The effect of contour sharpness on perceived brightness

Vision Rr,%Vol. 5, pp.559-564. Pergamon Press1965. Printed in GreatBritain.

THE

EFFECT

OF CONTOUR

PERCEIVED JAMES P. THOMAS

SHARPNESS

ON

BRIGHTNESS and

CONSTANCE

University of Caiifornia, Los

(Receiver!15

April

W.

KOVAR

Angeles

1965)

WHILE

the perceived brightness of a stimulus is determined mainly by its luminance, it is also influenced by the sharpness of the contours of the stimulus (ENOCH, 1958). To determine the extent of this influence we studied stimuli with edges consisting of gradual, rather than step-like, changes in luminance. We could thus determine the relationship between the perceived brightness and the sharpness of the luminance change at the edges. This relationship was examined for various contrast ratios of stimulus to background and at different adapting luminances. The results permit certain conclusions about the interactions which modulate brightness. APPARATUS AND PROCEDURE Figure 1a represents the stimuli. The subject looked with one eye at an illuminated field, 15” on a side. Superimposed on the fieId were two vertical stripes, 7-5” high, The left stripe, the Standard, was sharply focused and continuously exposed. It defined a standard brightness for the subject. The right stripe had vertical edges which were gradual or “blurred”. This stripe was exposed for only one second on each trial. During each exposure, the subject judged the stripe to be brighter or dimmer than the Standard. Between exposures, the experimenter adjusted the luminance of the “blurred” stripe according to the double staircase procedure (CORNSWEET,1962) in order to determine the luminance at which the stripe appeared to equal the Standard in brightness.

: i

FIG. 1. At left, the stimuli as seen by the subject. The stripe with “blurred” edges was adjusted to match the sharply edged stripe in brightness. At right, luminance across the width of the “blurred” stripe. Note edge width D and luminance increment f. superimposed on the background. The dotted line shows how a filter changes the luminance. 559

560

JAMES P. THOMAS

AND

CONSTANCE W. KOVAR

Figure lb illustrates the variations in luminance across the width of the “blurred” stripe. At the center there is a plateau of uniform luminance, lo wide. To either side, the luminance drops gradually to the level of the background. The decline is linear with respect to distance and extends laterally for distance D. This distance was approximately the same on both sides of the plateau in a given stripe but varied from stripe to stripe. The luminance adjustments which the experimenter made between presentations altered the stripe as is indicated by the dotted line. The purpose of these adjustments was to determine the luminance increment L,at which the stripe was judged equal to the Standard in brightness, where L was measured at the plateau. The purpose of the experiments was to study the relationship between this luminance and the width, D, of the edge zones.

w FIG. 2. Apparatus.

See text for explanation.

Under certain conditions, illusory light and dark bands (Mach bands) appeared at the edges of the “blurred” stripe. Subjects were instructed to ignore these bands, and base their brightness judgments only upon the appearance of the central plateau area. Figure 2 shows the apparatus. The stimuli were projected on a screen at A’B’. The screen was a rotating matt white disk. Rotation prevented texture from influencing the brightness matches. The subject looked through an artificial pupil (diam. = 2.8 mm) and saw the screen reflected in mirror ML (All mirrors are first surface. Mz, part of the projection system for the “blurred” stripe, was mounted just below Ml.) The background and the Standard stripe were projected by conventional optical systems, and reflected on to the screen by mirrors Ma and A44. The projection system for the “blurred” stripe is not standard, and will be described in some detail. Spherical lenses LZ and La form an image of aperture A on the screen at A’B’. However, the cylindrical lens, Lc, increases the power along the vertical axis and, along this axis, brings into focus the opening B. Thus, a rectangle is formed. Its height is determined by the height of opening B, its width by the width of aperture A. Given a rectangular opening at B, the luminance along any vertical is uniform from top to bottom and is proportional to the height of aperture A at the corresponding position. If aperture A is of uniform height (i.e. a rectangle), the stripe at A’B’ is of uniform luminance and has step-like edges. If the opening at A is higher on one side than on the other, there is a corresponding luminance gradient across the width of the stripe. If the opening is trapezoidal, with sides slanted, the stripe has ramp-like edges of the sort shown in Fig. 1b. Aperture B must be evenly illuminated, regardless of the shape of aperture A. For this reason, aperture A is illuminated by forming upon it the image of the ribbon filament of a tungsten lamp. A shutter, placed near A, controls exposure of the stripe. A neutral density wedge and filters control luminance. For their effect on the stripe, see Fig. 16. Stimuli were calibrated by scanning the disk at A’B’ with a Spectra photometer which was modified for close work.

The Effect of Contour Sharpness on Perceived Brightness

561

RESULTS

The results are presented in Fig. 3. One axis shows the luminance increment L required for a brightness match with the Standard. The other axis shows the width, D, of the edge zones. (See Fig. lb.) Luminance increment L is expressed in per cent in order to facilitate comparisons among the several conditions. In each condition the luminance of the stimulus with the smallest D is arbitrarily set at 100 per cent. The different plots show results obtained with different background luminances and with Standard stripes of different luminances. The Standard stripe luminance is given as a ratio (CR) of the background luminance. Since the stripe luminance includes the background, the ratio always exceeds unity. One plot gives the results for a detection task. In this case, increment L refers to the plateau luminance necessary for the subject to just-detect the presence of the “blurred” stripe. There are five points to be made about the results: (1) The brightness of the central plateau depends upon the sharpness of the edges. As the width, D, of the edge zones is increased, the plateau luminance must be increased in order to maintain constant brightness. The increase is approximately linear with respect to D. However, the increase is not rapid enough to maintain a constant ratio between plateau luminance and D. In other words, constant brightness is not associated with constant slope of the edge gradients nor with constant slope changes at the top or bottom of the gradients. (2) The roughly linear relationship between plateau luminance and D, holds for all edge widths studied. If there is a width at which further increases in D have a reduced effect, then that width is greater than 72 min. (3) Similar results are obtained with moderate and high background or adapting luminances. at the lowest background luminance the effect is reduced in magnitude and more variable.

However,

(4) The per cent increase in plateau luminance appears to be independent of the contrast ratio (CR) between the Standard stripe and the background, except at low background luminances. When the luminance of the Standard stripe is low (low background level and low CR), the effect nearly disappears. (5) The detectability of the stripe also depends upon the sharpness of the edges. The relationship between the plateau luminance and D is about the same for just-detectable stripes as it is for stripes matched in brightness with a sharply focused Standard. It should bc noted here that the slopes of the curves shown in Fig. 3 may dcpcnd partly upon the plateau width. Using a different apparatus, we experimented with stripes having plateaus only 30 min. wide. For brightness matches, we obtained curves nearly twice as steep as the curves shown in Fig. 3b. The background luminance and CR were comparable. On the other hand, detection data obtained with the narrow stripes agreed closely with the data shown in Fig. 3c.

DISCUSSION

These effects are not purely optical. Were the retinal image badly blurred, increasing the width D of the edge zones might augment the illuminance at the center of the retinal image and increase the apparent brightness. However, the actual finding was that increasing D reduced brightness. Similarly, the results cannot be attributed to a simple sensitivity to total flux of the stimulus field. These results may be discussed in terms of lateral inhibitory interactions. Such interactions have been observed in Limuh (HARTLINE and RATLIFF, 1957) and have been suggested for human vision (VON BEKESY, 1960). Similarly, the receptive fields of single cortical cells in the cat involve antagonism between one part of the field and another (HUBEL and WIESEL, 1962). In each case, the response to one part of the visual field is reduced as adjacent areas are illuminated. The analog in our experiment would be dimming of the center of the stripe as light is added at the sides by increasing D. In some sense, the response of each of these systems reflects the difference in illumination from one part of the field to another. Indeed, the cat’s cortical cell may not respond at all to uniform illumination.

562 200

180.

JAMES P. THOMAS AND CONSTANCEW. KOVAK

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incremental

in per cent,

with

Background

luminance

and

7

required

the increment each

’

64

to match

corresponding

contrast plot.

b

ratio

brightness to

between

FIG. 3c represents

D-4

min

standard

standard. arbitrarily

Increments taken

and background

the detectiontask.

areexpressed as 100 per cent. are indicated

on

72

The Effect of Contour Sharpnesson PerceivedBrightness

563

In this context, we propose that the perceived brightness of each stripe is determined by a weighted sum of the luminance at points across the width of the stimulus field:

where B is the brightness of the stripe, lr is the luminance at point i, and ct is a constant which reflects the effect of stimulation at point i upon the brightness of the stripe. The values taken by ci specify the receptive field of the visual subsystem responsible for the perceived brightness of the stripe. Antagonistic areas of the field are represented by positive and negative ~oe~~ients, and cr becomes zero for points which lie outside of the receptive field and which do not affect the brightness of the stripe. Even without further specification, this formulation leads to a prediction which is tested and confirmed by our data. The test is of broad interest, since the same prediction can also be derived from VON BEKESY’S theory and from the application to human vision of the concept of the optical transfer function (see review by BOYNTO~, 1962, p. 174). To develop this prediction, we must first rewrite equation (1) to reflect the fact that the luminance at each point on our stimuli is the sum of two superimposed luminances: k, the background luminance common to all points; and xt, the luminance added to that particular point by superposition of the stripe on to the background. B= &

CI (xi $ k)] = f(;

i=l

i=l

ctxt + k &) i=l

If two stimuli, of edge width D and D’, are judged equal in brightness, then the corresponding luminance sums must also be equal:

b cfxi

k ZZci = $ c
+

i=l

i=l

i=l

i=t

CI

(2) weighted

(3)

.z CfXf = E CiX’( , i=I

i::

where xi and x’f are the luminances added to the background by the superimposition of the stripes of edge width D and D’, respectively. Let the brightness of stripe D be altered. In our experiments, the change is made by changing a filter in the stripe projector, which has the effect of multiplying each value of xf by a factor n. Now, let the brightness of stripe D’ be changed so that it is again judged equal to D. This change is also made by manipulating a filter, which has the effect of multiplying each value of x’s by n’. Since the stripes are again matched in brightness, the new weighted lurnin~~ sums are also equal. ;: C$ptyi= ,E C@z’X’f

i-l

i-l

(4)

Given equation (3), it follows that n=n’. Thus, the weighted luminance sum formulation predicts that, once the stripes are equated in brightness, they will remain equal to each other when xi and x’f are multiplied by the same factor. The relevance of the foregoing is that the luminance increment L is the value taken by xi (or x’f) when point i is in the plateau portion of the stripe. Luminance increment L has been previously defined and is the quantity graphed in Fig. 3. Figure 36 shows the relative value of increment L for various edge widths when the stripes are equal by virtue of having been matched to the same low contrast standard. Figure 3~ shows the same information for stripes equated by matching to a brighter standard. The curves, in per cent, are nearly the same. This means that if L were expressed in absolute, rather than relative, units curve 3a could be obtained by multiplying every point on curve 3b by the same factor. This relationship is the one predicted at the end of the last paragraph. Curves 3e and 3f are also relevant, since here too standard stripes of different luminance are projected on to the same background. These results do not conform to the prediction. However, essentially no effect of edge conformation is seen in Fig. 3f. This fact indicates that perhaps the curves differ because the very dim stimuli represented in 3f were below the threshold of the interaction system operating in the other conditions.

JAMES P. THOMAS AND CONSTANCE W. KOVAK

564

Acknow/edge/rren/s-This research was supported in part by United States Public Health Service Grant NB05185 from the National Institute of Neurological Diseases and Blindness. We thank Professor GEORGE E. MOUNT for his helpful criticisms, and RICHARD G. MCEUEN, a National Science Foundation undergraduate research participant, for serving as a subject. REFERENCES BEKESY, G. VON (1960). Neural inhibitory units of the cyc and skin. Quantitative description of contrast phenomena. J. opt. Sot. Amer. 50, 1060-1070. I~OYNTON, R. M. (1962). Spatial vision. Arrntr. Rev. Psycho/. 13. I7 I ---200. COI~NSW~~T, T. N. (1962). The staircase method in psychophysics. Anrer. J. /?~yc/ro/. 75, 485-491. ENOCH, J. M. (1958). Summated response of the retina to light entering different parts of the pupil. J. opt. Sot. Amer. 48, 392-405. HARTLINE, H. K. and RATLIFF, F. (1957). Inhibitory interaction of receptor units in the eye of Lin~ulus.

J. gen. Physiol. 40, 357-376. HUBEL, D. H. and WIESEL, T. N. (1962).

in the cat’s striate

cortex.

Receptive

fields, binocular

interaction

and functional

architecture

J. Physiol. 160, 106-154.

Abstract-The present experiment demonstrates the effect of the sharpness of the contour separating stimulus from background upon the perceived brightness of the stimulus. With increasing blur of the stimulus edges the perceived stimulus brightness decreases monotonically. The effect is found over all degrees of blur, all stimulus-to-background intensity ratios, and all levels of light adaptation examined. There seems to he a decrease in the magnitude of the effect in a detection task and at extremely low adaptation levels. Relevance of the findings to possible underlying mechanisms for brightness perception is discussed. RCum&-L’experience presentte tend a demontrer I’effet de la precision du contour separant le stimulus du fond, sur la clarte du stimulus perCu. La clarte du stimulus percu decroit en fonction de l’estompage des bords du stimulus. Cet effet s’observe pour tous les degres d’estompage, tous les rapports d’intensitt stimulus-fonds et pour tous les niveaux d’adaptation a la lumiere, alors examines. II apparait que l’ampleur de I’effet decroit dans le cas d’une tpreuve de detection et aux niveaux d’adaptation cxtremement bas. Presentation sur les conclusions applicables aux mecanismes relatifs a la perception de la clartt du stimulus. Zusammenfassung-Dieses Experiment zeigt die Wirkung, die die Schlrfe der den Reiz vom Hintergrund abtrcnnendcn Kontur auf die wahrgenommenes Hclligkeit des Reizes hat. Mit zunehmcnder Unklarheit des Reizrandes gibt es eine zunehmcnde Untersch&ung dessen Helliakcit. Diese Wirkuna hndet man tibcr alle Grade der Unklarheit. alle Verhlltnisse der Inter&t des Reizes zum I%ntergrund und alle Niveaus der Lichtshearhei&ng die wir untersucht haben. In einer Suchaufgabe und in sehr dunklen Niveaus der Bearheitung scheint eine Abnahme in der G&se der Wirkung stattzufinden. Die Bedeutung der Ergcbnisse fur moghche zugrundeliegende Mechanismen der Helligkeitswahrnehmung wird diskutiert. Pe3mMe-npeACTaBneHHbl~ 3KCHepHMeHT BeMOHCTpHpyeT BnHBHHe YeTKOCTH KOHTypa, oT~en~mmer0 CTnMyn OT @OHa, Ha BocnpnHuMaeMym @KOCTb (CBeTJlOTy) cTnMyna. flpu yBenHHeHwu cTeneHsi HeflcH0CTn rpaHns cTwMyna ceeTnoTa crHMyna MOHOTOHHOyMeHbmaeTcrr. 3~0~ 344eKT Ha6JHOAaeTCB npn Bcex cTeneHIfx HeBcHOCTn, BCeX OTHOmeHHRX HHTeHCHBHOCTH CTHMyJla U @OHa H Ha BceX ypOBHXX CBeTOBOii aHanTaqnw, KOTOpble 6bmn HCCneAOBBHbr. flOBHAUMOMy, BenHrlHHa s@#h3KTa yMeHbl.HaeTCR B Cny’iae nOHblTKH o6HapyBceHna H HpH OYeHb HH3KOM ypOBHe anrUlTaHHH. 06cyHcflaeTcs 3HBYeHHe HOny’ieHHbIX pe3yJlbTaTOB &ml HOHUMaHHll B03MOXCHblX MeXaHH3MOB, ne%tmHX B OCHOBe BOCHpHBTHX RPKOCTM.