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Relations between brightness and luminance under induction
Vision Rcs. Vol. 5, pp. 331-340.
RELATIONS
Pergamon Press 1965. Printed in Great Britain.
BETWEEN
BRTGHTNESS
UNDER
AND
LUMINANCE
INDUCTION
H. W. HOKEMAN lnstiluul vooc Perccptic Ondcrzoek, (Received
lnsulindelaan
2,
Eindhoven,The Netherlands
8 Sepfenrber 1964)
PSYCHOPHYSICALmethods vary in the extent to which they give preponderance to subjective impressions. In threshold measurements the observer expresses his decision as to whether or not there is a signal present. In matching experiments the observer uses a criterion of subjective equality of two impressions. A third possibility is to ask the observer to assess numerically his subjective impression of a stimulus. Many examples of these methods can be cited, among them the work of Vos (1963) on the effect of glare on threshold data, the work of HOREMAN (1963) on brightness induction using a matching technique, and the work of STEVENS(1961) on numerical estimation of brightness. The threshold and matching techniques both employ the subjective impression as a criterion for the adjustment of a physical stimulus. The stimulus intensity (e.g. luminance) is adjusted until the observer reports the stimulus to be just visible or to give an impression similar to that of another stimulus. The experimenter reads the adjusted value and collects results in terms of objective values of luminance, Both methods yield relations between stimulus values, the only subjective element being that the relation defines a constant sensory impression, about the value of which nothing can be said. In an effort to scale the sensory impression the method of numerical assessment tries to relate directly the value of a presented luminance to the magnitude of the sensory impression experienced by the observer. The method is based on the assumption that the observer can match one magnitude, such as brightness, to another magnitude, such as number. Several procedures for the scaling of sensory magnitudes have been described, some of which do not use numerical assessments but allow the observer to match sensory magnitudes in two different sense modalities (STEVENS, 1961). It is important to determine whether sensory scaling gives results that can be compared with results of the more traditional methods of threshold measurements or interocular matching. It is the aim of the following to show that such a comparison can be made. Using subjective assessments, STEVENSand STEVENS(1960) investigated the influence of simultaneous contrast on the brightness-luminance relation. For conditions of dark adaptation, and in the absence of simultaneous contrast, the brightness-luminance relation as seen in Fig. 1 is a power function. This function becomes a straight line in double-logarithmic co-ordinates. At fixed points on this straight line other lines branch off, at a steeper slope. Each line branching off corresponds to a fixed value of the luminance of a surround by which a contrast effect was induced. In Fig. 1 each curve relates the subjective brightness (B) to the objective luminance (L) of the test field, and the luminance of the surround (L.1)serves as the parameter.
331
332
H. W.
H~REMAN
Results of interocular brightness matclling ex~rin~ents have been presented in a previous paper (HOREMAN, 1963), some of which are shown in Fig. 2. The curves relate the test field luminances (L) needed to maintain a brightness match with a comparison field, to the luminance of an inducing field (LI), by which the simultaneous contrast effect is produced. In this set of curves the parameter is the subjective brightness (B). Along each curve the brightness of the test field is constant but unknown. It is equal to the brightness of the fixed comparison field.
Luminance, db
Fro 1. Brigfitness contrast functions, from STEVENS and STEVENS (1960). The lines show the subjective estimation of the brightness of a disk placed within an annulus. The black dots, at the points where the lines branch off from the original power function, indicate the luminance values of the annulus.
When interocular matches are performed for a fixed luminance of the inducing field one obtains sets of luminances of test and comparison field that fall along the lines shown in Fig. 3. Such lines relate test field luminance to comparison luminance based on the criterion To distinguish between the lines, the fixed inducing of an equal brightness sensation. iuminan~e may serve as a parameter. Except for the difference in the co-ordinates, Fig. 3 shows a remarkable resemblance to the results reproduced in Fig. 1. This leads to the hypothesis that results of interocular brightness matches and those of subjective estimations are merely different aspects of one and the same phenomenon.
log
L,(cd
/m2)
FIG. 2. Lines of equal brightness, from H~REMAN(1963). The lines give the luminance values as a function of the inducing luminance in matching inter~ulariy the bri~tness of the test geld with a comparison brightness.
Relations between Brightness and Luminance under induction
333
Such an hypothesis can be tcstcd and confirmed if a simple transformation could be found by means of which results of interocular matching, plotted as in Fig. 2, could be transformed into a result consistent with that of Fig. I, and vice versa.
§2 A simple transformation that may serve this purpose is found by using a power-law relation, as proposed by STEVENS(1961), to transform comparison luminances into values of subjective brightness. Thus, applying a power function with an exponent of 0.45 (valid for fields of half a degree), the parameter in Fig. 2 may be scaled in terms of brightness.
FIG. 3. Lumin~ce valuesof test and comp~ison field which lead to a brightness match under the induction of an annuius-shaped
field at constant luminance.
Now, the independent variable (inducing luminance) and the parameter (brightness) can be transposed by plotting the intersections of the equibrightness lines with lines of constant inducing luminance in a graph of brightness vs. test luminance. Intersections corresponding to the same equ~brightness iine are plotted at a constant ordinate value, viz. the brightness value of that line. Abscissa values are taken to be equal to the corresponding ordinates of the intersection points in Fig, 2. Since it contains four equibrightness lines for one subject, Fig. 2 leads to four sets of points at the corresponding brightness levels. In the new plot, points can be grouped according to values of the inducing luminance at which the intersections were determined. Thus we obtain a set of curves with the inducing luminance as the parameter, as shown in Fig. 4. The luminances are given in decibels re a base levet of O-3pcdlrn2, which corresponds to the luminance state used by STEVENS. There is a striking resemblance between Fig. 4, deduced from brightness matches in which the observer equated two sensations in strength, and Fig. 1 obtained with brightness estimations in which the observer scaled sensations according to a magnitude that was expressed numerically. Apart from the question whether the psychophysical law is a power law or not and which value the exponent should have, it is of interest to note the fact that a subjective scale can be expressed numerically. Also, one is able to adjust stimuli in intensity so as to equate their subjective impressions. It is by no means certain apriori that the mechanisms underlying the two abilities to express a subjective scale, and to match sensory impressions, are the same.
H. W. HOREMAN
334
The latter ability could be present without the existence of an internal subjective scale, quite apart from the ability to express such a scale. Therefore, comparability of data obtained by interocular matching and data found by numerical estimations makes it plausible to hypothesize that matching of sensations is done by comparing values on a built-in subjective scale. The representations in Figs. 1 and 2 may be considered as two-dimensional representaan~ong three vm-iablcs: the brightness of it lest field, its luminance and the effect of simultaneous contrast as governed by the luminance of a sllrround or inducing fietd. tions af ;1 relation
I
60
70
I
80
I
Luminance, db FIG. 4. Replotting of the lines of equal brightness of
Fig. 2. Brightness is taken as the dependent variable; the luminance of the test field is the independent variable; the inducing luminance is the parameter. There is a striking resemblance with Fig. I.
It remains to be seen whether these representations differ in the amount of insight they yield about the actual form of the three-dimensiona relation. From the results of brightnessmatching experiments, HOREMAN (1963) has tried to show the effect of the figuration of the stimulus fields used. In Fig. 5 a reproduction is given of some of the results he obtained by comparing experimentally the configurations used by HEINEMANN (1955), DIAMOND (1953) and FRY and ALPERN (1953) with an I.P.O. configuration. Though the configuration is differentially effective, it is not easy to express the effects of the brightness induction in the various configurations in quantitative terms. Moreover, the concept of equibrightness lines, although quite correct in itself and in its use, is not very easy to understand, while the absence of numerical values to be attached to the various equibrightness lines forms an extra disadvantage in using this concept. Relations of brightness to luminance for various inducing luminances can be obtained by appiying the power law transformation. Figure 6 shows these transformed reiations for the four configurations. All the curves can be represented very weil by sets of straight lines, each inducing luminance giving rise to a straight line branching off from the original brightness vs. luminance relation. In this respect it is probably useful to introduce a concept of visual gradation,1 analogous to the gradation of photographic materiaf, namefy the slope of the density characteristic. This visual gradation is given numerically by the slope of the line in the E vs. L graph; it thus represents the exponent of the luminance in the brightness-luminance relation. With the aid of this visual gradation the differences between 1 The concept was suggested by Dr. .I. F. Schoutcn, to whom I express my gratitude for valuable discussions on the subject.
Relations between Brightness and Luminance under Induction
335
the induction effects of the four configurations can be described as follows: Each inducing field luminance changes the visual gradation from an original value, taken as 0.45, to a higher value; the higher value being applicable for a test luminance smaller than a critical value. 3
-..--
---
----
.-.-_* _.__.i l ’ L/f A 2____---- .._. CII 1 .k’,.’ -0 -.& 1. , __._ _ C.I ,_2’ 0 0 ’ -I 2
7
-n!3
FIG. 5. Graphs of equal brightness contours for four different configurations fields (from HOREMAN, 1963).
60
70
60 log
60
70
90 L,
60 l%l
60
db
70 log
90 L,
50
100
db
IO0
0
50
of the various
L,
60
60 db
60
70 log
L,
db
FIG. 6. Replotting of the equal brightness contours, with the inducing luminance as parameter, for several brightness-luminance relations. X
H. W. HOREMAN
336
Table 1 gives the visual gradations found under the four different experimental conditions. TABLE 1. VISUAL GKADATIONSvs.
INDUCING
LUMINANCE UNDER
FOUR
DIFFERENT
EXPERJMENTAL
CONDiTlONS
log Lf
in cd/m”
0.5 6O
in dB Configuration HEINENANN (1955) DIAMOND (1953) 1.P.O. FRY and ALPERN(1953)
o-45 0.45 0.68 @45
0 65
O-5 70
0.70 0.57 0.95 0.45
I*0 75
f&
I.5 80
2.8 O-67 2.2 0.65
1.4 0.60
0.69 2.9 o-77
2.0 85
0.71 3.9 0.88
2.5 90
3.0 95
0.72 1-o
1.2
From these values it can be deduced that the four ~on~gurational conditions can be split up into two groups with rather different trends. The first group consists of the ~on~guration used by HEINEMANN(1955) and the I.P.O. configuration. In these cases the visual gradation increases very steeply with inducing luminance. The second group, with the configurations used by DIAMOND (1953) and FRY and ALPERN (1953), shows moderate increases of the visual gradation. The same effect can be found in the graphical representation in Fig. 7. It
0
60
70 tog
80
LI,
FIG. 7. Visual gradation as a function of inducing
90
db
luminanceobtainedunderfour ~n~~tion$.
hardly needs further comment that the representation in Fig. 6, where the brightness values have been introduced, offers a better means of describing the effect of the brightness induction by simultaneous contrast under various configurations than can be found with the representation shown in Fig. 5. It has been said that the higher value of the visual gradation applies to test luminances smaller than a critical value. For the four configurations the critical values of the test luminance are plotted against the inducing luminance in Fig. 8. STEVENSand STEVENS (1960), in their work on brightness assessments in the presence of a surround (cf. Fig. I), state that the critical values are equal to the Iuminances of the surround, which in our case would mean equality of critical value and inducing luminance. From Fig. 8 it appears that this equality was not always obtained in the experiments. Again one finds two groups of conditions. The configurations used by DIAMOND (1953) and FRY and ALPERN (1953) show a line with a slope of about 40” at high critical values. In other words the brightness induction, though causing a moderate increase of visual gradation, starts at critical values where the test luminance is still higher than the inducing luminance. The group consisting of the
RelationsbetweenBrightnessand Luminanceunder Induclion
337
configuration used by HEINEMANN(1955) and the I.P.O. configuration gives lines with a slope at 25-30” and crossing the 45” median. This means, relatively speaking, that the higher the inducing luminance the lower the critical value. In other words, with the configurations that lead to steep increases in the visual gradation, the brightness induction that gives rise to high visual gradation starts at test Iuminances below the inducing luminance.
log LI. FIG. 8.
db
Criticall~inan~ values beyond which the brightness impre~i~ fa& off more rapidly than can be expected from the decrease in luminance of the test field.
The conclusion that the critical luminance exceeds the inducing luminance remains doubtful. At L=LI the test and inducing stimuli merely add up to a stimulus of increased area. If the size of the stimulus does not affect brightness, the larger stimulus results in the same brightness estimation. Thus the critical luminance must be equal to or smaller than the inducing luminance. The cffcct ofstimulus size on brightness (HANES, 1951) do not seem large enough to account for the results of Fig. 8. It seems likely that the differences in Fig. 8 should be explained by systematic errors in the experiments (different subjects, interocular differences, etc.). The interesting effect in Fig. 8 remains, i.e. the slope difference for the two groups of configurations. With respect to the three-dimensional relation among brightness, luminance and inducing luminance, the question can be raised about the actual shape of such a solid. Figure 9 shows a drawing in orthogonal projection of the three-dimensional solid, with the luminance (L) and the inducing luminance (Lr) along axes in the horizontal plane and the brightness (B) in the vertical direction. From Fig. 9 it can be seen how the lines found in the original brightness-matching experiments (cf. Fig. 2) are intersections of planes of constant brightness (B=constant) through the surface of the solid. The transformed lines (cf. Fig. 4) relating brightness to luminance are found on the surface by intersecting it with planes of constant inducing luminance. Thus the three-dimensional surface shows in a single picture how the brightness varies for different values of test and inducing luminance. In addition to the intersections mentioned, a third type of intersections can be found, namely with planes of constant test luminance (L=constant). These intersections have been drawn on the surface in Fig. 9. When plotted on one graph they relate brightness to inducing luminance for fixed values of test luminance, and they actually are very similar to trans-
338
H. W. HOREMAN
formations of lines found in brightness-matching experiments. In Fig. 10 this comparison is given of the intersections for the results of HOREMAN (1963). The subject adjusted comparison luminances to re-establish the match with the depressed brightness of the test field. The latter results have been transformed by applying the powerlaw relation on the comparison luminances to transfer them into brightness values. The comparison is not very good since the rate of decrease in the values is not as steep as predictable from the intersections. However, in this region small differences in adjustments may lead to large deviations.
FIG. 9. Orthogonal projection of the three-dimensional solid, the surface of which gives the relation between the inducing luminance, the luminance and the brightness. The trajectories of the surface with three types of planes are indicated; the horizontal XYplane leading to lines of equal brightness; the vertical A’2 plane in which it is shown how the brightness is depressed by the inducing luminance; and the verticat YZ plane yielding brightne~~ont~st functions.
How can the three-dimensional body be described? If logarithmic axes are used, it turns out to have a flat surface for large test field luminances. That flat surface is parallel to the inducing luminance axis and shows an inclination from which one can deduce the exponent to which the luminance should be raised in the brightness vs. luminance relation for the plain test field. An edge can be indicated on the surface of the solid beyond which the flatness of the surface turns into a falling slope. In Fig. 8 projections of these edges are shown. The falling slope is present for larger values of the inducing luminance combined with smaller test luminance values. Configurations which lead to a moderate effect of brightness induction tend to show flat portions in the falling part of the surface. The representation in Fig. 9 has been deduced from old measurements by recombining them in another way. This recombination might have introduced an accumulation of experimental errors and therefore should be checked by direct measurements. A crucial control measurement is to find out whether, in a configuration used by HEINEMANN (1955) for high inducing luminances, the visual gradation actually reaches an unbounded infinite
Relations bctwccn Brightness and Luminance under Induction
339
From a direct experiment asking for subjective assessments of the brightness of a disc of half a degree surrounded by a very bright annulus we found high values of visual gradation, but we could not confirm that the slope of the brightness-luminance relation reached an infinite value. In conclusion it turns out to be possible to compare results obtained by brightness matching with results of subjective estimations of brightness. Furthermore, from such a comparison it can be concluded that the ability to match brightnesses finds its basis in a comparison of sensations with respect to a built-in subjective scale. Finally it can be stated that a numerical expression of the results in terms of subjective brightness is best suited to describe effects found in situations where simul~neous contrast occurs. value.
70
60 Induction
90
60 luminance,
db
10. Intersections of the three-dimensional surface with planes of constant test luminance compared with transformations of results obtained in brightness matching experiments by adjusting the comparison luminance (cf. Fig. 10, HOREMAN, 1963). FIG.
REFERENCES DIAMOND, A. L. (1953).
Fovea1 simuitan~us brightness contrast as a function of inducing and testfietd luminances. J. exp. Psychol. 45, 304-314. FRY, G. A. and ALPERN, M. (1953). The effect of a peripheral glare source upon the apparent brightness of an object. J. opf. Sm. Amer. 43, 189-195. HANES, R. M. (1951). Suprathreshold area brightness relationships. J. opt. Sot. Amer. 41, 28-31. HEINEMANN, E. G. (1955). Simultaneous brightness induction as a function of inducing and test-field luminances. .I. exp. Psychoi, 50, 89-96. HOREMAN, H. W. (1963). Inductive brightness depression as influenced by configurational conditions. Vision Res. 3, 121-135. STEVENS,S. S. (1961). To honor Fechner and repeal his law. Scietzce 133,80-86. STEVENS, S. S. and STEVENS,J. C. (1960). Tlte dynartticso/‘vbuuf brightness. Report PPR-246. Harvard University, Cambridge 38, Mass. Vos, J. J. (1963). On ~ec~a~j~fft~ofgkzre (in English). Thesis Rij~unive~iteit, Utrecht.
Abstract-A comparison has been made between results of interocular brightness matching and of asking for brightness estimations. The matching results have been translated by applying a power function ~fo~ation to the l~inan~ values of the com~rison field. The translated results of brightness matching turned out to be completely analogous to results of subjective estimations. By means of plotting the results in terms of subjective estimations relations between brightness and luminance under induction could be easier described. This has been shown in respect to effects of field configurations on these relations. Description of the relations in terms of a concept “visual gradation” analogous to gradation of photographic material has been proposed. Under induction the visual gradation has been increased for test luminances below a critical value depending on the inducing luminance.
340
H. W. HOREMAN Resume-I1 est possible de comparer les r&rhats obtenus par egalisation de luminosites et ceux qui resultent dune estimation subjective de huninosite. En outre, on peut deduire de cette comparaison que la possibilite d%galiser des luminosit6.s se fonde sur la comparaison des sensations avec une 6chelle subjective inteme. Enfin on Ctablit qu’une expression numtrique des r&hats en termes de lwninosite subjective est la plus appropriee pour d&ii les effets obtenus dans des situations oh se produit un contraste simultant. Zusammenfassung-Es ist moglich, die durch subjektiven Helligkeitsabgleich erhahenen Ergebnisse mit den Ergebnissen subjektiver Helligkeitsschiitzung zu vergleichen. Dart&r hinaus kann man aus diesem Vergleich schliessen, dass die Ftihigkeit Helligkeiten abzugleichen ihre Grundlage in einem Vergleich von Empfindungen beziiglich eines eingebauten subjektiven Masstabes hat. Endlich kann man feststellen, dass eine zahlenm&sige Erfassung der Ergebnisse in Einheiten einer subjektiven Helligkeit am besten geeignet ist Effekte zu beschreiben, wie sie beim Simultankontrast auftreten.
RELATIONS
Pergamon Press 1965. Printed in Great Britain.
BETWEEN
BRTGHTNESS
UNDER
AND
LUMINANCE
INDUCTION
H. W. HOKEMAN lnstiluul vooc Perccptic Ondcrzoek, (Received
lnsulindelaan
2,
Eindhoven,The Netherlands
8 Sepfenrber 1964)
PSYCHOPHYSICALmethods vary in the extent to which they give preponderance to subjective impressions. In threshold measurements the observer expresses his decision as to whether or not there is a signal present. In matching experiments the observer uses a criterion of subjective equality of two impressions. A third possibility is to ask the observer to assess numerically his subjective impression of a stimulus. Many examples of these methods can be cited, among them the work of Vos (1963) on the effect of glare on threshold data, the work of HOREMAN (1963) on brightness induction using a matching technique, and the work of STEVENS(1961) on numerical estimation of brightness. The threshold and matching techniques both employ the subjective impression as a criterion for the adjustment of a physical stimulus. The stimulus intensity (e.g. luminance) is adjusted until the observer reports the stimulus to be just visible or to give an impression similar to that of another stimulus. The experimenter reads the adjusted value and collects results in terms of objective values of luminance, Both methods yield relations between stimulus values, the only subjective element being that the relation defines a constant sensory impression, about the value of which nothing can be said. In an effort to scale the sensory impression the method of numerical assessment tries to relate directly the value of a presented luminance to the magnitude of the sensory impression experienced by the observer. The method is based on the assumption that the observer can match one magnitude, such as brightness, to another magnitude, such as number. Several procedures for the scaling of sensory magnitudes have been described, some of which do not use numerical assessments but allow the observer to match sensory magnitudes in two different sense modalities (STEVENS, 1961). It is important to determine whether sensory scaling gives results that can be compared with results of the more traditional methods of threshold measurements or interocular matching. It is the aim of the following to show that such a comparison can be made. Using subjective assessments, STEVENSand STEVENS(1960) investigated the influence of simultaneous contrast on the brightness-luminance relation. For conditions of dark adaptation, and in the absence of simultaneous contrast, the brightness-luminance relation as seen in Fig. 1 is a power function. This function becomes a straight line in double-logarithmic co-ordinates. At fixed points on this straight line other lines branch off, at a steeper slope. Each line branching off corresponds to a fixed value of the luminance of a surround by which a contrast effect was induced. In Fig. 1 each curve relates the subjective brightness (B) to the objective luminance (L) of the test field, and the luminance of the surround (L.1)serves as the parameter.
331
332
H. W.
H~REMAN
Results of interocular brightness matclling ex~rin~ents have been presented in a previous paper (HOREMAN, 1963), some of which are shown in Fig. 2. The curves relate the test field luminances (L) needed to maintain a brightness match with a comparison field, to the luminance of an inducing field (LI), by which the simultaneous contrast effect is produced. In this set of curves the parameter is the subjective brightness (B). Along each curve the brightness of the test field is constant but unknown. It is equal to the brightness of the fixed comparison field.
Luminance, db
Fro 1. Brigfitness contrast functions, from STEVENS and STEVENS (1960). The lines show the subjective estimation of the brightness of a disk placed within an annulus. The black dots, at the points where the lines branch off from the original power function, indicate the luminance values of the annulus.
When interocular matches are performed for a fixed luminance of the inducing field one obtains sets of luminances of test and comparison field that fall along the lines shown in Fig. 3. Such lines relate test field luminance to comparison luminance based on the criterion To distinguish between the lines, the fixed inducing of an equal brightness sensation. iuminan~e may serve as a parameter. Except for the difference in the co-ordinates, Fig. 3 shows a remarkable resemblance to the results reproduced in Fig. 1. This leads to the hypothesis that results of interocular brightness matches and those of subjective estimations are merely different aspects of one and the same phenomenon.
log
L,(cd
/m2)
FIG. 2. Lines of equal brightness, from H~REMAN(1963). The lines give the luminance values as a function of the inducing luminance in matching inter~ulariy the bri~tness of the test geld with a comparison brightness.
Relations between Brightness and Luminance under induction
333
Such an hypothesis can be tcstcd and confirmed if a simple transformation could be found by means of which results of interocular matching, plotted as in Fig. 2, could be transformed into a result consistent with that of Fig. I, and vice versa.
§2 A simple transformation that may serve this purpose is found by using a power-law relation, as proposed by STEVENS(1961), to transform comparison luminances into values of subjective brightness. Thus, applying a power function with an exponent of 0.45 (valid for fields of half a degree), the parameter in Fig. 2 may be scaled in terms of brightness.
FIG. 3. Lumin~ce valuesof test and comp~ison field which lead to a brightness match under the induction of an annuius-shaped
field at constant luminance.
Now, the independent variable (inducing luminance) and the parameter (brightness) can be transposed by plotting the intersections of the equibrightness lines with lines of constant inducing luminance in a graph of brightness vs. test luminance. Intersections corresponding to the same equ~brightness iine are plotted at a constant ordinate value, viz. the brightness value of that line. Abscissa values are taken to be equal to the corresponding ordinates of the intersection points in Fig, 2. Since it contains four equibrightness lines for one subject, Fig. 2 leads to four sets of points at the corresponding brightness levels. In the new plot, points can be grouped according to values of the inducing luminance at which the intersections were determined. Thus we obtain a set of curves with the inducing luminance as the parameter, as shown in Fig. 4. The luminances are given in decibels re a base levet of O-3pcdlrn2, which corresponds to the luminance state used by STEVENS. There is a striking resemblance between Fig. 4, deduced from brightness matches in which the observer equated two sensations in strength, and Fig. 1 obtained with brightness estimations in which the observer scaled sensations according to a magnitude that was expressed numerically. Apart from the question whether the psychophysical law is a power law or not and which value the exponent should have, it is of interest to note the fact that a subjective scale can be expressed numerically. Also, one is able to adjust stimuli in intensity so as to equate their subjective impressions. It is by no means certain apriori that the mechanisms underlying the two abilities to express a subjective scale, and to match sensory impressions, are the same.
H. W. HOREMAN
334
The latter ability could be present without the existence of an internal subjective scale, quite apart from the ability to express such a scale. Therefore, comparability of data obtained by interocular matching and data found by numerical estimations makes it plausible to hypothesize that matching of sensations is done by comparing values on a built-in subjective scale. The representations in Figs. 1 and 2 may be considered as two-dimensional representaan~ong three vm-iablcs: the brightness of it lest field, its luminance and the effect of simultaneous contrast as governed by the luminance of a sllrround or inducing fietd. tions af ;1 relation
I
60
70
I
80
I
Luminance, db FIG. 4. Replotting of the lines of equal brightness of
Fig. 2. Brightness is taken as the dependent variable; the luminance of the test field is the independent variable; the inducing luminance is the parameter. There is a striking resemblance with Fig. I.
It remains to be seen whether these representations differ in the amount of insight they yield about the actual form of the three-dimensiona relation. From the results of brightnessmatching experiments, HOREMAN (1963) has tried to show the effect of the figuration of the stimulus fields used. In Fig. 5 a reproduction is given of some of the results he obtained by comparing experimentally the configurations used by HEINEMANN (1955), DIAMOND (1953) and FRY and ALPERN (1953) with an I.P.O. configuration. Though the configuration is differentially effective, it is not easy to express the effects of the brightness induction in the various configurations in quantitative terms. Moreover, the concept of equibrightness lines, although quite correct in itself and in its use, is not very easy to understand, while the absence of numerical values to be attached to the various equibrightness lines forms an extra disadvantage in using this concept. Relations of brightness to luminance for various inducing luminances can be obtained by appiying the power law transformation. Figure 6 shows these transformed reiations for the four configurations. All the curves can be represented very weil by sets of straight lines, each inducing luminance giving rise to a straight line branching off from the original brightness vs. luminance relation. In this respect it is probably useful to introduce a concept of visual gradation,1 analogous to the gradation of photographic materiaf, namefy the slope of the density characteristic. This visual gradation is given numerically by the slope of the line in the E vs. L graph; it thus represents the exponent of the luminance in the brightness-luminance relation. With the aid of this visual gradation the differences between 1 The concept was suggested by Dr. .I. F. Schoutcn, to whom I express my gratitude for valuable discussions on the subject.
Relations between Brightness and Luminance under Induction
335
the induction effects of the four configurations can be described as follows: Each inducing field luminance changes the visual gradation from an original value, taken as 0.45, to a higher value; the higher value being applicable for a test luminance smaller than a critical value. 3
-..--
---
----
.-.-_* _.__.i l ’ L/f A 2____---- .._. CII 1 .k’,.’ -0 -.& 1. , __._ _ C.I ,_2’ 0 0 ’ -I 2
7
-n!3
FIG. 5. Graphs of equal brightness contours for four different configurations fields (from HOREMAN, 1963).
60
70
60 log
60
70
90 L,
60 l%l
60
db
70 log
90 L,
50
100
db
IO0
0
50
of the various
L,
60
60 db
60
70 log
L,
db
FIG. 6. Replotting of the equal brightness contours, with the inducing luminance as parameter, for several brightness-luminance relations. X
H. W. HOREMAN
336
Table 1 gives the visual gradations found under the four different experimental conditions. TABLE 1. VISUAL GKADATIONSvs.
INDUCING
LUMINANCE UNDER
FOUR
DIFFERENT
EXPERJMENTAL
CONDiTlONS
log Lf
in cd/m”
0.5 6O
in dB Configuration HEINENANN (1955) DIAMOND (1953) 1.P.O. FRY and ALPERN(1953)
o-45 0.45 0.68 @45
0 65
O-5 70
0.70 0.57 0.95 0.45
I*0 75
f&
I.5 80
2.8 O-67 2.2 0.65
1.4 0.60
0.69 2.9 o-77
2.0 85
0.71 3.9 0.88
2.5 90
3.0 95
0.72 1-o
1.2
From these values it can be deduced that the four ~on~gurational conditions can be split up into two groups with rather different trends. The first group consists of the ~on~guration used by HEINEMANN(1955) and the I.P.O. configuration. In these cases the visual gradation increases very steeply with inducing luminance. The second group, with the configurations used by DIAMOND (1953) and FRY and ALPERN (1953), shows moderate increases of the visual gradation. The same effect can be found in the graphical representation in Fig. 7. It
0
60
70 tog
80
LI,
FIG. 7. Visual gradation as a function of inducing
90
db
luminanceobtainedunderfour ~n~~tion$.
hardly needs further comment that the representation in Fig. 6, where the brightness values have been introduced, offers a better means of describing the effect of the brightness induction by simultaneous contrast under various configurations than can be found with the representation shown in Fig. 5. It has been said that the higher value of the visual gradation applies to test luminances smaller than a critical value. For the four configurations the critical values of the test luminance are plotted against the inducing luminance in Fig. 8. STEVENSand STEVENS (1960), in their work on brightness assessments in the presence of a surround (cf. Fig. I), state that the critical values are equal to the Iuminances of the surround, which in our case would mean equality of critical value and inducing luminance. From Fig. 8 it appears that this equality was not always obtained in the experiments. Again one finds two groups of conditions. The configurations used by DIAMOND (1953) and FRY and ALPERN (1953) show a line with a slope of about 40” at high critical values. In other words the brightness induction, though causing a moderate increase of visual gradation, starts at critical values where the test luminance is still higher than the inducing luminance. The group consisting of the
RelationsbetweenBrightnessand Luminanceunder Induclion
337
configuration used by HEINEMANN(1955) and the I.P.O. configuration gives lines with a slope at 25-30” and crossing the 45” median. This means, relatively speaking, that the higher the inducing luminance the lower the critical value. In other words, with the configurations that lead to steep increases in the visual gradation, the brightness induction that gives rise to high visual gradation starts at test Iuminances below the inducing luminance.
log LI. FIG. 8.
db
Criticall~inan~ values beyond which the brightness impre~i~ fa& off more rapidly than can be expected from the decrease in luminance of the test field.
The conclusion that the critical luminance exceeds the inducing luminance remains doubtful. At L=LI the test and inducing stimuli merely add up to a stimulus of increased area. If the size of the stimulus does not affect brightness, the larger stimulus results in the same brightness estimation. Thus the critical luminance must be equal to or smaller than the inducing luminance. The cffcct ofstimulus size on brightness (HANES, 1951) do not seem large enough to account for the results of Fig. 8. It seems likely that the differences in Fig. 8 should be explained by systematic errors in the experiments (different subjects, interocular differences, etc.). The interesting effect in Fig. 8 remains, i.e. the slope difference for the two groups of configurations. With respect to the three-dimensional relation among brightness, luminance and inducing luminance, the question can be raised about the actual shape of such a solid. Figure 9 shows a drawing in orthogonal projection of the three-dimensional solid, with the luminance (L) and the inducing luminance (Lr) along axes in the horizontal plane and the brightness (B) in the vertical direction. From Fig. 9 it can be seen how the lines found in the original brightness-matching experiments (cf. Fig. 2) are intersections of planes of constant brightness (B=constant) through the surface of the solid. The transformed lines (cf. Fig. 4) relating brightness to luminance are found on the surface by intersecting it with planes of constant inducing luminance. Thus the three-dimensional surface shows in a single picture how the brightness varies for different values of test and inducing luminance. In addition to the intersections mentioned, a third type of intersections can be found, namely with planes of constant test luminance (L=constant). These intersections have been drawn on the surface in Fig. 9. When plotted on one graph they relate brightness to inducing luminance for fixed values of test luminance, and they actually are very similar to trans-
338
H. W. HOREMAN
formations of lines found in brightness-matching experiments. In Fig. 10 this comparison is given of the intersections for the results of HOREMAN (1963). The subject adjusted comparison luminances to re-establish the match with the depressed brightness of the test field. The latter results have been transformed by applying the powerlaw relation on the comparison luminances to transfer them into brightness values. The comparison is not very good since the rate of decrease in the values is not as steep as predictable from the intersections. However, in this region small differences in adjustments may lead to large deviations.
FIG. 9. Orthogonal projection of the three-dimensional solid, the surface of which gives the relation between the inducing luminance, the luminance and the brightness. The trajectories of the surface with three types of planes are indicated; the horizontal XYplane leading to lines of equal brightness; the vertical A’2 plane in which it is shown how the brightness is depressed by the inducing luminance; and the verticat YZ plane yielding brightne~~ont~st functions.
How can the three-dimensional body be described? If logarithmic axes are used, it turns out to have a flat surface for large test field luminances. That flat surface is parallel to the inducing luminance axis and shows an inclination from which one can deduce the exponent to which the luminance should be raised in the brightness vs. luminance relation for the plain test field. An edge can be indicated on the surface of the solid beyond which the flatness of the surface turns into a falling slope. In Fig. 8 projections of these edges are shown. The falling slope is present for larger values of the inducing luminance combined with smaller test luminance values. Configurations which lead to a moderate effect of brightness induction tend to show flat portions in the falling part of the surface. The representation in Fig. 9 has been deduced from old measurements by recombining them in another way. This recombination might have introduced an accumulation of experimental errors and therefore should be checked by direct measurements. A crucial control measurement is to find out whether, in a configuration used by HEINEMANN (1955) for high inducing luminances, the visual gradation actually reaches an unbounded infinite
Relations bctwccn Brightness and Luminance under Induction
339
From a direct experiment asking for subjective assessments of the brightness of a disc of half a degree surrounded by a very bright annulus we found high values of visual gradation, but we could not confirm that the slope of the brightness-luminance relation reached an infinite value. In conclusion it turns out to be possible to compare results obtained by brightness matching with results of subjective estimations of brightness. Furthermore, from such a comparison it can be concluded that the ability to match brightnesses finds its basis in a comparison of sensations with respect to a built-in subjective scale. Finally it can be stated that a numerical expression of the results in terms of subjective brightness is best suited to describe effects found in situations where simul~neous contrast occurs. value.
70
60 Induction
90
60 luminance,
db
10. Intersections of the three-dimensional surface with planes of constant test luminance compared with transformations of results obtained in brightness matching experiments by adjusting the comparison luminance (cf. Fig. 10, HOREMAN, 1963). FIG.
REFERENCES DIAMOND, A. L. (1953).
Fovea1 simuitan~us brightness contrast as a function of inducing and testfietd luminances. J. exp. Psychol. 45, 304-314. FRY, G. A. and ALPERN, M. (1953). The effect of a peripheral glare source upon the apparent brightness of an object. J. opf. Sm. Amer. 43, 189-195. HANES, R. M. (1951). Suprathreshold area brightness relationships. J. opt. Sot. Amer. 41, 28-31. HEINEMANN, E. G. (1955). Simultaneous brightness induction as a function of inducing and test-field luminances. .I. exp. Psychoi, 50, 89-96. HOREMAN, H. W. (1963). Inductive brightness depression as influenced by configurational conditions. Vision Res. 3, 121-135. STEVENS,S. S. (1961). To honor Fechner and repeal his law. Scietzce 133,80-86. STEVENS, S. S. and STEVENS,J. C. (1960). Tlte dynartticso/‘vbuuf brightness. Report PPR-246. Harvard University, Cambridge 38, Mass. Vos, J. J. (1963). On ~ec~a~j~fft~ofgkzre (in English). Thesis Rij~unive~iteit, Utrecht.
Abstract-A comparison has been made between results of interocular brightness matching and of asking for brightness estimations. The matching results have been translated by applying a power function ~fo~ation to the l~inan~ values of the com~rison field. The translated results of brightness matching turned out to be completely analogous to results of subjective estimations. By means of plotting the results in terms of subjective estimations relations between brightness and luminance under induction could be easier described. This has been shown in respect to effects of field configurations on these relations. Description of the relations in terms of a concept “visual gradation” analogous to gradation of photographic material has been proposed. Under induction the visual gradation has been increased for test luminances below a critical value depending on the inducing luminance.
340
H. W. HOREMAN Resume-I1 est possible de comparer les r&rhats obtenus par egalisation de luminosites et ceux qui resultent dune estimation subjective de huninosite. En outre, on peut deduire de cette comparaison que la possibilite d%galiser des luminosit6.s se fonde sur la comparaison des sensations avec une 6chelle subjective inteme. Enfin on Ctablit qu’une expression numtrique des r&hats en termes de lwninosite subjective est la plus appropriee pour d&ii les effets obtenus dans des situations oh se produit un contraste simultant. Zusammenfassung-Es ist moglich, die durch subjektiven Helligkeitsabgleich erhahenen Ergebnisse mit den Ergebnissen subjektiver Helligkeitsschiitzung zu vergleichen. Dart&r hinaus kann man aus diesem Vergleich schliessen, dass die Ftihigkeit Helligkeiten abzugleichen ihre Grundlage in einem Vergleich von Empfindungen beziiglich eines eingebauten subjektiven Masstabes hat. Endlich kann man feststellen, dass eine zahlenm&sige Erfassung der Ergebnisse in Einheiten einer subjektiven Helligkeit am besten geeignet ist Effekte zu beschreiben, wie sie beim Simultankontrast auftreten.