ENGINEERING RESEARCH INSTITUTE THE UNIVERSITY OF MICHIGAN ANN ARBOR Final Report THE EFFECTS OF SIZE AND SHAPE ON VISUAL DETECTIONi FOR CONTINUOUS FOVEAL TARGETS AT MODERATE BACKGROUND LUMINANCE H. Richard Blackwell A. B. Kristofferson Vision Research Laboratories ERI Project 2455 BUREAU OF SHIPS, DEPARTMENT OF THE NAVY CONTRACT NO. Nobs-72038 WASHINGTON, D. C. June 1958

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2455-11-F The experziments reported here represent the basis for the doctoral dissertation, "Foveal Intensity Discrimination as a Function of Area and Shape" by Alfred Bo Kristofferson University of Michigan, 1954

The University of Michigan * Engineering Research Institute 245511-F TABLE OF CONTENTS Title P List of Figures iii List of Tables iv Sury v I o Introduction 1 IIo Procedures and Apparatus IIo Results 5 V~ Ma Ampirical Summary 8 V Theoretical Analalysis 9 VI o Discussion 1 References 13

The University of Michigan ~ Engineering Research Institute 2455 11.F LIST OF FIGURES Number Tit le 1 MC~Artist's conception of the basic psychophysics test facility Optical schematic drawing of the target projector.3 Examples of the multiple-legged targets 1.4 The geometrical form targets 5 The average area function for circular targets 6 The average data for rectangular targets 7 The "formr factor'" function for rectangular targets 8 The average data for multiple-legged targets 9 Summary data for all targets9 in terms of difference from circular targets of equal area 10 Derivation of the "shape" correction function 11 Derivation of the "inhibition" correction function 12 Derivation of the I"utilization" correction function 13 Summary data for all targets, after correction for the three empirical factors 14 Summry data for all targets, in terms of difference from predictions based on the element contribution theory 15. Derivation of the "asymmetry" correction function 16 Derivation of the second "utilization" correction function 17 Summary data for all targets, after allowance for theoretical predictions and correction for the two empirical factors

The University of Michigan * Engineering Research Institute 2455-11-F LIST OF TABLES Io Chronological Order of Experiments IIo Goodness of Fit of Psychophysical Data to a Normal Ogive III o Average Data for Circular Targets IVo Average Data for Rectangular Targets V o Average Data for Multiple-legged Targets VIo Average Data for Geometrical Figures VIIo Average Values of "Form Factors",. VIIIo Residual Errors,'Empirical Analysis TXo Errors of Prediction From Theory Xo Residual Errors, Theoretical Analysis. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ v _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

The University of Michigan * Engineering Resear'ch Institute 24551ll1F This paper presents a snummr y of experlmental studies of the effects of target area and ihape upon the detection of the eye, at 9o52 foot-lamberts back-ground luminance The temporal forced&choice variant of the method of constant stimuli was utilized0 Target presentation was foveal6 with an exposure duration of 0.01 seconds. The targets were of uniform luminance, differing in area from 1 to 4096~ square minutes and in shape over a wide range of target typeso A set of 60 targets was studied, intended to cover a very wide range with rea spect to target types to be expected in practical visibility situations, Three classes of non-circulaT targets were investigated. rectangles covering a wide range of areas and length-to-width ratios, multiplelegged figures (c rosses etco)~ and a series of simple geometrical figures o The data demonstrate that circular targets are more detectable for given area than any other target type studied -in generala, the more non-circular a target, the less detectable is it it comparison with a circular target of equal area. This suggests the use of a "form factor" to allow for the nonCircularrity of targets In describing their visibilityo An effort has been made to derive empirical methods for analyzing the form factor require d for different targets. We have found that form factor can be analyzed into three empirical factors relating to what are called "shape", t"utilization", and "inhibitionI"0 These constructs have sufficient generality so that, utilizing them, the data for all targets studied are quantitatively ordered with a high degree of precision~ The data from.these studies have also been analyzed in terms of a general theoretical formulation of the effects of target area and shape, designated the elewent contribution theory, which is.;described in detail elsewhere (Ref0 1)o Essentially, this formulation states that a target is detected whenever it produces an amount of excitation at some point within its neural pattern which exceeds a critical value, Eco Each point within the neural pattern receives excitation from every other point in an amount proportional to the distance, R, separating themto The amount of contribution as a function of distance is denoted by ( (R). Thus, targets which are symmetrical and presented with their center at the point of fixation will be detected whenever the amount of excitation delivered to the center from all points stimulated by the target-equals or exceeds Eco The present experiments are restri ted to targets which produce an excitation distribution having a single, central.ly plaaed, peak of excitationa A0 explained in Ref0 1, the eX~ penimental pn-~ognr invo lves deterining qp (R) from~ the data f:or'ilcular targets and using this information to predict the detectability of targets of non-cir clan shape v~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The University of Michigan * Engineering Research Institute 2455-11-F SUMARY (cont d) The general formulation was of considerable usefulness in ordering the experimental data but there was a clear need in addition for empiLrical factors of "asymmetry" and "utilization"l There was little difference in the adequacy of ordering the data obtained for all targets with the three-factor empirical system or the two-factor empirical and theoretical system, I.____________________________________________________________________

The University of Michigan * Engineering Research Institute 2455-11-F I INTRODUCTION* Since the initial observations by Ricco in 1877 (Ref, 3), many investigators have explored the effects of target area on detectability. In nearly every instance these studies utilized circular targets0 In a few cases non-circular targets, usually rectangular in shape, have been used (Ref0 45,96,7). However, in no study have targets of different shape classes been compared in a comprehensive manner. It was the purpose of the studies reported here to do thiso A study of the effects of target size and shape is of obvious practical significance for predictions of the visibility of military targets, since the targets of military interest vary enormously with respect to these variables0 The wide range of sizes and shapes of practical military targets suggests the desirability of obtaining a general underv standing of the effects of target size and shap-. so that it will not be necessary to study a vast number of specific targets, The present study was designed to provide such a general understanding of the effects of target size and shape~ The targets studied were stylized so that geometrical descriptions are possible. The targets studiec. represent much more extreme cases of asymmetrical shape than will usually be encountered with practical military targets. The use of extremes of the target shape variable was intended to provide a stringent evaluation of the adequacy of descriptive systems developed on the basis of the present experiments0 A concerted effort has been made to develop general statements of the effects of target size and shape. Insofar as these provide adequate descriptions of the data from the present experiment, they should be very useful in predicting the visi$bility of military targets of practical interest0 II o PROCEDURES AND APPARATUS All experiments were conducted in special experimental rooms, an arttisits conception of which is shown ii Figure 1. Two such rooms had to be used because the locati'n of the Vision Research Laboratories was changed during the course of the experiments0 The two rooms do not differ significantly as far as these experiments are concerned, This s$tudy was Jointly sponsored by Project MICHIGAN, operating under Contract DA 36-039-sc-52654 between the UoSo Signal Corps and the University of Michigan.o The Project MICHIGAN report of these studies has been made elsewhere (Refo 2)( 0

The University of Michigan * Engineering Research Institute 2455- 11- F Only the uniformormly illuminated large white field produced by the inside of the cube was visible to the observers. A circular plastic screen 51 inches in diameter (25Pdegrees of visual angle at the average viewing distance) was located at the center of the fieldo The target was projected from a rtom at the rear of the cube onto the center of this translucent screen. In every case, observers had full knowledge of target position, shape, size and orientation0 To aid the observer in fixing on the center of the target to be presented, four points of light were projected on the screen in a symmetrical pattern with respect to the target0 Each orientation light subtended one minute of arc and each was located 18 minutes from the nearest point on the target0 In other experiments we have shown that the 18 minute separation is sufficient to eliminate interaction effects for spatial cornfigurations siml$ar to the orientation light pattern used here. The intensity of the orientation lights was approximately ten times their threshold luminance0 This luminance is the dimmest which is comfortable when used for fixation and orientation continuous ly| Three female laboratory technicians and one of us (ABK), all between 20 and 30 years of age, served as observers. All, except obserTer NS, were previously experienced in the experimental procedures~ Observer NS's inexperience was reflected in her initial data, the earliest of which were discarded. With the exception of these few data, observer NS provided over-all results of satisfactory stabilityo Since the observers did not differ widely in sensitivity it was always possible for all four to serve simultaneouslyo When an observer was absent, the experimental sessions were repeated in order to obtain data for all observers under all stimulus conditions Measurements of refractive error were made under the constant viewing conditions of the experiments, using stigmatoscopic techniques~ Lenses were prescribed for observers LP and AM which resulted in adequate correctiono Observers AK and NS required no corrections0 Observers AK and AM were assigned permanent front seats, and NS and LP rear seats in the experimental rooms0 The average viewing distance from eye to screen was 114 inches for the front seats, and 144 inches for the rear seats0 Target exposure duration was 0.010 seconds for all experiments Thi$s duration is brief enough so that eye-movements cannot occure during a target presentation, and so that detection presumably represents a single neural evento Long exposure durations might be expected to result in more complex relations between target area and shape, and target detectability, than those obtaained in these experiments0 A relatively constant, moderately high background luminance was maintained0 Background and target luminances were measured independently before and teer each experiment by stanldard visual photometric

The University of Michigan * Engineering Research Institute 2455-11-F techniqueso From day to day the background luminance, B, ranged from 8035 to 12 41 foot lamberts, the average being 9.52 foot.lambertso To simplify data reduction, threshold measurements were normalized to the mean background luminanceo This normalizing process involved computing the change in threshold contrast attributable to background changes from the systematic, highly comparable data previously reported (Ref. 8)~ The only assumption involved is that individual differences in the slope of the threshold contrast-background luminance function are negligible over the range relevant here p The latter data (Ref 8) are average data for two observers0 This correction amounted to very little for the normal day-to-day background variations9 the maximum correction being 5olo However, during one period of the experiments, that in which the series of rectangular targets was run, a calibration error resulted in the average background luminance being 23o3 foot-lamberts~ These data were nrormalized to 9 52 foot-lamberts in the same way, the maximum correction being 41%Q All experiments employed the temporal forced-choice psychophysical method which has been described in detail in previous artilels (Ref g9), where is contained data concerning the reliability of the method and its validity as a measure of sensory function0 Essentially, the task assigned the observer is to identify in which of four immediately successive time intervals the visual target is presented0 The four time intervals are set off by auditory signals and are i mmdiately successivee Following each trial, or block of four time intervals, each observer is allowed sufficient time to indicate his choice of the "correct'" interval by pressing one of four buttons on a cosncealed response box at his side, The time interval in which the target appears is determined at random and controlled automatically by a pre-punched program (Refo 10)o Each target was presented many times at each of five luminance levels which were about equally spaced over the threshold range0 These levels were obtained by inserting appropriate neutral density filters in the optical path so that the luminance of the target varied between that at which approximately 95% correct responses and that at which approximately 25% correct responses are obtained. Obviously, in the forcedchoice method when the probability of target detection is zero, the probability of a correct response is 0O25. By plotting the target luminance against the percent of correct responses, threshold luminance was deterisned by interpolation at the 6205% correct levelE This process is described in greater detail below. All filters were calibrated periodically on an optical bench photometer. A target was presented ten times at one luminance level, then at another, and o 6forth, the order of the blocks of ten being determined at random0 A coded auditory signal informed the subjects of the luminance level to be presented next0 The entire threshold determination for each target consisted of 250 presentations of the target in five groups of five blocks of ten ftrials8 o Each group contained every luminance level Thus, the data for each threshold determination co:3nsisted of the

The University of Michigan * Engineering Research Institute 2455-11-F number of correct responses out of fifty at each of five target luminance levels, for each observer.0 A single threshold determination required about one and one-quarter hours of observing timeo Usually, only one session was held each day. The data were recorded automatically on pu shed cards as described in a previous article (Rei. 10), which also describes in detail the apparatus used for program scheduling and control of presentations. The optical system of the target projector is shown schematically in Figure 2. Target size and shape were determined by a plate containing a cutout of the target. The plate was placed in the center of the projector beam, flush against the rear of the plastic screen. This produced a positive target with sharp edges on the front surface of the screen, the amount of edge blurring being Less than four seconds of arc. The target configurations fall into four groups: circles, rectangles (including squares), multiple-legged targets, and simple, regular geometrical figureso These classes of targets were run in the chronological order indicated in Table I. Inasmuch as all data are to be compared with data on circular targets, targets of this shape were distributed throughout the experiments0 In this way changes with time. such as practice effects, could be observed and taken into account, There were seven basic circular targets (an eighth was used on one occasion)o For the observer in the near seats, the diameters of these circles subtended angles of about 1, 2, 4, 8, 169 32, and 64 minutes of arc at the fovea. Seven squares and twenty-one rectangles were used. The dimensions of these figures were chosen so that the areas of the squares were equal to those of the circles..The sqirter~Tl wTre Arun:twice once before and once after the other rectangleso Taresholds were determined for each rectangle oriented both horizontally and vertically Length-towidth ratios varied from one to 640 Samples of the multiple-legged figures can be seen in Figure 3 These figures consisted of crosses made up of lx64 minute of arc rectangles arranged with the angle between the legs varying from 100 to 90~ a three-legged figure made up of three lx32 segments, and six-legged figure composed of lx64 segments, The spokes, shown in the bottom row of Figure 3, consisted of one minute wide rectangular segments added to a four minute diameter central circleo Two, four, and eight-legged spokes were run. The angle between legs of the four-legged spokes was varied from 10~ to 90~, Two complete series of spokes were run, one with an over-all length of 32 minutes, the other of 64 minutes0 The six non-circular geometrical figures are displayed in Figure 4. They were constructed to be equal in area to the 32 minute diameter circular target, which was also run as part of the series|:___ _-__ _ -__ _- ___.___.__ __

The University of Michigan * Engineering Research Institute 2455-11-F Overall, the four observers each observed all of the 60 targets. The total number of responses was 130,000e The data will be presented in terms of threshold contrast, d, which is defined as: B in which AB is the target luminance above background, B, corresponding to a detection'probability of -50t The computation of ~B involves adjusting the percent of correct answers at each target luminance level for the probability of a correct answer by chance,.25, and fitting a normal ogiFve to the corrected data. This procedure is described elsewhere (Ref,. 11). For each set of threshold data, a chi-squared test of goodness of fit to the normal ogive-is obtained, The results of this test are summarized in Table II for all experiments. One set of data accounts for much of the large chi-squared in the case of observer AM. If this one set of data (an 8-minute diameter circle) is omitted, the chi"-squared sum for this observer becomes 366.78 with 345 degrees of freedom. This value has an associated probability of ~20~ The over-all goodness of fit of the ogives is considered to be excellent. III RESULTS Some significant differences between the four observers exist in the data. Analysis of the data for circles indicates that observers LP and AM had consistently lower thresholds than either observers AK or NSo Furthermore, observer NS had a lower threshold for small diameter circles, and a higher threshold for large diameter circles, than did observer AKo All of the data were analyzed in detail for the individual observers~ There were no differences in the conclusions reached in comparing circular and non-circular targets. Therefore, to facilitate exposition, and to make the data available in the most useable form; they will be presented as average logarithmic values throughout the following discussion. The experiments extended over a long period of time and small average differences in threshold appeared for each observer from period to period~ For this reason, adjustments were made by bringing all of the data to the average sensitivity level of the Series 2 circular targets0 This was accomplished for each observer by fitting a smooth curve to the data for circualar targets, as discussed below, adjusting it so that the average deviation of the Series 2 circular targets was aero, and computing the average deviation of circular targets from the values given for them by the curve for each of the majo Li-!time periods. The largest correction factor obtai~ned in this was was.0.153 log units for observer NS during the initial series of circular targets and the average factor for all observers was -0o035 log units~ All targets, including the noncircuaslar ones, were adjusted by the most appropriate ___ ___ ___ __ ___ 5 ____ __ _ _____

The University of Michigan * Enginsoring Res*rcih Inrtitute 2455-11-F correction factors The data from the four observers were combined in the following way. For circular targets, after the adjustment discussed in the preceeding paragraph, the mean of the threshold values read from the four curves was computed for the mean target area for each target. The obtained data was averaged for each target by taking the mean value of the deviation of the data point from the curve for each observers This mean deviation was then expressed with respect to the average smooth curve, A similar procedure was used for the data for non-circular targetso A. Circular Targets A total of 90 separate threshold determinations were made for circular targets, divided approximately equally among the four observers and distributed throughout the area range for each observer. A smooth curve, required to have an orderly first derivative, was fit to the log area versus log threshold contrast plot for each observer. In Table III these data are summarized as averages over observers and over replications of targets. Table III, and the graphical plot of these data in Figure 5 ae are based on 22500 observations. In Table III, log ~c is the average log threshold contrast determined by the smooth curves, and log 6 is the average obtained log threshold contrast, The algebraic average deviation of log from logc hereafter denoted and defined as Z(log d - log Cc)N, is~ -.000. The absolute average deviation, 5:1 4 defined as fllog C - log r/Nt is.006, or less than 2%. The "area function" for circular targets, Figure 5, is of the general form usually found~ Below a target diameter of about 2.8 minutes, area and threshold contrast are reciprocally related, ine., Ricco's law holds. Above this "critical angle", area makes a continuously decreasing contribution to detectability. B. Rectangular Targets Each of the 28 rectangular targets was studied twice, For those with a dimensionality, viz0 length-to-width ration, greater than unity, the targets were run once with the longer dimension,, oriented vertically and once with 3 horizontal. There was no systematic difference between the vertical and horizontal orientations, hence they were averaged for each observer, and each threshold value in Table IV is an average of at least eight individual measurements. The data in Table IV are a summary of 77,000 responseso Table IV contains the nominal target dimensions in the first column, and the exact dimensions in columns two and three, where c: is the shorter dimension in minutes of arc. The threshold contrast for a circular target of the same area, A, as each rectangular target, is given in column six, denoted ec. The threshold contrast predicted by

The University of Michigan ~ Engineering Research Institute 22455-11-F the element contribution hypotheses, Ct, appears in the last column and will be discussed in a later section0 Plotted in the same manner as the area function, the data for rectangular targets appear in Figure 6 in which the numbers indicate dimensionality and the smooth curve is the area function for circular targets from Figure 5. In general, the rectangular targets have higher threshold contrasts than circular targets of the same area, the extent of the difference being a function of dimensionality and being little affected by area within a narrow, middle range of areas The loss in detectability due to increasing dimensionality is indicated by the average log unit difference between the obtained threshold contrast and the threshold contrast for a circular target of the same area, for a given dimensionalityo Figure 7 summarizes these data from this point of view0 It is clear that "form factor", or the loss in detectability associated with dimensionality, c, is a negatively accelerated function of dimensionality, reaching a maximum of 0.41 log units at 64, the largesta. dimensionality studied0 The smooth curve fitted through the data in Figure 7 is empirical0 C. multiple-legged Targets The cross targets were all constructed of 1x64 rectangles, but varied in the number of legs, having either three, four or six legs. Of the four-legged crosses, the angle @ between legs assumed several values: 100~ 22.50, 24o0, 600, and 900. These target characteristics are given in column -one of Table V. The spoke targets were similar, except that the number of legs were either two, four or eight, with angles g of values indicated in Table V. The over-all length of the targets was 32 minutes in one series and 64 minutes in the other. Entries in Table V are the same as in Table IV, with one excepi tion, The shorter and longer dimensions of the targets a and p in this case refer to the dimensionsr of the rectangle which exactly encloses the multiple-legged target, and are denoted a' and B'. Figure 8 displays the data, again with respect to the area functions The numbers indicate the over-all length of the target, either 32 or 64 minutes0 The data for four-legged targets were averaged and appear in the figure as a single point for crosses, one for lx32 spokes, and one for lx64 spokes. Inspection of log C values in Table V reveals little difference attributable to the angle between legs. Clearly, noncircular targets of this class are less detectable than circular targets of the same area~, A being 0o25, 0,158, and 0,48 for the lx52 spoke, 1x64 spoke and 1x64 cross t argets, respectively, D* Geometrical Figures These targets, which were relatively large and equal in area, differed extensively in shape. However, they differed little in

The University of Michigan Engineering Resqs.rch Institute 2455-11-F detectability, as an examination of the log C values in Table VI clearly indicates~ In. Table VI,' and O' have the same meaning as they did in Table Vo The average log d for the six targets is -1.084), while for a circular target of the same area log C is-1l118, a difference of only.034 log units, or 8%. This difference is in the same direction as for the other target classes. All non-circular targets studied support the general con-, clusion that non-circular targets are less detectable than circular targets of the same areas This conclusion is illustrated by Figure 9 which is a summary of all the data plotted in terms of Ec. The average difference is 00169 log units, contributed mostly by themul.: tiple-legged targets as indicated in Table VII, which gives eI fic the mean of the absolute values of Cc, and ic for each of the four target classes. IV. AN EMPIRICAL StMMARY A number of methods of summarizing the data have been tried. All have attempted to account for the variance in the data in terms of simple geometrical characteristics of the targets, and have been guided by general theoretical consliderations0 One method has emerged which is superior to all others'trided. It will be described in this section. We begin by considering Ecvalues for the sample of rectangular targets0 These values can be ordered in terms of a variable (D /ca) where D is the target dimensionality (length-to-width ratio) and a is the linear extents in minutes, of the smaller dimension of the target0 Note, in Figure 10, that ~e, the loss in detectability due to shape, increases as (DA ) increases beyond a value of approximately 1o This variable orders the data much better than simple dimensionality alone. From this analysis we may extract a shape correction (S), which is described by: S.25 1log (D/aO)i -.020 (2) The S correction should be applied to all targets and it may then be determined what further order can be found in the residual E) or C/e values. For multiple-legged and geometrical form targets, the Scorrection is based upon the dimensions of the smallest rectangular box into which the targets can be fitted, Examination of the multiplelegged targets in this way revealed one primary additional ordering trend, and one secondary one. The primary ordering trend concerns the extent to which the target "utilizes" the area of the rectangular box into which it just fits. In terms of target geometry, this is expressed

The University of Michigan ~ Engineering Researchi Institute 245511-F by (A/as'a), where A is target areas and a'and F" are the dimensions of the box, The secondary ordering trend concerns the extent of "inhibition" of parts of the target upon each other, measured by the angular separation between adjacent legs of the multiple-legged targets, denoted by G0 The functions in terms of (Ark) and were determined reiteratively in the following mannerQ To the data for all two-legged and four-legged, 900, multiple-legged figures a function was fit to c versus log (A/c'B')o These data were found to be ordered according to the function, U -. 33 [log (A/&aP)] -.033. (3) then, equation (3) was applied to all multiple-legged target data, yielding values of Cc', the values adjusted for both (D/a ) and A/a'B ) These proved to be ordered in terms of log as shown in Figure 11 The resulting equation is: I = -.5 (16,g ) +.29 (4) Finally, all of theecvalues were adjusted according to equation (4), resulting incEa values representingg>adjusted for S and I. These, plotted against log (A/W"I'), fit the previously established equation (3) adequately, as can be seen in Figure 12. Thus, four factors have been extracted from.the data, Target detectability depends on area, a.n terms of the area function for circular targets, on shape as described by equation (2), on the extent to which the target utilitizes the area it "occupies" in the sense of equation (3), and on the angular separation of parts of the target according to equation (4). If each of our four'targets~ classes are adjusted in accordance with those factors relevant to it, the results are as contained in Table VIII. This table also indicates which adjoustments were applied to each target class. These residual errors are arrayed in Figure 13 as a function of log area for each of the 60 targets. The over-all average residual error is,037 log units, or 9%. V THEORETICAL ANALYSIS For each non-circular target, the value of threshold contrast predicted by the element contribution hypothesis was computed from the threshold contrasts for circular targets by the method of integration described previously (Ref.1). This procedure was carried through on the data for each observer individually, but will be prewsented here in terms of averages, since, again, the over-all pattern is highly similar for the different observers, The average values of predicted log threshold contrast are given in the righthand colurn of Tables IVJ, V and VI for each of the non-'circular targets. In the following discussion Etlog obtained threshold contrast

The University of Michigan ~ Engineering ResearCh Institute 245 5- l-F minus log predicted threshold conftrast, will be the quantity of interest, Average values of Ctf:ar;dltlj, are summarized for each target class in Table IX. For civrcular target:sk &, and Cc, are identical, tl providing a standard against Which evaluation of the adequacy of prediction of the theory can be made, All targets are summarized in Figure 14 with respect to Et Over-all, the theory performs deceptively well, the grand algebraic mean of the tvalues being.007 log units} or less than 2%. However, inspection of Table II suggests that this result is to some extent an artifact of the sample of targets which was chosen, On the whole, rectangular targets have thresholds lower than predicted and multiple-legged targets have thresholds higher than predicted, The extent to which the theory reduces the average error of prediction can be demonstrated bj comparing,065, 1'1 for all non circular targets, with.91,i 1for non circular targets, and.006, -~cl for circular targets, In terms of these log unit deviations, the theoretical predictions account for 64% of the error, That is, the prediction of thresholdcobntrast for non-circular targets on the basis of the theory is a 64% improvement over prediction on the basis of the area function alone,. There are systematic trends in the errors of prediction with-' in target classes, The rectangular targets are more detectable than predicted and the error of prediction increases as the rectangles become longer and thinner, Figure 15 shows that 64 increases in the negative direction as ( -ca ), the difference between the longer and shorter dimension, increases, This "asymmetry" variable does the best job of ordering the Etvalues. The line represents the relation A= - 003 ( B-c). (5) For the most extreme rectangular targetO,Etis -.18 log units. Following the same procedure as in the preceeding empirical analysis, theCtvalues for all multiple-legged targets were adjusted in accordance with equation (5) and one additional ordering trend became apparent, indicated in Figure 16. As in the empirical analysis, utilization was found to be a significant second-order effect. The following equation resulted: U 1: [log (A/(' ] -.012 (6) in which (A/c'p) is the percentage of the area of the best fitting rectangular box occupied by the target, The residual errors of prediction after 4djustment according to equations (5) and (6) are given in Table X and Figure 17.? Comparison of Table X and TableY.i~:r!eveals little difference in the outcomes of the empirical and the theoretical-empiricAl analyses, the former having a slight advantage in the extent to which it orders the data of these experiments. The theoretical analysis, of course, has the advantage of greater generality, 10

The University of Michigan ~ Engineering Research Institute 2455-11-F MVI DISCUSSION These experiments have shown that target area in terms of visual angle, is a major factor determining target detectability. In addition, target shape has been shown to influence detectability to a significant extent, but in a complex mannfer Maximal ordering of the data required extracting three factors related to target shape- dimensionality, utilization and inhibition, These terms are almost wholly descriptive at the present stage of research; the factors are defined by equations (2), (3) and (4) A general formulation of the effects of target size and shape, the element contribution hypothesis, has been tested through these experiments and has been found to account for the effects of target shape to a significant extent0 However, reliable second-order departures from theoretical prediction have been clearly defined indicating that as target dimensionality increases, detectability becomes greater than expected theoretically and that as the extent to which a target "utilizes" the area surrounding it decreases, target detectability becomes less than the theory predicts. These factors are defined by equations (5) and (6), Several possible revisions and extensions of the element contribution theory have been entertained to account for the observed departures. The theory assumes thatcp(R), the element contribution function, is independent of, the direction from the center. Since all rectangular targets were oriented only vertically and horizontally, it is possible that the A-function, equation (4)> is due to a violation of this assumption, -i' brief series of experiments which determined threshold contrast for the 1x64 rectangular target in several orientations other than vertical and horizontal clearly eliminates this possibility. There is a slight tendency for the target to be more detectable in the vertical and horizontal orientations, but CZis negative and large for all orientationso In all experiments the observers were given full knowledge of the geometry of the target, its place and orientations The notion that the visual system acts as a flexible, narrow-beam scanner with respect to space can be made to account for the departures from theoretical prediction when used in conjunction with an element contribution hypothesis. A direct test of this has been performed by measuring the detectability of the 1x64 rectangle in the horizontal and vertical orientation with full knowledge of orientation on the part of the observer and, in another series$ with the orientation on any tria1 determined randomly. No effect due to knoswledge:c.:orientation was measureable eThus a simply hypothesis of this nature must be discarded. Another as$sumption of the theory, that detection is determined solely by the height of the excitation distribution at the centers may hold the answer~ If detection is determined in p'a:rt by the area 11I

The University of Michigan * Engineering Research Institute 2455-11-F of the excitation distribution which is near the criterion level, then the relatively high detectability of the rectangular targets and the relatively low detectability of the multiple-legged targets, can be understood. This possibility deserves further consideration. Finally it may be that an understanding of the data will develop through considerations of signal and noise in the central nervous system. Noise is seldom ordered in a long, thin array, for example, and it may be that a signal of this type has an advantage over isotropic neural signal displays.

The University of Michigan * Engineering Research Institute 2455-11-F REFERENCES 1. Kincaid, Wo 14., Blackwell, Ho R., and Kristofferson, Ao B., "A Neural'Formulation of the Effects of Target Size and Shape upon Visual Detection", University of Michigan, Engineering Research Institute Report 2144280-T (in press) 2, Kristofferson, A. B. and Blackwell, H. R,, "The Effects of Target Size and Shape on Visual Detection: I.o Continuous Foveal Targets at Moderate Background Luminance", University of Michigan, Engineering Research Institute Report 2144-279-T (in press) 3, Ricco, Ann, Ottal,, Pavis, 3A, VI, 373 (1877) 4 o Brown, Ho R., and Niven, J. I., "The Relation between the Foveal Intensity Threshold and Length of an Illuminated Slit'l, J.j_. Psychol. ai 464-476 (1944) 50 PFry, GA.A, "The Relation of the Configuration of a Brightness Contrast Border to its Visibility-i', J Ot0 Soco Amer. 37 166-175 (1947) 6. Lamar, EoS., Hecht, S,, Hendley, CD.. and Shlaer, S., "Size, Shape, and Contrast in Detection of Targets by Daylight Vision: IIo Frequency of Seeing and the Quantum Theory of Cone Vision'', Jo Ot. Soc. Amero 8,741755 (1948) 7 o Nachman,, M4, "The Influence of Size and Shape on the Visual Threshold of the Detectability of Targets", Boston Univ. Opt, Res6 Lab, Tech. Note 109 (1953) 8. Blackwell, HoR,, "Brightness Diserimination Data for the Specification of Quantity of Illumination"', Illum, EngU,_47. 602-609 (1952) 9. 0 Blackwell, H.Ro, /EPtj.........T.hreshaolds: Experimental Studies of Methods of Measurement Univ. of Michigan — I1 SUniv oof Michigan Engineering Research Institute Bull. No. 36, 227 p. (1953) 10.o Blackwell, HoR, Pritchard, B oS, and Ohmart, J.G, "Automatic Apparatus fior Stimulus Presentation and Recording in Visual Threshold Experiments", J. Opt SocE FAmer. 4 322-326 (1954) 11, Kincaid, WoM., and Blackwell H.R., "Application of Probit Analysis to Psychophysical Data: Io Techniques for Desk Computation"', Univ of Michigan, Engineering Research Institute Report 2144-283-T (in press) 13

The University of Michigan * Engineering Research~ Institute 2455-11-F TABLE I Chronological Order of Experiments FIRST EXPERIMENTAAL ROOM C IRCLES RECTANGLES C IRCLES RECTANGLES Series I Series 1 Series 2 "Sies'2 SECOND EXPERIMENTAL ROOM RECTANGLES CROSSES SPOKES GEOM)MTRICAL Series 3 (Circles) (Circles) FIGURES (Circles) I I (Circles) 14

The University of Michigan * Engineering Research Institute 245511-iTABLE II Goodness of Fit of Psychophysical Data to a Normal Ogive Degrees of Observer 2 Freedom Prob Pbility LP 353038 336 o248 AK 310 93 348.924 AM 422.08 348.004 NS 385 ~35 342.052 15

The University of Michigan ~ Engineering Research Institute 2455 -11-F TABLE III Average Data for Circular Targets Nominal Target Log A Log d Log Cc Diameter:2 -.14.734.730 2.42.162.174 4' 1.09 -.393 -.400 8' 1.66 -.738 - 741 16' 2.22 -.961 -.958 32' 2.80 -1.119 -1.114 64' 3.35 -1.238 -1.243 16

The University of Michigan * Engineering Research Institute 2455-11-F TABLE. IV Average Data for Rectangular Targets Nominal Target Dimensions log p log ca log A log C log Cc log C t lxl -.06 - 078 -.141.777.733.731 2x2.228.22.451.206 o146.151 4x4 ~ 509.502 1.011.- 257 - 334 - 3.4 8x8 - 828,822 1.650 - o705 - 735 - 729 16x16 1,107 1.10o3 2.21 -.936 -.955 -.947 32x32 1.410 1.410 2,820 -1.129 1.118 -1.117 64x64 1,711 1.709 3.420 -1o221 - 1.245 -1,o241 1x2.226 -.056 170.368.421.416 2x4.518.222.740 -.100 -,123 -.111 4x8 o792.489:1.281 -.489 -.534 -.505 8x16 1,098.813 1.911 -.849 - 850 -.831 16x32 1.401 1.100 2,501 -1.05. - 1o4.2 -1.o27 32x64 1,701 1.400 3-101 -1.235 - 1.184 -1.179 1x4.526 -.056.470.182.126.157 2x8.797.203.594.261 -.341 -.261 4x16 1.083.487.596 -.587 -.695 -.613 8x32 1.405 o805 2210 -.933 -.955 -.876 16x64 1.700 1.100 2.800 -1.118 - 1,118 -1.064 lx8.792 -.032.760.020 - 149 -.045 2x16 1o103.197 1.300 -.442 -.546 - -335 4x32 1406 o514 1.920 -.766 -.846 - 668 8x64 1.704.786 2.490 -1.079 - 1.037 -.893 1x16 1o087 -.087 1oO000 -.039 -.341- 061 2x32 1 o411.249 1.660 -.588 -.741 -.421 4x64 1.700.500 2.200 -.849 - 955 -.673 1x32 1o393 -.063 1.330 - 202 -.558 -.124 2x64 1,721.239 1.960 -.572 - 868 -.432 1x64 1,738 - O.058 1.680 - -345 -.756 -.153 17

The University of Michigan * Engineering Research Institute 2455-11-F TABLE V Average Data for Mlltiple-legged Targets Nominal Target log A log ac' log B' log C log CG log Ct lx64 90go" 2~07 1.761 1.761 - o410.908 -.503 1x64- 60~ 2 03 1.703 1.761 -.334 -893.460 - 4x64, 24' 2.03 1.386 1.761 -.422 -.893 -.468 lx 1x64, 22o5~ 1,99 1.347 1.748 -.450 -.879 -.397 lx64, 10~ 2,00 1 020 1.740 -.530 -883 - 356 1x64, 3 legs 1.93 1.641 1.703 -.368 -.857 -.366 lx64, 6 legs 2.22 1*700 1.758 -.389.- 958 -.631 4 legs, 900 1.78 1.461 1.461.5377 95 - o610 a 4 legs, 600 1,79 1.406 1.460 - 505:o800.605 $4 legs, 45 0 1 77 1.325 1.461 -i::94.791 -591. 4 legs, 240 1,78 1.100 1.460 -:584 795 -597 - 2 legs -.57.623 1.460 -.523 - e 695 - o 572' 8 legs 2.02 1,458 1.458 -.595 -.890 -.724 4 legs, 90 2.06 1,755 1.755 - o524 - 904 -.613, 4 legs, 600 2.04 1.704 1.763 -.484 -:;97 -.628 4 legs, 450 2,07 1.620 1.763 -.534 -;908 - -6i608 4 legs, 240 2,07 1.388 1.762 -.527 -.908 -.626 42 legs 1.80.620 1.763 -.504 -.804 - 531 23 legs 2.33 1,763 1.763 -.534 -.991 -.750 L _ _ _ _ _ _ _ _ _ _ __ ~ 18

The University of Michigan * Engineering Research Institute 2455-11-F TABLE VI Average Data for Geometrical Figures Target log A log ac logy' log C log Cc log Ct Diamond 2,81 10470 1.645 -1.101 -10118 -1,120 Cross 2.80 1.531 1.531 -1.093 -1.116 -1.109 Hexagon 2.81 1.438 1.490 -1.102 -1.118 -1.,124 Star 2.81 1.626 1*689 -1.009 -1.118 -1.107 Square 2080 1o405 1.405 -1.097 -1.116 -1.121 Triangle 2.80 1.524 1.587 41.103 -1.116 -1.115

The University of Michigan * Engineering ResearCh Institute 2455-11-F TABLE VII Average absolute deviation, and and algebric average deviationjjcl,, of threshold contrasts for non-circular targets from threshold contrasts for equal-area circular targets. Logarithmic unit differences. Mltiple- Geometric Circuar Rec tangular legged Forms c-.000 086.379.033 6I l:..006.098 79 0033 ___ __ __ __ ___ __ __ __ ___ __ __ _ 00_ _ _ __8

The University of Michigan * Engineering Research Institute 2455- 11-F TABLE VIII Residual Errors, Empirical Analysis Multiple- Geometrical Circles Rectangles legged Figures Mean Ec - o000 O004 002 0- o24.000 Icl.006.035 p054.032.037

The University of Michigan * Engineering Research" Institute 2455-11-F TABLE IX Errors of Prediction from Theory Multiple- Geometrical Circles Rectangles legged figures Mean ~-~ -. ~.o000 -o4a2 0073 o032.oo007 006 o065.097 o032.065 22

The University of Michigan ~ Engineering Researbh Institute 2455-11-F TABLE X Residual Errors~, Theoretical Analysis Multiple- Geometrical Circles Rectangles legged Figures Mean Et 000oo.o 00oo6 o029.008 its ol.oO6 ~ 035 0063 ~o30 O40 23

Auxiliary.Proiector Light Cube Target Presentation Scheduling System and Recording Response Buttons Scheduling Device $1A. Response. Recorder Recording Apparatus Observing Booth and Light Cube Fig. 1. Artist's conception of the basic psychophysics test facility. 0A 1143 Fig. 2. Optical schematic drawing of the target projector. 64 R MULTIPLE LEG TARGETS A B C D E F G H Fig. 3. Multiple-leg targe's. 24

A B C D E F Fig. 4. Geometrical form targets. CIRCULAR TARGETS N ~22,500 II1 50% FORCED CHOICE DETECTIONS -I-2 -; 0; 2 LOG TARGET CONTRAST Fig. 5. Threshold data for circular targets.

0 RECTANGUAR TARGETS # 7 7,000 I -2.4 0 0 LOG TARGET CQN4AASI Fig. 6. Threshold data for rectangular targets. GA- L356 REC TANGULAR TARGETS N a 77,000 +1.9O 4. 1Io 0 11. 1 2 4 a IS 32 64 TARGET DIMENSIONALITY Fig. 7. Form factor graph. 26

MULTIPLE LEO TARGETS N 24,600 S 40 50% FORCED CHOICE DETECTIONS *2 -I 0 I t LOG TARGET CONTRAST Fig. 8. Threshold data for multiple-leg targets. SUMMARY: ALL TARGETS CA-1346 N 130,000 GORRECTED FOR: AREA *.6 a x ~~+.4 XA~ A A A 0a A AA -.2 -.4 -.6 LEGEND: o CIRCLES A RECTANGLES x MULTIPLE-LEGS * GEOMETRICAL FORMS Ic I ".169 O....; -. t 3 -E LOG TARGET AREA (SQI)ARE MINUTES) Fig. 9. Summary data analysis. 27

cGA-1347 RECTANGULAR TARGETS N 77,000 CORRECTED FOR: AREA.4 - -.2 LINE REPRESENTS RELATION s.25 [LOG (0D/.)]-.020 -2 -t O I 2 LOG {D/da) Fig. 10, Empirical shape factor. CA-1349 MULTIPLE-LEG TARGETS N' 24,500 CORRECTED FOR: AREA S-.25 (LOG (0/.)] -.020 U —.33 (LOa (A/'8')] -.033 +.4 -.2 LINE REPRESENTS RELATION s -.15 (LO0G 9) +.29 O I 2 3 LOG a Fig. 11. Empirical inhibition factor. 28

GA- 1348 MULTIPLE - LEG TARGETS Ns 24,500 CORRECTED FOR AREA S.25 [LOG (D/.)] -.020 Is -.15 (LOG ) *.29.6... 4 W 0-.2 LINE REPRESENTS RELATION U -.33 [LOG (A/'B,')] -.033 -2 -g O LOG (A/'f') Fig. 12. Empirical utilization factor,. A-1350 SUMMARY: ALL TARGETS N- 130,000 CORRECTED FOR: AREA t.6 S-.26 [LOG (D/<)] -.020 U.-.33 CLOG (A/d'.')] -.033 8.4 1 -.15 (LOG 8)+.29 x u0, 4 8. M L. -.2 -.4 -.6 LEGEND: o CIRCLES A RECTANGLES x MULTIPLE-LEGS. GEOMETRICAL FORMS I'" ".037 0 I 2 3 LOG TARGET AREA (SQUARE MINUTES) Fig. 13. Summary data analysis. 29

GA- 1352 SUMMARY: ALL TARGETS N. 130,000 CORRECTED FOR: ELEMENT CONTRIBUTION e*.6 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~ A. -.2 b aa aa a A -.4 -.6L LEGEND: o CIRCLES A RECTANGLES X MULTIPLE- LEGS * GEOMETRICAL FORMS J il *.061 0 1 2 3 LOG TARGET AREA (SQUARE MINUTES) Fig. 14. Summary data analysis. DEVIATION FROM THEORETICAL PREDICTION VERSUS (0 —a) FOR RECTANGULAR TARGETS NW 77,000 +-.4LINE REPRESENTS RELATION A,-.0033 (3-a) * _. I..I..1... 1 0 10 20 30 40 60 60,8-a (MINUTES OF ARC) Fig, 15. Empirical asymmetry factor.

MULTIPLE -LEG TARGETS DEVIATION FROM THEORETICAL N 24,500 PREDICTION AFTER CORRECTION FOR A.0033 ('-'o ) VERSUS LOG (,-i) *.4 0y -.2 LINE REPRESENTS RELATION u..12 CLOG (A/a'j,')3-.012.I I I' -2 -i 0 LOG (A/ape,) Fig. 16. Empirical utilization factor. a&-1536 SUMMARY: ALL TARGETS DEVIATION FROM THEORETICAL PREDICTION No 130,000 AFTER CORRECTION FORS A. -.0033 (C-a) U' —.12 [LOG (A/a'')'] -.012..4 - x x w ~ 9 a A -.2 -.4 LEGEND: -.6_ o CIRCLES a RECTANGLES x MULTIPLE - LEGS * GEOMETRICAL FORMS | -'".040 _! - l, ". 0.. 0 I 8 3 LOG TARGET AREA (SQUARE MINUTES) Fig. 17. Summary data analysis. 31

~//p/[~UNIVERSITY 3 9015 02514 7847 THE UNIVERSITY OF MICHIGAN DATE DUE to( 4L; (ft/