CONTRAST ADDITIVITY: AN ALTERNATIVE APPROACH’ HOWARDLODGE Department of Psychology. Ursinus College. Collcgeville. PA 19426. U.S..-\. (Recriced 22 July 1974; accepted 15 October 197-l) Abstract--Several investigators have demonstrated luminance additivity when subjects are required to detect the presence of abrupt luminance discontinuities (“edges”) in chromatically mixed fields. Experiment I shows that this result occurs for stimuli other than edges. Low and high frequency and contrast sine wave gratings approximate additivity more than homogeneous fields. Experiment II shows that additivity of contrast detection is destroyed when the B-W system is fatigued by a black and white grating. This non-additive result is explained within an opponent process model assuming that contrast detectors pool information from chromatic and B-W systems. The model can also explain additive results during conditions in which the B-W system is not fatigued.
INTRODCCTION Several investigators (Boynton and Kaiser, 1968; Boynton, 1973; Myers, Ingling and Drum, 1973; Guth and Graham, 1975) have shown luminance additivity when a subject is required to detect the presence of abrupt luminance discontinuities (“edges” or an “edge”) in chromatically mixed fields. The typical procedure in these experiments is to present a monocular, foveally viewed monochromatic stimulus spatially modulating in luminance (for example, a square wave grating) and to have the subject adjust the space-average mean luminance until he detects the modulation of the grating. This is done for each of two different wavelength monochromatic gratings and then the two are superposed in phase and the mixture is adjusted to modulation detection threshold. If the mixture is composed of equal parts of the two monochromatic colors, then luminance additivity is demonstrated if the components of the threshold mixture are each one-half of their values determined when each component is separately presented. That is, luminance additivity is demonstrated if unity is the sum of the two ratios formed by dividing the component monochromatic luminances in the mixture by the luminances required for each wavelength when separately presented. Detection of the same field without “edges” present, a “homogeneous field”. results in non-additivity. Typically, the sum is greater than unity (Guth, Donley and Morrocco. 1969) meaning that more luminance is required to bring the mixture to detection threshold than linear addition of luminances (Abney’s Law) would predict. The finding of luminance additivity for edge detection. but not homogeneous field detection, has been interpreted
by Boynton
and Kaiser (1968) as suggest-
’ This research was conducted while the author was a post-doctoral fellow at the University of Pennsylvania. It was supported bt a National Institutes of Health Fellowship (FO 2 EY 11. 960) from the National Eye Institute and an N.S.F. Grant (GB 24100X) to Dr. Jacob Nachmias.
ing that edge detection results from differential stimulation of cortical “white units”. Since these units are presumed to have additive input from the three underlying cone mechanisms. additivity would result. Similarly, Guth and Graham (1975) suggest that edge detectors receive input only from an additive B-W system. When the subject is required to detect a homogeneous field. a differenr set of detectors is responsible. They receive the pooled output of the B-W and chromatic systems and because of the subtractive nature of the latter systems, non-additivity results. The purpose of the first experiment was to determine the generality of luminance additivity for stimuli other than edges. Edges contain more high spatial frequency information than homogeneous fields. If this frequency difference is crucial in determining whether addmvity occurs. then only high spatial frequency sine wave gratings should show additivity. As the frequency and possibly the contrast is reduced. non-additivity of the type found for homogeneous fields should result. ESPERISIE\-l’ 1 Subjects. The subjects who served in both Experiments I (HL and SU) and II (HL and JZ) had corrected acuity of 20~20 or better and no anomalies of color vision as tested by Dvorine Pseudoisochromatic color plates. To paralyze the accommodation r&x. two drops of Mydriacyl (1%) were administered to the right eye of each subject 15 min prior to Experiment I and-two- drops of Cyclosvl (1%) 15 min urior to Exoeriment II (see below for detailsj. AlI subjectswere screened by an ophthalmologist to insure no ill effects of the drugs. Apparatus. The apparatus used for Experiment I is shown in Fig. I. Light from a 500-W. tungsten bulb passed through a Wratten no. 70 filter (perceived as red) and by a different channel through a jlO-nm (perceived as green) interference filter, two Inconel linear transmittance wedges and was combined by a pelicle beam splitter (Pa). Combined light from both channels then either transilluminated a photographic negative (PN) or an unmodulated diluting field (DF). The height of the black region of the black
263
8 IW-
Red
W -
-,-
-
FS
-
5’s eye
PT
0 6
Fig. I. Schematic view of the apparatus used in Experiment I. S-adjustable slit. IW-Inconel neutral density L-movable lens, wedges, SH,,. B.nd rshutters. P 4 Jnd,--pellicle beam splitters, PT-phototube. Ddiffusers. PN-photographic negative. DF-diluting field, VS-vertical slit. FS-field stop. clear photographic negative varied as a function of distance. By means of a cylindrical lens system’ (see Thomas, 1967). this variation in height deterrnmed the one-dimensional luminance variation from left to right across a 1’ high by 2” wide field which was imaged at optical infinity at the eye. The width (3 mm) of the entire light beam at the cornea and the height (1 mm) was determined by the width of the vertical slit (VS) and height of a mask covering part of the photographic negative (PN), respectively. Different photographic negatives were used to generate different frequency sine or square wave gratings. an edge vertically bisecting the field or a homogenous field. For all stimuli except the homogenous field. two different contrast values of 10 and 66:); were generated by manipulating the proportion of light from the negative and diluting fields. The per cent contrast values were determined by scanning with a photo-multiplier an enlarged aerial image of each spatial frequency and color used. Procedure. Fifteen minutes prior to the 2-hr session, two drops of Mydriacyl(15’,) were administered to the subject’s right eye. The subject was aligned with a bite-bar apparatus so that with both color present. he observed no fringes at the edges of the field. This was not difficult to do although presumably due to slight longitudinal chromatic aberration, both the red and green edges were not simultaneously in focus when the accommodation reflex was paralyzed. This aberration would erroneously generate non-additivity in an unparalyzed eye, because it would not be possible to simultaneously focus both monochromatic gratings in mixture. Therefore. the accommodation reflex was paralyzed with either Mydriacyl or Cyclogyl throughout Experiments I and II. This insured that the accommodative state was constant for mixture trials as
’ I am indebted to Dr. Lawrence Arend for allowing me IO use his equipment for part of this apparatus.
.Aftsr niiynmwr. ths subjc‘ct dark .~dapted I;>: !I/ m!r; One tit’ four r>pcs of helds uas then chosen ;br :h::sho!d adjustments--a homogeneous field ( i. high b) 2 N ;&a;. dn edge (abrupt luminance transition bisecting the homogeneous field). ~1 square G\:I\~ or sine ~2~s grating. The jtrb!cct adjusted the mean luminance to threshold detection for the homogeneous field or threshold for modulation detection of the other stimuli. The means of the mtenslti readings of 12 trials IS~Y with red light onI> and six with green light onI>) were used to determine ths proportion of red to green to be used in the mixture trials. One of the three proportions was chosen--?: ;. I: I, or I:3 The subject adjusted rhe stimulus to threshold for IS trials -sis red. six green and six mixture trials. .A new proportion u’as then chosen and the procedure repeated. After all mixture proportions had been presented. the subject took :I IO-min break during which two more drops b+sr? administered to the right eye. If the stimulus was a homogeneous field. the entire procedure was then repeated. For other types of stimuli. the contrast not presented in the first part of the session \v;Ls presented in the second part. For each subjtc: 2 da>s of homogeneous field stimuli and 3 daqs for each of the other types of stimuli generated four estimates of each of the three proportions for homogeneous fields and three estimates of each proportion for the other stimuli at both IO and W,, contrast. Each of thssr: estimates consisted of two ratios-the average luminance for red in the mixture relative to the averape luminance for red when presented alone and a similar rastsm but the wntrst IS reduced 51 the factor 0414. This particular case for squai proportion red to green was ths one presented in the example above. Comparing the models predictions in Fig. 7 to the
;I5
m ._
0.1
02
IO
05
Relative red
luminance
Fig. 7. Additivity plot generated within the model shown in Fig. 6 for different proportions of red and green gratings in mixture. Each curve represents 3 different overall reduction of the chromatic image (.Y) and reduction in contrast (Y).
data for edge detection in Fig. 3 demonstrates that all values except (.Y = $0. Y= 025) are consistent with the additivity obtained for edge detection. Thus. ths two main results of Experiment II can be explained within a pooling model. ;Von-additivity results after black-white fatigue because the additive BW system is less responsible for contrast detection. Additlvlty occurs in the absence of fatigue either because the chromatic neural effect is uniformly depressed or its “ripple” is depressed or some combination of either of these factors. dckflo,~lrdgrmrnts-The author wishes to thank Drs. S. L. Guth. 1. Hurvich and D. Jameson for aiding in the formulation of some of the ideas developed. Also. the patient guidance of Dr. Jacob Nachmias who made this research possible. REFERESCES
trast of the chromatic system was reduced relative to the B-W system. The two ways of generating additivity within the pooling model (reduction of overall effect or just contrast in the chromatic system) were combined. In addition, mixture trials when the proportion was other than 1: 1 were included. The results of these calculations are shown in Fig. 7. This figure is a plot similar to Fig. 3. It shows a family of points for different overall reductions (X) and contrast reductions (Y) of the chromatic neural effect relative to that in the B-W system. Points along any particular curve were generated by assuming different proportions of one color to the other in mixture. In addition, the X and Y values for all curves were chosen so that additivity would result when equal proportions of the two colors were mixed. That is, all curves pass through the point (X = 05, Y= 05). Consider the curve defined by the open triangles (X = IQ Y= O-414).This means that the mean effect in the R-G chromatic system is assumed the same
Boynton R. M. (1973) Implications of the minimally distinct border. /. ODE.Sot. rim. 63. 103?-1043. Boy,nton R. M. and’Kaiser P. K. (1968) Vision: the additivlty law made to work for heterochromatic photometry with bipartite fields. Scirnc~ 161. 366365. Guth S. L.. Donley N. J. and Morrocco R. T. (1969) On luminance additivity and related topics. &ion Res. 9. 537-575. Guth S. L. and Graham B. y. (1975) Heterochromatic additivitv and the acuity response. lisiou Res. 15. 317319. Hurvich L. 51. and Jameson D. (1955) Some quantitative aspects of an opponent-colors theorv--II: Brightness, saturation and hue in normal and dichromatic vision. J. opt. Sot. Am. 45. 601-616. Myers K. J.. Ingling C. R. and Drum B. .A. (1973) Brightness additivity for a grating target. Vision Res. 13. I1651173. Thomas J. P. (1967) Equipment for varying the intensity of light. Am. J. Ps)-chbl.‘SO. 297-301. _ Van Nes F. L. and Bouman M. A. 1196;1 Soatial modulation transfer in the human eye. J.‘opt. Sof. Am. 57. 401406. Winer B. J. (1962) Staristicd Principles in Experimvnrnl Design. McGraw-Hill. New York.
INTRODCCTION Several investigators (Boynton and Kaiser, 1968; Boynton, 1973; Myers, Ingling and Drum, 1973; Guth and Graham, 1975) have shown luminance additivity when a subject is required to detect the presence of abrupt luminance discontinuities (“edges” or an “edge”) in chromatically mixed fields. The typical procedure in these experiments is to present a monocular, foveally viewed monochromatic stimulus spatially modulating in luminance (for example, a square wave grating) and to have the subject adjust the space-average mean luminance until he detects the modulation of the grating. This is done for each of two different wavelength monochromatic gratings and then the two are superposed in phase and the mixture is adjusted to modulation detection threshold. If the mixture is composed of equal parts of the two monochromatic colors, then luminance additivity is demonstrated if the components of the threshold mixture are each one-half of their values determined when each component is separately presented. That is, luminance additivity is demonstrated if unity is the sum of the two ratios formed by dividing the component monochromatic luminances in the mixture by the luminances required for each wavelength when separately presented. Detection of the same field without “edges” present, a “homogeneous field”. results in non-additivity. Typically, the sum is greater than unity (Guth, Donley and Morrocco. 1969) meaning that more luminance is required to bring the mixture to detection threshold than linear addition of luminances (Abney’s Law) would predict. The finding of luminance additivity for edge detection. but not homogeneous field detection, has been interpreted
by Boynton
and Kaiser (1968) as suggest-
’ This research was conducted while the author was a post-doctoral fellow at the University of Pennsylvania. It was supported bt a National Institutes of Health Fellowship (FO 2 EY 11. 960) from the National Eye Institute and an N.S.F. Grant (GB 24100X) to Dr. Jacob Nachmias.
ing that edge detection results from differential stimulation of cortical “white units”. Since these units are presumed to have additive input from the three underlying cone mechanisms. additivity would result. Similarly, Guth and Graham (1975) suggest that edge detectors receive input only from an additive B-W system. When the subject is required to detect a homogeneous field. a differenr set of detectors is responsible. They receive the pooled output of the B-W and chromatic systems and because of the subtractive nature of the latter systems, non-additivity results. The purpose of the first experiment was to determine the generality of luminance additivity for stimuli other than edges. Edges contain more high spatial frequency information than homogeneous fields. If this frequency difference is crucial in determining whether addmvity occurs. then only high spatial frequency sine wave gratings should show additivity. As the frequency and possibly the contrast is reduced. non-additivity of the type found for homogeneous fields should result. ESPERISIE\-l’ 1 Subjects. The subjects who served in both Experiments I (HL and SU) and II (HL and JZ) had corrected acuity of 20~20 or better and no anomalies of color vision as tested by Dvorine Pseudoisochromatic color plates. To paralyze the accommodation r&x. two drops of Mydriacyl (1%) were administered to the right eye of each subject 15 min prior to Experiment I and-two- drops of Cyclosvl (1%) 15 min urior to Exoeriment II (see below for detailsj. AlI subjectswere screened by an ophthalmologist to insure no ill effects of the drugs. Apparatus. The apparatus used for Experiment I is shown in Fig. I. Light from a 500-W. tungsten bulb passed through a Wratten no. 70 filter (perceived as red) and by a different channel through a jlO-nm (perceived as green) interference filter, two Inconel linear transmittance wedges and was combined by a pelicle beam splitter (Pa). Combined light from both channels then either transilluminated a photographic negative (PN) or an unmodulated diluting field (DF). The height of the black region of the black
263
8 IW-
Red
W -
-,-
-
FS
-
5’s eye
PT
0 6
Fig. I. Schematic view of the apparatus used in Experiment I. S-adjustable slit. IW-Inconel neutral density L-movable lens, wedges, SH,,. B.nd rshutters. P 4 Jnd,--pellicle beam splitters, PT-phototube. Ddiffusers. PN-photographic negative. DF-diluting field, VS-vertical slit. FS-field stop. clear photographic negative varied as a function of distance. By means of a cylindrical lens system’ (see Thomas, 1967). this variation in height deterrnmed the one-dimensional luminance variation from left to right across a 1’ high by 2” wide field which was imaged at optical infinity at the eye. The width (3 mm) of the entire light beam at the cornea and the height (1 mm) was determined by the width of the vertical slit (VS) and height of a mask covering part of the photographic negative (PN), respectively. Different photographic negatives were used to generate different frequency sine or square wave gratings. an edge vertically bisecting the field or a homogenous field. For all stimuli except the homogenous field. two different contrast values of 10 and 66:); were generated by manipulating the proportion of light from the negative and diluting fields. The per cent contrast values were determined by scanning with a photo-multiplier an enlarged aerial image of each spatial frequency and color used. Procedure. Fifteen minutes prior to the 2-hr session, two drops of Mydriacyl(15’,) were administered to the subject’s right eye. The subject was aligned with a bite-bar apparatus so that with both color present. he observed no fringes at the edges of the field. This was not difficult to do although presumably due to slight longitudinal chromatic aberration, both the red and green edges were not simultaneously in focus when the accommodation reflex was paralyzed. This aberration would erroneously generate non-additivity in an unparalyzed eye, because it would not be possible to simultaneously focus both monochromatic gratings in mixture. Therefore. the accommodation reflex was paralyzed with either Mydriacyl or Cyclogyl throughout Experiments I and II. This insured that the accommodative state was constant for mixture trials as
’ I am indebted to Dr. Lawrence Arend for allowing me IO use his equipment for part of this apparatus.
.Aftsr niiynmwr. ths subjc‘ct dark .~dapted I;>: !I/ m!r; One tit’ four r>pcs of helds uas then chosen ;br :h::sho!d adjustments--a homogeneous field ( i. high b) 2 N ;&a;. dn edge (abrupt luminance transition bisecting the homogeneous field). ~1 square G\:I\~ or sine ~2~s grating. The jtrb!cct adjusted the mean luminance to threshold detection for the homogeneous field or threshold for modulation detection of the other stimuli. The means of the mtenslti readings of 12 trials IS~Y with red light onI> and six with green light onI>) were used to determine ths proportion of red to green to be used in the mixture trials. One of the three proportions was chosen--?: ;. I: I, or I:3 The subject adjusted rhe stimulus to threshold for IS trials -sis red. six green and six mixture trials. .A new proportion u’as then chosen and the procedure repeated. After all mixture proportions had been presented. the subject took :I IO-min break during which two more drops b+sr? administered to the right eye. If the stimulus was a homogeneous field. the entire procedure was then repeated. For other types of stimuli. the contrast not presented in the first part of the session \v;Ls presented in the second part. For each subjtc: 2 da>s of homogeneous field stimuli and 3 daqs for each of the other types of stimuli generated four estimates of each of the three proportions for homogeneous fields and three estimates of each proportion for the other stimuli at both IO and W,, contrast. Each of thssr: estimates consisted of two ratios-the average luminance for red in the mixture relative to the averape luminance for red when presented alone and a similar rastsm but the wntrst IS reduced 51 the factor 0414. This particular case for squai proportion red to green was ths one presented in the example above. Comparing the models predictions in Fig. 7 to the
;I5
m ._
0.1
02
IO
05
Relative red
luminance
Fig. 7. Additivity plot generated within the model shown in Fig. 6 for different proportions of red and green gratings in mixture. Each curve represents 3 different overall reduction of the chromatic image (.Y) and reduction in contrast (Y).
data for edge detection in Fig. 3 demonstrates that all values except (.Y = $0. Y= 025) are consistent with the additivity obtained for edge detection. Thus. ths two main results of Experiment II can be explained within a pooling model. ;Von-additivity results after black-white fatigue because the additive BW system is less responsible for contrast detection. Additlvlty occurs in the absence of fatigue either because the chromatic neural effect is uniformly depressed or its “ripple” is depressed or some combination of either of these factors. dckflo,~lrdgrmrnts-The author wishes to thank Drs. S. L. Guth. 1. Hurvich and D. Jameson for aiding in the formulation of some of the ideas developed. Also. the patient guidance of Dr. Jacob Nachmias who made this research possible. REFERESCES
trast of the chromatic system was reduced relative to the B-W system. The two ways of generating additivity within the pooling model (reduction of overall effect or just contrast in the chromatic system) were combined. In addition, mixture trials when the proportion was other than 1: 1 were included. The results of these calculations are shown in Fig. 7. This figure is a plot similar to Fig. 3. It shows a family of points for different overall reductions (X) and contrast reductions (Y) of the chromatic neural effect relative to that in the B-W system. Points along any particular curve were generated by assuming different proportions of one color to the other in mixture. In addition, the X and Y values for all curves were chosen so that additivity would result when equal proportions of the two colors were mixed. That is, all curves pass through the point (X = 05, Y= 05). Consider the curve defined by the open triangles (X = IQ Y= O-414).This means that the mean effect in the R-G chromatic system is assumed the same
Boynton R. M. (1973) Implications of the minimally distinct border. /. ODE.Sot. rim. 63. 103?-1043. Boy,nton R. M. and’Kaiser P. K. (1968) Vision: the additivlty law made to work for heterochromatic photometry with bipartite fields. Scirnc~ 161. 366365. Guth S. L.. Donley N. J. and Morrocco R. T. (1969) On luminance additivity and related topics. &ion Res. 9. 537-575. Guth S. L. and Graham B. y. (1975) Heterochromatic additivitv and the acuity response. lisiou Res. 15. 317319. Hurvich L. 51. and Jameson D. (1955) Some quantitative aspects of an opponent-colors theorv--II: Brightness, saturation and hue in normal and dichromatic vision. J. opt. Sot. Am. 45. 601-616. Myers K. J.. Ingling C. R. and Drum B. .A. (1973) Brightness additivity for a grating target. Vision Res. 13. I1651173. Thomas J. P. (1967) Equipment for varying the intensity of light. Am. J. Ps)-chbl.‘SO. 297-301. _ Van Nes F. L. and Bouman M. A. 1196;1 Soatial modulation transfer in the human eye. J.‘opt. Sof. Am. 57. 401406. Winer B. J. (1962) Staristicd Principles in Experimvnrnl Design. McGraw-Hill. New York.
