analyzing the properties of electro-optic view-ing systems in the frequency domain and suggested sev-eral criteria for determining acquisition ranges of mili-tary vehicles. These criteria are, in essence, thecapability of the viewing instrument to resolve resolutiontargets of specific spatial frequencies, which are depen-dent on the nature and complexity of the task to be per-formed. The Johnson model is the central element incurrent widely used models for predicting target acquisi-tion ranges of monospectral sensors.2 The main short-comings of such models are as follows3–5:

1. They deal only with uniform targets on uniformbackgrounds. The spatial structure of target and back-ground (clutter) are not included in these models.2. It is not clear that a model based on resolving peri-

odic resolution targets is a good basis for evaluating theefficiency of observing nonperiodic targets, such as thosethat are encountered in real everyday situations.3. The human vision mechanisms are dealt with only

in an empirical manner. No scientific insight into theprinciples governing these mechanisms is included.

A physical approach of analyzing the performance of anideal imager was made by Rose.6 Unfortunately, his pa-per does not attempt to deal with the problem of targetrecognition. More recently, van Meeteren5 presented ex-perimental evidence that identifying a set of military tar-gets embedded in nonuniform backgrounds is equivalentto detecting uniform disks on uniform backgrounds, andhe used this empirical finding to calculate recognition dis-

0740-3232/97/0701431-08$10.00 ©

tances of targets in natural backgrounds. No explana-tion of this empirical finding was offered, however.A large volume of work has been published concerning

the human visual system (HVS) and the mechanisms un-derlining its operation. Extensive research, spanningmany years, was performed by Blackwell and others.7–13

These studies concentrated mainly on the psychophysicalaspects of the human visual system and on attempting tofind empirical mathematical models to predict the diffi-culty of performing visual tasks, but they did not attemptto understand why the HVS behaves as it does.Many papers can be found that deal with the HVS,

color perception, frequency response of the HVS, and theeffects of resolution and noise in images on the perceptionof embedded targets in them.14–21 Other approaches tothe problem of target recognition can be found in thefields of multispectral sensing,22–26 pattern recognition,27

and information theory.28 Generally, the first two ap-proaches tend to solve a given recognition problem byadapting known techniques of pattern recognition or byinventing a new technique tailored to the specific problemat hand. The field of information theory seems to bemore promising for dealing with the general problem oftarget recognition. Unfortunately, we are unaware ofany general framework for dealing with target recogni-tion issues based on that approach.The scope of the current paper does not allow us to

cover even a small portion of all the work on target recog-nition. The papers we mentioned are those that we feelare representative of the field and have direct bearing onthe subject we want to address.From the above discussion, it is clear that a few basic

problems in the field of target recognition still have to besolved:

1. A first-principles model of the HVS and target rec-ognition mechanisms, that is, a model based on well-established basic scientific principles.

1997 Optical Society of America

1432 J. Opt. Soc. Am. A/Vol. 14, No. 7 /July 1997 D. Sheffer and D. Ingman

2. Taking into account the spatial structure of the tar-gets and backgrounds, such as clutter in the backgroundand nonuniformity of the radiance of the target.

Moreover, it is desirable that in developing models for tar-get recognition, the following issues be addressed and, ifpossible, their solutions be incorporated into the models:

3. Modeling the HVS and artificial intelligence (AI)systems and approaches, such as neural networks anddigital image-processing techniques, in one framework.4. Taking into account some a priori knowledge that

an observer might have about the target and background.

We present here an approach toward such modeling oftarget recognition that promises to deal with the prob-lems and issues in 1–4 above. In Section 2 we show howthe divergence concept, which is used in the fields of pat-tern recognition and information theory, can be used todefine the informational difference (InDif) between twoimages. In Section 3 a first-principles model of the HVSis introduced, and we show how, when a simplistic modelof viewing experiments is assumed, the divergence andthe InDif are used to predict both the well-known Piperand Ricco laws of target recognition experiments5 and theapparent ‘‘log-ogive’’ behavior of the contrast thresholdsof the human eye for performing simple visual tasks.7,8

The equivalence between the real tasks of identifyingmilitary vehicles and the task of detecting uniform diskson uniform backgrounds, which was reported by vanMeeteren,5 is easily explained by the InDif concept, as areother aspects of target recognition experiments reportedin Ref. 5. In Section 4 the results of computer calcula-tions of more realistic models of viewing experiments arepresented. In Section 5 we discuss how the approachmay be used to put the HVS and the AI systems for targetrecognition into one framework.

2. DIVERGENCE CONCEPTThe divergence between two probability distributions is adistance measure between them. It is used in informa-tion theory to quantify the difference between the twoprobability distributions. The units of measure are theunits of information, usually bits, but other units, such asnats, are also used, depending on the base chosen for thelog operation. Given the two probability distributionfunctions p1(x) and p2(x), the divergence between themis defined by the relation

J12 5 Ex

@p1~x ! 2 p2~x !#lnFp1~x !

p2~x !Gdx. (1)

It is easily verified that the divergence has most of thenecessary properties of a metric defined in the space of allprobability distribution functions.For two normal distributions, p1(x) ; N(I1 , s1) and

p2(x) ; N(I2 , s2), it is easy to show that the divergenceJ12 is given by

J12 51

2 F S 1

s12 1

1

s22D ~I1 2 I2!2 1 S s1

s22

s2

s1D 2G .

(2)

And if s1 5 s2 5 s, the divergence simplifies to

J12 5~I1 2 I2!2

s2 . (3)

Equation (3) may be recognized as a quantity that hasbeen referred to as the deflection ratio in a book edited byLawson and Uhlenbeck.29

Suppose we are given two images, a and b, from thesame sensor. We treat each image as representing a cer-tain natural phenomenon. An image of a certain back-ground, for example, is just one sample from a whole setof images of the same background. This set of imageshas statistical properties that are manifested also in thestatistical distribution of gray levels of each pixel amongall the images constituting the set. Let us consider justone pixel (i, j) in the two image sets. We calculate thedivergence at the pixel (i, j), J12(i, j) and define theInDif Jab between the two image sets by

Jab 5 (i, j

J12~i, j !, (4)

where the indices i and j refer to the position of the pixelunder consideration in both images. That is, Jab is com-puted by calculating the divergence between correspond-ing pixels in the two images and summing up over all thepixels. A few words of caution are needed here: Thereare many other statistical properties of the image set, no-tably the correlation among the gray levels of neighboringpixels. If the pixels in each image are considered inde-pendent, the summation in the expression for Jab is asimple summation. If the individual pixels are not inde-pendent, the summation in the expression for Jab is not asimple one, and the summation symbol stands for a sum-mation process that takes into account the conditionalprobabilities of finding gray levels in neighboring pixelsand that has to be carried out properly.The InDif is a good basis for quantifying the difference

between two images of the same scene: one with the tar-get and the background present and the other with thebackground only. The reasons for this are as follows:

1. It takes into account the statistical properties ofthe two images, such as noise and correlation between ad-jacent pixels.2. It takes into account some a priori knowledge that

a human observer might have about the target and thebackground. This knowledge is manifested in the knownprobability density functions of the target and back-ground image sets. Thus a mechanism similar to alearning process is incorporated into the pattern recogni-tion model.3. The divergence between two statistical distribu-

tions is a general concept. It is independent of the sys-tem that is used to analyze the observed measurements.The analyzing agents may be human, computerized, orany mixture of human and AI systems.

The basic concept that we wish to present is that theInDif between two images is a fundamental entity thatshould be used in any model of target recogni-tion: In order for a target to be detected in a certainbackground, the InDif between the image of the back-ground with and without target should be greater than acertain threshold.


An obvious choice for the ultimate threshold for the In-Dif is 1 bit. The reason is that 1 bit of information is re-quired for distinguishing between two equally likely pos-sibilities. In a general target recognition scenario, anInDif of 1 bit means that the targets are detected with a50% reliability: The two equally probable cases are ei-ther that there is a target in the observed image or thatthere is not. Of course, this threshold should be usedonly in the case of a perfect viewer and recognizer. In ac-tual systems, the threshold should be set at a highervalue, which might have to be found experimentally.

3. MODELING THE HUMAN VISUALSYSTEM AND PREDICTING EXPERIMENTALRESULTSIn this section we will first present a basic-principlesmodel of the HVS. Second, we will show how the InDifcan be used to predict the functional dependencies of ex-perimental results of viewing experiments performedwith human observers.

A. Human Visual System in Target Recognition TasksWe model the HVS as a system for extracting informationabout the image sets under consideration. As such, onlythe basic principles of information theory can be appliedto it. More explicitly, given two image sets that repre-sent different physical situations, one must extract aminimal amount of information by viewing them in orderto be able to determine from the viewing experimentalone that they indeed represent different physical situa-tions. On purpose, we do not make any assumptionsabout the actual mechanisms that are employed by theHVS to extract the necessary information. Thus the re-sults that will be presented are general and are applicableto any information-seeking system.

B. Predicting Experimental ResultsWe will concentrate on two sets of such experiments, re-ported by van Meeteren5 and by Blackwell.7,8 A brief de-scription of the results reported in these papers follows.The work in Ref. 5 deals with measuring the identifica-

tion ranges of military vehicles in real backgrounds dur-ing observation by human observers. The conclusionsare as follows:

1. The task of recognizing a real target set is visuallyequivalent to the task of detecting a uniform disk on auniform background.2. As a consequence, the relation between the con-

trast c of the target and the size of the target as sub-tended at the eye of the observer is given by the followingrelations:

Ricco’s law:1c

' S a

abD 2 1s , a ! ab ,

Piper’s law:1c

' S a

abD 1

s, a @ ab , (5)

where a, ab , and s are the diameter of the target, the di-ameter of the blur circle of the eye, and the standard de-viation of the noise in the image, respectively. Relations

(5) are supported by Blackwell’s well-known work.7 Thecontrast c is the relative contrast of the target with re-spect to the background.

In Ref. 8 Blackwell reports the results of viewing ex-periments performed on Landolt rings. In these experi-ments, human observers were required to determine theposition of the opening in Landolt rings among eight pos-sible positions. The contrast of the rings relative to auniform background was varied, and the percentage ofcorrect answers (corrected for chance guesses) was deter-mined. The conclusions were that the percentage of cor-rect answers, denoted by p8, was very well fitted by a re-lation of the form he called ‘‘log-ogive’’:

p8 51

gA2pE

2`

x

expF2S a 2 a

2gD 2Gda, (6)

where a 5 log(c/c* ); c is the absolute contrast betweenthe object and background; c* is the value of c when p85 0.5, g 5 log(s), and s is the standard deviation of anormal probability distribution. No explanation wasgiven of why the form expressed in Eq. (6) was chosen, ex-cept for the reason that the ogive function is related tonormal distributions. In fact, other mathematical func-tions can be fitted to the data with the same apparent suc-cess.In what follows, we shall show that the results de-

scribed above can be accounted for by using the InDif for-mulation. Moreover, the InDif formulation can predictother characteristics of target recognition experiments,such as the equivalence of positive and negative con-trasts, all other things being equal.

1. Piper’s and Ricco’s LawsDeriving Piper’s and Ricco’s laws for observations of uni-form disks can be done in two ways: elementary, whichis based only on basic principles, and realistic, whichtakes into account some of the physical effects. We willpresent, first, the elementary development. The realisticone will be presented in Section 4. The basic assump-tions are the following:

(a) The observing system has a linear response.(b) The target observed is a uniform disk of diameter

a on a uniform background.(c) Both background and target emit radiation with

point intensity that is distributed normally as describedbelow, with average intensities L1 and L2 , respectively.

Derivation of Piper’s Law. Let us assume that a diskof diameter a and of uniform radiance L2 is embedded ina background of uniform radiance L1 . We further as-sume that the radiances of the disk and the backgroundare normally distributed around their means L2 and L1 ,respectively. That is, the number of photons observedfrom any point on the disk or on the background, over theintegration time of the observer, is distributed normally.The last assumption is justified because it is known thatthe number of photons emitted by an incoherent sourceper unit time obeys a Poisson distribution. However, forreasonable integration times (;0.1 s for the human eye)and source intensities the number of photons received by


the human eye in one integration time is so large that thenormal approximation to the Poisson distribution may besafely used. In the case of Piper’s law we add another as-sumption:

(d) The disk diameter a is very large compared withab , the diameter of the point-spread function (PSF) of theobserving system.

With the four assumptions given above, let us calculatethe divergence J12(x) at any point x in the two images aand b (with and without target, respectively):

J12~x ! 5~L1* 2 L2* !2

s 2,(7)

where the asterisk denotes the quantity as observed atthe exit of the observing system. In effect, the image atthe exit of the observation system is made up of an arrayof small overlapping disks, each of diameter ab . Fur-thermore, the divergence between the two images van-ishes outside the target area. Therefore, when we sumup over all of the points in the images, we get

Jab 5 (x

J12~x ! 5 K 2a2

ab2 J12~x !, (8)

where K is a proportionality constant. By use of Eq. (7)we obtain

Jab 5 K 2S a

abD 2 DL2

s2 , (9)

where

DL 5 ~L2* 2 L1* !.

Now let us set the threshold value of Jab for performinga certain task at M2: J ab

thresh 5 M2, and we obtain

1DL

5 MKa

ab

1s. (10)

Hence

1c

5L1

DL' L1

a

ab

1s. (11)

Equation (11) is recognized as Piper’s law.

Derivation of Ricco’s law. The assumptions for the de-velopment of Ricco’s law are the same as for the develop-ment of Piper’s law except for assumption (d), which nowis

(d) The disk diameter a is very small compared withab , the diameter of the PSF of the observing system.

In this case the image of the disk of radius a is anotherdisk of diameter ab . Therefore all of the energy from theobserved disk of diameter a is spread over a much largerdisk of diameter ab after passing through the observingsystem. Hence DL, the original intensity difference be-tween target and background at the target plane, is re-duced by a factor (ab /a)

2 at the image plane, and expres-sion (7) for the point divergence J12(x) is now

J12~x ! 5DL2

s 2

a2

ab2 , (7a)

and Eq. (9) becomes

Jab 5 K 2S a

abD 4 DL2

s 2 . (9a)

Similarly, Eq. (11) becomes

1c

5L1

DL' L1S a

abD 2 1s , (11a)

which is a manifestation of Ricco’s law.A few important remarks are called for here: First, it

is apparent from Eqs. (9) and (11) that the contrastthreshold is dependent on the background radiance L1 .This dependency was reported experimentally byBlackwell7 and by van Meeteren.5 Second, it is clearfrom the development of those equations that there is aninteresting dependency of 1/c on the value M2 chosen forthe threshold of performing the given task successfully.A more difficult task requires a higher value ofM. Thus,if one were to plot the relationships of Eqs. (9) and (11) ona logarithmic scale, the curves corresponding to differenttask difficulties would be plotted as parallel curves. Thisfact was reported experimentally by van Meeteren,5 usingreal targets on real backgrounds. While Ricco’s and Pip-er’s laws may be developed with approaches other thanInDif (which has been done by a few authors), the last ob-servation, which follows naturally from our model, isharder to predict. Third, under some simplifying as-sumptions, it can be shown that the divergence between anoisy signal and the pure (uncorrupted) signal is simplythe signal-to-noise ratio (SNR). Thus the SNR concept isa particular case of the divergence concept.

2. Blackwell’s ExperimentsWe wish to arrive at an expression for the percentage ofcorrect answers in target recognition experiments, hopingthat the relation we will arrive at will fit Blackwell’sdata8 at least as well as the relation expressed in Eq. (6).A promising starting point can be found in the field of

statistical pattern recognition. Tou and Gonzalez27 ad-dressed the following problem: Suppose we are giventwo pattern classes, wi and wj , for which the pattern vec-tors are characterized by multivariate normal densityfunctions with equal covariance matrices. What is theprobability of error associated with the Bayes classifier?After analyzing carefully the two types of error thatmight be made (misclassification and false alarm), theyarrived at the following expression for the total probabil-ity of error:

p~e ! 5 E1/2Arij

`

1/A2p exp~2y2/2!dy, (12)

where rij is the Mahalanobis distance between the twopattern classes.Taking into account that the Mahalanobis distance and

the divergence are identical in the case of normal distri-bution patterns, the probability of correct classificationbecomes


Fig. 1. Probability of correct classification versus contrast as given by Blackwell8 and as expressed in Eq. (16), with the Bayes clas-sifier and two pattern classes. Curve a, p8 5 F(log DI, 0.0363, 0.145); curve b, p8 5 F(1/2 log DI, 0.0363, 0.145); curve c, p85 F(1/2 log DI, 0.0363, 0.072).

p8 5 1 2 p~e ! 5 F~12AJ12, 0, 1! (13)

where F(x, m, s) is the cumulative normal probabilitydistribution of variance s 2 and mean m at point x.In trying to use these results for analyzing the experi-

ments reported by Blackwell, we model them according tothe basic InDif formalism: First, we use the relationJ12 5 (DL)2/s 2. Second, if the classifier is a human ob-server, the response of his or her eyes is a logarithmicone, and we have to substitute the logarithm of all thequantities appearing in Eq. (13) for the quantities them-selves. Consequently, the expression for p8 becomes

p8 5 F@log~DL !, 0, log~s!#, (14)

or, with Blackwell’s notation,

p8 5 F@12 log~c !, 0, log~s!#

5 F@12 log~c/ c !, log~ c !, log~s!#. (15)

Hence

p8 5 F@12 log~a!, a, g# (16)

Equation (16) is very similar to the relation expressed inEq. (6), which was found by Blackwell. The main differ-ence between the two expressions is the factor 1/2 appear-ing in Eq. (16). This minor difference does not interferewith the ability of Eq. (16) to fit Blackwell’s experimentalresults: All one has to do is use for g in Eq. (16) a differ-ent numerical value from the one used in Eq. (6). Figure1 is a plot of the relations expressed in Eqs. (6) and (16).Three different plots are shown in Fig. 1: curve a,Blackwell’s8 experimental parameters; curve b, the rela-tion of Eq. (16) with the same parameters; and curve c,the same as curve b, but a different value of g. It is ob-vious that the plots of Eq. (16) can be made as close toBlackwell’s experimental plots as one might want.In the past, simple recognition models assumed that a

fixed SNR was needed to achieve fixed levels of perfor-mance in target recognition experiments. Indeed, suchassumptions are needed to derive Ricco’s and Piper’slaws. No doubt the SNR concept is an important param-

eter that affects performance levels. However, we nowsee that the assumption about a fixed SNR is not needed.Setting a threshold value for the InDif and correlating itwith statistically significant performance levels isstraightforward and can be done analytically by using ba-sic principles.

3. Van Meeteren’s ExperimentsPredicting the results of van Meeteren’s5 experiments isalmost trivial in the InDif formulation: Computing theInDif between a circular, uniform disk and its backgroundis not inherently different from computing it between amilitary vehicle and its background. The informationaldifference ‘‘doesn’t care’’ which mechanisms contributedto its numerical value. Thus the equivalence betweenthe task of detecting military vehicles and the task of de-tecting uniform disks is a natural outcome of the InDifformalism. In fact, we can predict the equivalence ofthose tasks with the task of detecting uniform squares oncluttered backgrounds, for example. All those tasks canbe modeled in a similar fashion in the InDif model.

4. COMPUTER CALCULATIONSIn this section we want to use the InDif formulation to ar-rive at Ricco’s and Piper’s laws when the viewing mecha-nism is modeled more realistically. To that end, we willassume the basic assumptions of Section 3. However, in-stead of modeling the image of the target in a simplisticmanner as before, we will now take into account the two-dimensional PSF of the imaging system and introducenoise into the images. Given a scene of a uniform disk ona uniform background, the following convolution opera-tion has to be carried out:

Dm~x, y ! 5 Di~x, y ! ^ PSF~x, y !, (17)

where Dm(x, y) is the resultant image of the scene, thatis, the image at the exit of the imaging system, andDi(x, y) is the image original scene itself, that is, the the-oretical image that would have resulted had the PSF beena two-dimensional delta function. After Dm(x, y) is ob-


tained, the InDif Jab between an image with a target andan image without a target has to be computed and set to athresholdM2, and the resultant contrast threshold has tobe computed—all in the manner described in the previoussections. Adding noise to the image Dm(x, y) beforecomputing the InDif will introduce noise into our model.We will present here the results of our computer calcula-tions of that process. In the calculations, the convolutionprocess of Eq. (17) and the following required calculationswere carried out numerically.The calculations were based on the assumption that

the PSF of the imaging system has the functional form

PSF~x, y ! 51

2prexpF2S x2 1 y2

2r2D G . (18)

The parameter r in Eq. (18) determines the effective spa-tial extent of the PSF. In our model, it represents the ra-dius of the blur circle of the imaging system. The calcu-lations proceed as follows:

1. Two digital images, Dia(x, y) and Di

b(x, y) weregenerated: Di

a(x, y) consisted of a uniform backgroundonly, and Di

b(x, y) was a uniform circular disk of diam-eter a on a uniform background; i.e., the original targetand the background were modeled as having constant ra-diances.2. A convolution of each of the two images with the

PSF of the sensor was carried out, and the resultant im-ages were computed.3. Normal random noise with variance equal to the

background radiance and zero mean was added to the re-sultant convoluted images.4. The InDif of the final images was computed by

means of equations (3) and (4), and the contrast c be-tween the target and the background was varied until theInDif reached a value ofM2 5 20000. Let us denote thatparticular value of c by c* . The value of M2 was chosenpurely for reasons of convenience: It produced values forthe contrast c that were convenient for further calcula-tion. For the same reasons, the value of the proportion-ality factor K of Eq. (10) was chosen as 1.5. The above steps were repeated for several values of

the target diameter a. The diameter ab of the blur circleof the sensor was kept constant by keeping constant thevalue of the parameter r of the PSF.6. The different values of 1/c* thus computed were

plotted as a function of a. We hoped that the resultingplots would resemble those of Ref. 5.

Results. The results of the calculations are shown inFig. 2(a). In those calculations the value of a was variedbetween 1 and 201 pixels and the value of r in Eq. (18)was set at 8 pixels, representing a value of 17 pixels forab . The size of the digital images used in the calcula-tions was 201 3 201 pixels. The results of the calcula-tions are plotted in Fig. 2(a) for different values of thebackground radiance L1 . The values of the contrast sen-sitivity are plotted versus distance (in arbitrary units),which has a numerical value equal to 1/a. This was doneto present the results in a format as close as possible tothe format of the results of Ref. 5. The solid lines connectthe calculated points, and the dashed lines are tangentsto the graphs.

Fig. 2. (a) Results of computer calculations concerning contrastthresholds for monospectral target detection. The contrast sen-sitivity is plotted versus observation distance for two levels ofbackground radiance L1 (arbitrary units). Blur spot size is 17.See explanations in the text. (b) For comparison, the resultsfrom Ref. 5.


Examining Fig. 2(a), we can see that the contrast sen-sitivity decreases as the distance from the target in-creases. This means that the contrast needed to performthe recognition task has to increase as the size of the ob-ject being viewed decreases. While this is not a surpris-ing result, it is nice to observe that the InDif model givesout familiar and well-known results. In fact, contradic-tory results would have indicated that the formalism wasbasically incorrect. Furthermore, one can notice that forsmall values of a, when the relation a ! ab holds ap-proximately, the slope of the graph approaches (22).Similarly, for large values of a, when the relation a@ ab holds, the slope of the graph approaches (21).Thus, both Ricco’s and Piper’s laws emerge. In addition,the transition zone between the two extreme cases is ob-served. It is important to note that the slope of the graphdoes not change abruptly from (21) to (22); rather, thechange occurs gradually, as one would expect. In Fig.2(b) the results of Ref. 5 are reproduced for comparison.There the lines are drawn so as to best fit the experimen-tal data, with the assumption of linear relationships, andan abrupt transition between the two slopes is postulated.An important observation is that the dependency of the

threshold contrast on the background radiance, whichwas reported by van Meeteren5 (Fig. 2b), is reproduced inthe computer calculations. This dependency causes thethreshold contrast to increase as the background radiancedecreases. In plain words, it means that as the scenegets darker, it is more difficult to detect the targets, evenif the contrast between them and the background is keptconstant.

5. HUMAN VISUAL SYSTEM ANDARTIFICIAL INTELLIGENCE SYSTEMAs mentioned earlier, the InDif lets us view the HVS andAI systems for target recognition tasks in one framework.The InDif formalism is general; it does not assume any-thing about the exact mechanism by which the informa-tion about the presence or absence of a target in an imageset is extracted from the observations. It deals only withthe problem of determining whether there exists enoughinformation to distinguish between the two cases in thefirst place. Viewed in that light, AI systems and the HVSare just two different mechanisms for extracting the in-formation from observations of the image sets. In prac-tice, two such mechanisms might require different thresh-old levels for the InDif in order to achieve the sameperformance levels for a certain task. An efficientmechanism might require a lower threshold than a lessefficient one. Strictly speaking, a threshold of 1 bit is alower bound for the InDif, applicable only to an idealobservation/recognition system.

6. CONCLUSIONSIn this paper a new approach toward dealing with targetrecognition issues was presented. The informational dif-ference (InDif) between two images, which is based on thedivergence concept of information theory, was defined.The use of the InDif as a similarity measure between thepurely background image set and the target with back-

ground image set was suggested. The InDif formalismhas proved to be successful in explaining important func-tional dependencies of actual observation experimentswith human observers on some of the parameters in-volved in those experiments. The InDif approach lendsitself naturally to extensions such as the inclusion oflearned knowledge by the observer. Ongoing research atthe Technion Institute is concentrated on those issuesand on developing a general physical approach towarddealing with target recognition problems.

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