Chromatic border perception: The role of red- and green-sensitive cones

Research.Vol.i8. pp. 683-697 * Persam**PressL.td1978.Printed in

Vsion

Great BIilaln

CHROMATIC OF RED-

BORDER PERCEPTION: AND GREEN-SENSITIVE

THE ROLE CONES

BRIAN W. TANSLEY’ and R. M. BOYNTON Department

of Psychology, University of California, San Diego, La Jolla, CA 92093, U.S.A. (Received 29 April 1977; in

revisedform 9 September 1977)

Attract-Where

the perception of borders is concerned, the normal visual system is found to be tritanopic. The strength of a border depends on the relative activity of only R and G cones, no matter what the B cones are doing. Since normal color vision depends on the activity of all three cone types, chromatic border strength alone cannot be used as an index of color differences. Borders produced by spatial luminance steps or chromatic steps appear similar, except that Mach-type lateral inhibitory mechanisms, which enhance the visibility of low-contrast luminance borders, are unnecessary to predict chromatic border strength. Two functions are presented, using only the responses of R and G cones, which provide a way of expressing chromatic border strength in terms of either a subjective rating scale or a luminance step that appears to be equivalent in its distinctness.

INTRODUCIION have studied the relation between color differences and contour perception. Liebmann (KofTka, 1935), and Kof&a and Harrower (1931) studied the relationships among different chromatic stimuli in producing figure-ground “organization.” These authors observed that certain color pairs failed to support border perception at their junction: “A colored figure, . . say a blue one, on a neutral background, simplifies its shape, if it be intricate, when its luminosity approaches that of the ground on which it lies. When the two luminosities are equal the shape is completely lost; a vague and vacillating blotch is seen, and even that may disappear completely for short periods of time. Therefore differences of stimu~tion between an enclosing and an enctosed area, if it is a mere color difference, has, to say the least, much less power to produce a segregation of these two areas in luminosity. Thus, two greys which look very similar will give a perfectly stable organization if one is used for the figure and the other for the ground, whereas a deeply saturated blue and a grey of the same luminosity which look very different indeed will produce practically no such organization. This proves that difference of stimulation is not in itself equivalent to segregation of the area; the latter, far from being a mere geometrical projection of a retinal distribution, is a dynamic effect which occurs with some stimulus differences more than with others and may fail to appear at all with very large stimulus differences when these are not of the kind to produce forces necessary for organization.” (KoEka, 1935).

Many investigators

‘This paper is based in part on a doctoral dissertation submitted by the senior author as partial fuffillment of the requirements for the Ph.D. at the University of Rochester (N-Y.). The experimental work was carried out at the Universitv of California. San Diego. Reprint requests should bdsent to B. W. T&ley, who% now -at the Department of Psychology, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4Jl.

Although modern visual science may take a different theoretical approach, these observations of KotJka still have not been explained. In more contem~ra~ terms, the problem might be stated as follows: What is the nature of visual mechanisms that permit the perception of chromatic borders, in particular those which are seen in the absence of luminance differences? Since Koffka’s report, there have been relatively few studies that have been concerned with the nature of chromatic borders. MacAdam (1949) investigated the effects of “color contrast” on visual acuity. Using a set of colored papers that had been chosen to be of approximately the same Munsell Value, he asked observers to discriminate the location of the gap in a Landolt ‘%,, when the “c” was of one color and the background was of another. The results of this study were expressed in terms of an equivalent luminance contrast, for “C’s” and backgrounds of the same chromaticity, which yielded the same acuity measure as did a particular chromatic figure-ground combination. When plotted in chromaticity space, MacAdam’s data appear to be somewhat exaggerated versions of the color discrimination ellipses presented in his earlier reports of chromaticity discrimination (MacAdam, 1942; Brown and MacAdam, 1949). In particular, discrimination was found to be poorest in directions roughly corresponding to tritanopic confusion lines, where the visibility of the “c” would depend mainly upon di~erential stimulation, by ‘%,, and background, of the blue-sensitive (B) cones of the retina, without much change in the level of stimulation of the red- (R) and green- (G) sensitive cones. One of the difficulties in studying responses of the chromatic mechanisms psychophysically is making sure that the achromatic or spectrally non-opponent system is not contributing to the observer’s behavioral responses. Because heterochromatic stimuli are used, the problem of equating lights for luminance becomes important. In the past several years, the minimally distinct border (MDB) method has proved useful for equating 683

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W. TANSLEY

lights for the achromatic or non-opponent response that they apparently elicit (Boynton and Kaiser, 1968; Kaiser, 1971; Wagner and Boynton, 1972). With this method, the observer adjusts the radiance of one of the hemifields in a bipartite field (whose straight edges have been carefully aligned to yield a border that is invisible for two fields of equal radiance and color) until the border formed between them is minimally distinct. Any border visible at the MDB setting must be due to some aspect of chromatic (opponent system) processing only. This makes the MDB technique especially useful in psychophysicat studies of how the chromatic opponent system contributes to border perception. Several reports have attempted to relate this differential border-forming property to various aspects of the stimuli that elicited them, Boynton and Wagner (1972) and Ward and Boynton (1974) postulated that the border distinctness at MDB might be related to the perceived color difference between two lights presented in this way. If true, a measure of border distinctness at MDB could be a useful tool for scaling color differences psychophysically. Kaiser, Herzberg and Boynton (1971) presented evidence suggesting that the border distinctness at MDB might reflect differences in the saturation of the two fights in the photometric field. They noted that if a standard white iight of fixed retinal illuminance was presented in one hemifield and a series of spectral lights was presented in the other, the border distinctness produced between a given spectral light and white at the MDB point increased as the wavelength of the spectral light either increased or decreased relative to 570 nm, the wavelength of minimal saturation as established in many studies. Kaiser et ai. (1971) offered a model to account for the border distinctness produced by chromatic differences at the MDB setting. They postulated that there are “interlaced mosaics of chromatically significant elements (somewhere in the brain) to which the neurons of the retina project (p, 959)“. These elements were assumed to be of five types: R, Y, G, B and W. At the MDB setting it was assumed that the same number of achromatic W elements were active in response to either side of the photometric field. Therefore, border distinctness at the MDB setting was considered to be due to the differential activity of the chromatic brain elements, R, Y, G and B. In this scheme, brightness was considered to be related to a combination of the activity of achromatic (W) and chromatic (RYGB) elements, and thus for any two fields at the MDB point. the field eliciting more active chromatic elements would appear brighter than another field having the same number of active W elements. This treatment of brightness differences was intended to account for the observation that equi-luminous lights of different color are often not equally bright. For example, this difference in brightness is very noticeable when comparing a highly saturated spectral light of 640 nm with a relatively desaturated yellow of 57Om-n. In general, more saturated fields appear brighter than less saturated fields when compared at MDB. These are two aspects of this model that are proven wrong by the research described in this paper. First, the distinctness of borders will be shown to have a retinal. rather than a central basis. Second, rather

and

R. M. B~I’NTo~’

than being multiparameter (as imphed by the postulated activity of five kinds of elements), chromatic borders are one-dimensional and depend at constant luminance only upon the relative outputs of R (or G) cones stimulated by light from opposite sides of the border. The research to be presented here strongiy suggests that the R and G cones function both in the production of contour and color, insofar as their contribution to the red-green opponent-color pathways is concerned. Some of the work to be reported here has been described in a preliminary report (Tansley and Boynton, 1976). The present paper will permit the reporting of more detail than the short report allowed, both with respect to the experiments themselves and the bearing that they have in the context provided by related data already in the literature. For complete details, particularly of instrumentation and calibration, see the doctoral dissertation of Tansley (1976). EXPERIMENT

I

Boynton and Wagner (1972) and Ward and Boynton (1974) studied the relationship between color differences and border distinctness at the MDB setting with the use of an “analysis of proximities” which was first developed by Shepard (1962). As applied to their experiments, the analysis began with distinctness data for all possible pairwise comparisons among the set of n color stimuli used in a particular study. These n(n - I) values were used as input for a multidimensional-scaling algorithm designed to fmd a representation of the color stimuli as points in a space of minimal dimensionality in which the ex~rimentaIly obtained distinctness measures are monotonically related (ideally, proportional) to the distances between the points in space. In the resulting configuration, stimuli which produced very distinct borders with one another would be far apart, whereas stimuli which produced very indistinct borders with one another would be quite close together. Stimuli which produced no visible border when compared at MDB (such as a stimulus paired with one exactly like itself, for example) should plot in the same place. It was hypothesized that if border distinctness was a valid index of color differences, then a uniform color space--one capable of representing the color differences uniformly throu~out the entire gamut of achievable color-might result from such an analysis. The analysis of sets of spectral stimuli carried out in this way by Boynton and his collaborators generated a U-shaped array of points in two dimensions, quite reminiscent of psychological color diagram. It was therefore expected that the use of nonspectral colors would fill the previously empty interior of the diagram which had resulted from using spectral colors. The major surprise of the experiment to be reported was that this did not happen. Method apparatus. The basic apparatus used in this series of experhnents is a modified calorimeter originally designed and built by Wetherall (1961).It consists of a two-channel optical system capable of presenting light in a bipartite photometric-field configuration to a human observer (Fig. 1).

Chromatic border perception

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to scale A4

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Fig. 1. (Top) Side view showing part of the calorimeter. Beam-splitter (ES) should be visuahzed as being divided by the plane of the page. The part above the page has a transparent interface along the diagonal; the part below the page is aluminized. The subject at the right sees light from the bottom of ~n~ating sphere It in the left half of a circuhu field by means of light t~nsmitt~ throu~ BS. He sees the right side of the field filled by light reflected from the diagonal of BS coming from Ia. (Bottom) This part of the figure shows how the integrating spheres are illuminated.

BRIAN

686

W.

TANSLEY

and R. M.

Bouivroh

“Hot” mirrors (HM) were installed to reflect infrared energy back into the lamphouse to be exhausted by forcedair Row. Each Osram source was positioned with its fiiament in a plane pcr~ndicular to the optic axis, and with bulb horizontal rather than vertical. Although specifications supplied by the manufacturer permitted this position, we found that tungsten from the filament evaporated and coated the fused-quartz envelope rather seriously in this position, and required constant monitoring of the luminous intensity of these sources. To prevent interruptions of the experiment, three sets of these sources were aged to 15”, of their rated life and set aside to be used later as replacements. Photometric and calorimetric calibrations of these three sets showed them to be essentially identical to the original set in both luminous output and \ \ \ I I color temperature as a function of voltage. All three sets 0.1 0.2 0.3 were used in the experiments to be reported here. The x luminances of the sources as calculated in the apparatus Fig. 2. The chromaticity coordinates of the 36 nonspectral were also rechecked at time of replacement. stimuli used in experiment 1. The diagram in this figure To provide the desired range of chromatic stimuli. filter is the 1960 Uniform Chromaticity Space, with the transholders (FH,, FHJ were used which could be moved in formed 1931 CIE (x, J’)coordinates as axes. The three large the collimated portion of each beam in a plane perpendicuclosed triangles represent the chromaticity coordinates of lar to the optic axis. These holders were designed to accept the three Wratten filter primaries used to generate the rest aluminum and glass slides in frames that fitted precisely of the stimuli. and reproducibly. The positions of the slides in the filter holders (and also those of the linear neutral density wedges W, and W,) were indicated by digital readout. plane perpendicular to the optical axis, the areas of the The interior of each integrating sphere was coated with two bottom filters varied while that of the one at the top a barium sulphate and carboxymethyl cellulose “paint” mix- remained constant (see Fig. 3). A set of slides for each ture described by Middleton and Sanders (19.53). Light channel was constructed with each slide in the set having from the two integrating spheres emerged through exit a different filter area for the No. 74 filter, relative to the apertures and was passed to the observer’s eye via a first- ’ other two. surface mirror (Ml) and a beam-splitter cube (BS) that In theory, it would be possible to calculate the chromatihad an evaporated-metal coating on one-half of the hypocity change as a function of slide position with respect tenuse of one of its two prisms. Apertures were placed to the aperture (A,) if the following assumptions could in the system at A, and A., to limit the visual angle of be met: (I) constant top-filter area as a function of horizonthe photometric field to 1 35’. Finally. a shutter (SH). tal-filter-holder position; (2) homogenous light-flux density consisting of a rotary solenoid with an attached aluminium at every point in the rectangular aperture; and (3) specvane, was placed between the apertures and the subject. trally “flat” optics. Because none of these assumptions An achromatizing lens (AL) of the design given by Wysecould be met exactly, direct calibration of the stimuli was zecki and Stiles (1967. p. 212) was cemented in a blackened carried out. aluminum casing and mounted on a mirco-positioner adThe relative spectral-energy distributions for 45 stimuli justable in vertical and horizontal directions normal to the were calculated by taking the means of five radiometric optic axis of the apparatus. The observer’s head was held measurements (taken every IOnm from 380 to 7CQnm). in place with the use of a dental-impression bite bar on The CIE 1931 and UCS 1960 chromaticity coordinates a moveable mount. (Wyszecki and Stiles, 1967) were subsequently calculated. A series of tripartite filters was fabricated using various From these, a smaller set of 36 stimuli was chosen on proportions of three Kodak Wratten filters: 478 (blue). the basis of its distribution as visuahzed in the chromati70 (red) and 74 (green). Any chromaticity falling within city space of the 1960 UCS diagram. The 1931 (CIE x, p) the triangle defined by these three filters (see Fig. 2) could chromaticity coordinates for the selected subset of stimuli are listed by Tansley and Boynton (1976); their positions be produced in either hemifield by placing the appropriate proportions of each of the three filters in the aperture of in 1960 UCS chromaticity space are shown in Fig. 2. The neutral density wedges in each of the two channels Path A of each channel. Each slide contained a section used in this experiment were calibrated with the use of of the three filters: as the filter holder was moved in the Filter

holder

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---a

Filter

holder is vorioble with position relative to operture

Stimulus sltde (Fits in filter holder)

Fig. 3. A schematic of the filter holder into which various stimulus slides can be placed. Each slide has a set of filters in it that can be moved laterally across a square aperture with the use of a motorized drive assembly. For every position of this filter holder there is a unique ratio of filter areas that fall within the aperture. This ratio determines the chromaticity of the light that is mixed in the integrating sphere of a given channel. which subsequently is presented to the observer.

687

Chromatic border perception a Spectra spot meter aimed at the hemifield under consideration, from the position of the observer’s eye. The aperture used for sighting in the apparatus and for

distances in the solution, in addition to providing an indication of the direction of error.

measurement fell completely within the hemifield being measured.

Results

Procedure. Each of two normal trichromatic observers were presented with all possible pairs of the chromaticities, shown in Fig. 2. Including the left-right presentations of otherwise identical pairs, this amounted to 1296 conditions. The observer’s task in each trial was first to minimize the distinctness of the border formed by the two hemifields and then to rate the distinctness of this border on the &point subjective scale. Before the main experiment, each observer was shown a chromatic min~maiIy distinct border whose equivalent luminance contrast was 25-30%, as determined by previous studies (e.g. Ward and Boynton, 1974). This border was defined as having a distinctness rating of 7. At the other end of the scale, an equiluminous and isomeric pair of lights produced no visible border; this provided the distinctness rating of 0. Each of the 36 stimuli used in the left field were equated with respect to luminance to a standard white light of 25 td by the MDB method. During each trial, the observer could adjust the position of the achromatizing lens immediately before his eye in order to align precisely the two hemifields. The radiance of the variable right hemifield was adjusted to yield a minimally distinct border. The observer then occluded the fieids by pressing a button that activated a shutter (duty cycle: 1 set on, 1 see off). This was done to prevent fading of the border which would otherwise occur with steady fixation while the rating was being made (Buck, Frome and Boynton, 1977). As a check on the calibration of the chromaticities of the stimuli during the experiment, each stimulus was paired once with one of the same chromaticity; these were presented at random intervals. During these trails, the rating of border distinctness would be 0 if the lights were very nearly identical with respect to their spectral emittances, and of course no color difference or border would be visible. Because of the very large number of pairwise comparisons made by each observer, it was not practicable to rephcate the experiment. The analysis was therefore done on the averaged data for both observers, collapsed over the left-right positions. This provided a half-matrix of distinctness ratings based on the mean of four observations per cell. This matrix was subjected to the muttidimensional-scaling algorithms MDSCAL (version 5M) and KYST (an acronym for Kruskal, Young, Shepard and Torgerson). Both analyses were performed using the nonmetric options that assume the data to be ordinal in nature. For the analysis of the data in this experiment, we shall restrict our considerations to the output configurations of 3, 2 and 1 dimensions only. Along with each n-dimensional solution is provided a measure of the degree to which the interpoint distances of a given solution correspond to the border-distinctness ratings. This measure is called “stress” and is calculated by considering the variance of regression of the output distance upon the distin~ness ratings used as input to the algorithm. The stress value is inversely related to the variance accounted for by the solution. The plot of the scaled distance against the input data (border distinctness) is called a “Shepard diagram.” Reference to this diagram allows one to gain an impression of the extent to which the scaled distances correspond to the border-distinctness data. A linear reiationship between distances in the diagram and the input data, for example, would mean that the distances in the solution diagram are highly correlated with the border-distinctness ratings. Deviations from linearity provide insight into the range of distinctness ratings that do not correspond well to the

From the output configurations of both MDSCAL (SM) and KYST multidimensional scaling routines, all stimuli appear to plot on a line and not in a 2-dimensional space, as would be predicted from the assumption that border distinctness is based on trichromatic color differences. Whether in one, two or three dimensions, the output ~onfi~ration always defines a line. Although this line may be curved, as in the helical conjuration of the thr~-dimensional solution at the top of Fig. 4 (or the C-shape of the two-dimensional solution shown just below it), such a result implies that the

underlying structure is essentially one-dimensional (Shepard. 1974 and personal communication). By referring to the Shepard diagrams, one can see that the addition of more dimensions improves the linearity between the distances between the configuration points and the distinctness data. Thus, although a one-dimensional underlying structure may be able to account for the solution, a three-dimensional configuration provides a more accurate representation of the stimuli in the sense that the distances between points along the helix correspond more accurately to the border distinctness ratings than to distances along the straight line at the bottom of the figure. Shepard (1974) has noted that certain monotonic transformations of data may sometimes allow for more optimal solutions in fewer dimensions. This seems to be the case in these configurations; further discussion of the one-dimensional nature of the solution awaits experiment 3. The most significant outcome of this analysis is that, irrespective of the dimensionality of the solution, there are sets of stimuli in chromaticity space that apparently produce little or no border distinctness with one another. Figure 5 shows the chromaticities of stimuli that all plot close together in the multidimensional solutions (produce little or no border distinctness with one another at MDB). In this series of 1931 (CIE x, y) chromaticity diagrams are plotted sets of stimuli that were close together in the multidimensional scaling solutions. To a first approximation, the stimuli of a given small region in the output configuration all plot along a tritanopic confusion line in chromaticity space. This means that such stimuli stimulate the R cones and the G cones in the same proportion in both hemifields, thus being indistinguishable to the tritanope, who lacks functionaf B cones, The result implies that the B cones make little or no contribution to the perception of borders at the MDB point

EXPERIMENT 2

To test this conclusion more carefully and directly, an experiment was designed that makes use of “artificial dichromacy” as a means of isolating R and G cones from B cones in trichromatic observers (Brindley, 1953).

BREAN

W. TANSLEYand R. M.

BOYNTON

Mean

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Fig. 4. Shown here are the output configurations from the multidimensional scaling analysis of the data from experiment 1 (KYST program). A~ompanying each configuration is a modified “Shepard diagram” for each solution in a given dimension. Output distances are divided into class intervals of approximately 5 unit and are scaled so that a value of 7 corresponds approximately to the largest interpoint distance. Each bar represents the total range of distinctness ratings corresponding to that interval of interpoint distance. The degree to which this diagram is linear, and the shortness of the bars, indicates the degree to which the solution provides an accurate representation of the distinctness ratings between the stimuli positioned here as points in n-dimensional Euclidean space. (a) 3-dimensional solution with Ds as sphere size. (b) 2-dimensional solution. (c) l-dimensional solution. Aithough more than one dimension is needed to provide an accurate representation, it is apparent that. neglecting random error. the configuration always remains a single line. method

Apparatus. For this experiment, and the following one. a modification to the colorimetet was made which permitted monochromatic light (15 nm i/2 bandwidth) to be delivered to each hemifield. Outside the calorimeter the optical benches each contained a 400 W Sylvania tungstenhalogen source, a heat-absorbing filter and lens that imaged the source filament on a Schott-Veril variable interference filter. The monochromatic light that emerged from these filters was collected by two fiber-optic light guides (Edmund Scientific) which were inserted into apertures of the two integrating chambers, It and I2 of Fig. 1. The intensity in these two channels was varied by changing the voltages applied to the two sources. Although vari-

ations of voltage produce variations of the color temperatures of the sources as well as their luminous emittances, these changes were negligible with the narrow-band filters used. This system was calibrated for wavelength by using a Cd-Hg low-pressure source with known spectral lines, placed at the same optical distance from the variable interference filter as the original source. By use of a supplemental lens, light from the spectral source was imaged on the same aperture in front of the variable interference wedge as the tight from the original source. Blocking filters were placed in the path between the spectral source and the variabie interference filter to screen out unwanted stray light.

Chromatic border perception

a 7

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Fig, 5. The chromati~ty coordinates in 1931 CIE (x, y) space of sets of chromatic stimuli in experiment 1 that produced very indistinct borders with one another. Each of the overlapping panels represents a plot of the chromaticities on one set of stimuli that would all be found clustered in a fairly small region of the multi~mensional scaling solutions (a and b). Although the color up~e~runces of stimuli in a given panel are very different, there will be little or no visible border formed between them when the two stimuli are adjusted to MDB. Furthermore, all of the stimuli in each panel have roughly equivalent border-forming properties with respect to the stimuli from any other panel. In addition to this equipment, a bieaching light was produced by use of a high-wattage projector and interference filter, mounted on a separate table. The retinal illuminance of the 436 nm light generated by this apparatus was calcufated to be 10s td by the method outlined by Westheimer (1966). Procedure. This experiment was done under two stages of adaptation : normal trichromacy and “artificial tritanopia.” The latter state was established by gazing at the 10’ td, 436nm adaptation field for an initial period of about 3 min and by viewing that field repeatedly throughout the experimental session, except when settings were being made on the calorimeter. In one hemifield of the calorimeter, the subject was presented with a mon~~omatic light of fixed retinal iliuminance (30 td). In the other hemifield, the observer had control of the ratio of the mixture of two lights produced by two Kodak Wratten filters. He also had control over the total luminance of the hemifiekl Six spectral standards and three pairs of mixture lights were used, The chromaticities of these stimuli are shown as the filled circles in Fig. 6. The observer’s task was to find the particular ratio of a given mixture which produced a border with the spectral light whose distinctness was judged as close to 0 as possibfe. This determination involved an iterative procedure: varying the chromaticity, then varying the luminance to the MDB point and judging the. distinctness of the border formed between the standard and the variable hemifield. For each spectral light and for each of the three mixture

points are virtually superjmposed; there is no way to show any distinction between them. For all of the conditions of the experiment, combined, the correlation between instrument settings (related to the ratio of ~mponents of the two primaries of the matches) for the trichromatic vs artificial tritanopia conditions

0.6

pairs, five dete~inations were made by each of the authors, under both states of adaptation. Results

Figure 6 shows the calculated chromati~ities of the mixtures which produced very indistinct borders (usually zero) with a given spectral standard, for the condition of normal trichromaey. As can be seen from the calibrated positions of the chromati~ties, the mixture that produced the least distinct border with a given spectral light was invariably positioned on a tritanopic confusion line containing that spectral light, thus sharing the property of stimulating the R and G cones to the same extent, from the two sides of the bipartite field. For the condition of artificial tritanopia, the results are so similar to those shown in Fig. 6 that the data

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Fig. 6. The open circles (BWT) and open triangles (RMB) represent the chromaticities chosen in experiment 2 which, when compared with one of the spectra lights and adjusted to MDB, gave border distinctnesses that were very near 0 on the subjective rating scale. The solid lines radiating from the tritanopic copunctal point define chromaticities that have identical R to G cone ratios. When the experiment was repeated under a condition of artificial tritanopia, all data points were essentially the same as those shown here. Filled circles represent the chromaticities of the filtered light of the two components which, when mixed, could produce chromaticities along the line connecting them.

BRIAN W. TANSLEY and

690

was 0.995. the same for each subject. We believe therefore that the failure of the data points of Fig. 6 to fall exactly in tritanopic confusion in all cases is mainly due to calibration errors EXPERIMENT

3

R. M. BOVNION

data; the KSYT algorithm was used exclusively. Further analyses were carried out on the scaled configurations from KYST.

RtTult.5 Mulridimensionul-scalitly

atta/ysis.

Figure

7(a. b. c)

the KYST solutions in three, two and one dimension for the averages of all of the observers. The basic features to be noted arc the relatively more “linear” nature of the configurations, and the shorter bar lengths, compared to experiment I (Fig. 4). Just as in experiment 1, all stimuli plot along a singte line, regardless of the dimensionahty of the sotution, again suggesting that the most appropriate solution is onedimensional. The shortening of the bars as dimensionality is increased shows an improvement of the fidelity of the configuration with respect to the input distinctness data. As the number of dimensions in the solution increases, the extreme values of distinctness are, especially, more accurately represented. With a three-dimensional solution, the accuracy of representation is quite high; there is very little scatter of the actual distances about the estimates values. These solutions and the data on which they were based were subjected to further analyses in order to (i) try to quantitatively estimate the dimensionality of the most appropriate solution, and (ii) to justify the use of metric multidimensional scaling procedures. In order to account for the border-distinctness rating data with a function using the responses of R and G cones, it was necessary to determine whether the rating scale the observers used in experiment 3 was interval in nature. Our analyses indicated that the chromatic border distinctness ratings of the three observers in experiment 3 were on an interval scale. The details of the analyses reported above are included in the Appendix. shows

The question now arises: What is the nature of the configuration that was found by Boynton and Wagner (1972) and Ward and Boynton (1974) in their multidimensional scaling studies? From the results of the experiments just described, it seems that their configurations are essentially one-dimensional solutions which have little relationship to two-dimensional chromaticity diagrams. In an attempt to gain a more precise, and possibly quantitative, measure of chromatic border distinctness, a third experiment was carried out. Because it was by then clear that nonspectral lights have no special advantage, this study employed a set of spectral lights chosen to represent an approximately even distribution of R to G cone response ratios. Method Appararus. The calorimeter was again used in this study. with the modifications for providing monochromatic light to the integrating spheres that were noted in experiment 2. Sixteen spectral lights from the monochromatic channels were employed in addition to two narrow-band Kodak Wratten Filters (47B and 70) presented through paths “A” for a total of 18 spectral lights. (The Wratten Filters can be considered spectral equivalents, because they plot very near the spectrum locus in the chromaticity diagram.) Procedure. Before the main experiment began, each of three normal trichromatic observers was presented with a standard 30 td white light in the right hemifield. In turn, each of the 18 spectral lights was presented to the left hemifield and the observer adjusted the radiance and position of this hemineld (by adjustments of the achromatizing lens) until the MDB setting was found. This procedure was carried out six times for each light, and the mean value of these six settings was used in the main experiment to set the luminance at which each light would be presented when used as a standard. In the main part of the experiment, all possible pairwise combinations were presented to the observers in random order (324 pairwise comparisons). First, the experimenter preset one of the 18 spectral lights. at the previously determined average luminance. in one hemifield. This light was then a fixed standard with which another light was compared. The wavelength of the comparison light was also preset by the experimenter. but the observer could adjust its radiance until the MDB point was found for the pair. When the observer reached this point, he then interrupted the presentation of the bipartite field with a shutter, so as to minimize the fading of the border while rating its distinctness. The observer rated the distinctness on the usual g-point scale. The entire experiment was repeated 15 times; observer BT contributed six replications; observer TS contributed five and observer RMB contributed four. The averaged data of this experiment may be found in Tansley (1976). In order to keep the observers as free from bias as possible. none of them acted as experimenter in this study. The analysis of the data was done both for the average of the settings by each individual and for the average of all data collected (15 settings per condition). In addition, the left-right differences were collapsed to provide twice the number of settings per average in order to provide as accurate an estimate of distinctness as possible for each pair. Multidimensional analysis was carried out on these

EXPERIMENT

4

In the early studies of the MDB (Boynton and Kaiser, 1968; Kaiser et al., 1971). border distinctness was gauged by using an achromatic border, formed by a luminance difference in a nearby field, as an index of distinctness of each chromatic border at MDB. By this method an equivalent luminance contrast could be assigned to the perceived distinctness at MDB. It was reported that the chromatic and achromatic borders appeared similar when set to equal distinctness, An advantage of that method over the rating method used here is that it provides a physical measure-luminan~ contrast-- -which is more easily relatable to physiological models of border perception than are the ratings. Even though the ratings are quite repeatable, it is difficult to know what significance to attach, in any physiological sense, to a rating, say of 5. To provide a bridge to the luminance-contrast measure, to which the data of the first three experiments of this report can be related. the following experiment was carried out. Method

A~naratus. With the use of the modified cotorimeter described previously, each of the three observers who participated in experiment 3 was presented with a l”40 bipartite photometric field to the right eye. The spectral energy dis-

Chromatic border perception

691

Mean distinctness rating (bl

shown for experiment 1 (Fig. 4), carried out here for experiment 3. The input matrix to the scaling algorithm was the grand mean of the three observers (BT, RB and TS) employed in experiment 3. Each cell in the matrix was the average of 30 data points, with left-right differences being collapsed. The data, regardless of the dimensionality of the solution, all fit along a single line, as did the data in experiment 1. Analyses done with metric and nonmetric assumptions gave identical results. In comparing this figure to Fig. 4 it should be noted that equivalent configurations may be represented as mirror images of one another; that is. reflected about the x and/or y axis. Again, sphere size in the 3-D configuration represents a dimension-in this case, Dimension 1.

Fig. 7. The same type of analysis as

tributions of the two channels that were used to generate the bipartite field were sufficiently similar to allow adjustment of the neutral density wedge in one channel relative to the other to produce a bipartite field of zero contrast, also rated as zero for distinctness. A series of contrast values were determined for one side of the photometric field relative to the other, and in all cases one hemifield (the left or right one with equal probability) was always held fixed at 30 photopic trolands while the other was varied. The luminances of these fields were determined by use of a Spectra Photometer calibrated against a known luminance standard (Gamma Scientific). Procedure. With one of the hemifields held constant at 30 td on each trial, the experimenter varied the Iuminance of the other so that the observer saw, from trial to trial, a random presentation of luminance contrasts and borders of various degrees of distinctness. During each trial, the observer interrupted the beam of light reaching his eye by use of a ~ienoid-o~rat~ shutter and during this time made a border-distinctness rating, using the S-point scale described earlier. Each luminance contrast was presented and subsequently rated five times.

Results Figure 8 shows the results of this experiment for the three observers. Plotted in this figure are the avarage distinctness ratings, DA, for each observer as a function of the logarithm of measured luminance contrast, k, of the bipartite fields presented. Excepting very low contrast, the relation between border distinctness and the log of contrast, k, appears to be linear. In the low-contrast range, however, there is a significant departure from linearity which suggests that the distinctness ratings of these observers for stimuli of very low contrast are somewhat larger than would be expected on the basis of a logarithmic function, which very accurately describes the data for distinctness ratings of 2 or greater. This would be an understan~ble result if some form of edgeenhancement mechanism were contributing to the perception of luminance-contrast borders, whose function is to make low-contrast contours more

692

BRIAN

W.

TANSLEY

and R. M. BWNTOK

6

0 0.01

0.03

0.05

0.1

0.2

0.3

Contrast,

0.01

0.03

0.05

0.1

0.2

0.3

k

Fig. 8. Results of the distinctness ratings made by three observers to a set of luminance contrast borders in experiment 4. Note the departure from linearity in the region of low contrasts. We interpret this as evidence for the action of neural edge-enhancement mechanisms in the spectrally non-opponent channel. The data of observer TS have been multiplied by a factor of 10 for exposition.

visible than they otherwise would be, and thus reduce the threshold contrast. GENERAL DlSCUSSION

Prediction of chromatic border distinctness

It has been demonstrated by Valberg and Tansley (1977) that a simple R-G opponent function can be used to predict the ~stinctn~s of chromatic borders, as measured in many different experiments on the MDB. This function assumes that there is an R-C opponent signal from each side of the bipartite field, and that the logarithm of the difference between these two signals is proportional to the border-distinctness rating. As an example of the predictive utility of this functionally a “tritanopic purity difference” function-the logarithm of the tritanopic purity difference (log Ap,) for each pair of spectral lights used in experiment 3 was calculated and plotted against the average distinctness ratings of all three observers. Ttitanopic purity, p@ for any light whose relative spectral radiance distribution is known, can be calculated from p,

=$$(R - G)

where R and G are the tristimulus values calculated by use of Wahaven’s (1974) estimate of the fundamental response functions of the long and middle wavelength-sensitive cones. Although we have used Walraven’s (1974) functions, others could be used, such as those of Pokorny, Smith and Katz (1973). The tritanopic purity dl@rence, Ap,, is the difference between pI calculated for one side of the bipartite and that calculated for the other: IAPJ = IP~,- ~ttl.

The values of lAp,l were calculated for the stimuli of Exp. 3; these are plotted on a logarithmic scale against the average border-distinctness ratings of all three observers in Fig 9. Each data point in this figure

is the average of 15 border-distinctness ratings. As can be seen from the figure, the data fell in a cluster, which indicates a very high correlation between these two variables. A series of product-moment correlations was computed, each based upon the prediction of border distinctness for one monochromatic light when paired with all others in the study. 8 wavelengths were chosen from the 18 used in the study, and none of the correlations was less than 0.95. This suggests that the tritanopic purity difference function predicts border distinctness ratings about equally well, irrespective of the wavelength of the stimulus. 7=

6-

S-

4-

3-

2-

/-

L 0%

Fig. 9. The mean subjective border distinctness, D, taken by averaging the data from all three observers in experiment 3, plotted against the logarithm of the computed purity difference for each of the 324 pairwise comparisons in this study. Each data point represents the average of 30 distinctness ratings.

693

Chromatic border perception

IAP+I

Contrast

k

Fig. 10. Results of experiments 3 (left) and 4 (right) for the average of three observers, each of whom participated in both studies. In each case the average distinctness ratings (D) are plotted as a function of a measure of the response of R and G cones only. In the case of the chromatic borders (open circIes) the difference between responses of these two cone types is used, while in the case of luminance borders (filled circles) the sum is used.

In Fig. 10, the averaged data from Figs 8 and 9 (collapsed over all three observers) are plotted together for comparison. In general, both chromatic

border (left) and luminance-contrast border-distinctness ratings (right) are linear with the logarithm of their respective objective measures, tritanopic purity difference JAp,l, and contrast, k. In Fig. 10 it can be seen that the slope, m, for the borders formed by luminance contrast is greater, on average, than that for chromatic borders, because for the latter there seems to be littie or no deviation from a straight line of the form suggested by the equation. In the case of the luminan~~ontr~t border study, however, there is the marked devi@ion from linearity, previously noted, in the region of small values of luminance contrast. The increased slope of the luminance-contrast function and the fact that very low luminance contrast gives rise to distinctness ratings that ,are larger than predicted on the basis of the logarithmic function at higher contrast values suggest that there may be a contribution to luminance-contrast bordet-distinctness ratings from a neural edge-enhancement mechanism simiiar to that responsible for Mach bands. In the case of chromatic borders, however, there is no indication that such a mechanism is involved; the log tritanopic purity difference predicts the mean distinctness ratings accurately down to threshold levels. *Although we have used an opponent-type

difference function for the model, a mechanism semsmve to the difference across the border of only one cone type could also be conceived. It is clear that both cone types are capable of signalling the spatial difference as both protanopes and deuteranopes see edges. The opponent model is preferred here because of the increased sensitivity the difference between two cones of different spectral sensitivity would provide over that of single cone type’s responses.

It would appear then that whatever edge-enhancement mechanisms are present in human visual processing are to be found in connection with the R + G summative response and not in opponent channels or in differential stimulation of a single cone type. These quantitative data are consistent with the subjective appearance of the fields. In the case of chromatic borders, which by definition occur when there is no luminance contrast, each of the two halves of the field-however different they may appear-has a strikingly uniform appearance. This is not so in the achromatic case, where there are nonuniformities of appearance, in particular a dark region near the border on the darker side, suiting an inhibitory effect arising from activity in the brighter area. By combining the functions plotted in Fig. 10, it is possible to describe the relationship between an R-G opponent response (modeled here by a tritanopit purity difference function) and an R + G response (modelled here by a luminance contrast function) with respect to the border distinctness that each produc&. Figure 11 shows the relation between the log tritanopic purity difference and luminance contrast for a set of equal distinctness values, determined empirically. This function is linear on a log-log plot (except in the region of small luminance contrasts, described above). This indicates that the equivalent luminance contrast is a power function of the tritanopic purity difference k% = 14.28 IAp$‘.“.

This formula was calculated by least-squares regression. The equation has a practical utility in that an estimate of the distinctness of chromatic borders can now be made if the relative spectral energy distributions or chromaticities of two lights on either side of a border are known. For example, the ability to resolve a printed message of one color superimposed upon a background of another (where the luminous reflectances are very nearly equal) should be predict-

694

BRIAN W. TANSLEY and R. M. BOWTON r

I

50-

I

I

I

I

I 1.0

I 3.0

r

30-

io-

53-

lC

I 0.3

I 0.5

I

d

5i0

I AP+I

Il. The luminance contrast, k, and the absolute value of the tritanopic purity difference, Appl,are plotted for their equivalent border distinctness ratings using the data from experiments 3 and 4. Excepting the region below distinctness ratings of 2, it is possible to express a given border distinctness rating in terms of a chromatic luminance-contrast border by the equation S’k 0 =

14.28)Apt /0.77

The numbers are average border distinctness values from both experiments that fall within +O. I for an integer value of the distinctness scale.

able from a determination of the equivalent luminance contrast provided by the two colors. The legibility of the print could then be related to the many studies that have investigated the effect of contrast on detection and recognition. Refeuance for earfier psyc~o~hysicaf studies The so-called “Liebmann Effect,” described earlier, can now simply be explained by assuming that the stimuli used in the observations of Liebmann, and of Koflka and Harrower were such that the figure/ background combinations which did not “articulate” well with one another were stimuli whose chromaticities fell nearly along a tritanopic confusion line; thus stimulating only the B cones differentially at the equal-luminance point. Because Koffka and Harrower reported no physical specifications of their stimuli, their experiment cannot be replicated and our interpretation cannot be tested. There is no way in which Kolika and Harrower could have arrived at quantitative conclusions without measuring their stimuli in objective terms. Boynton and Greenspon (1972) came to an incorrect conclusion in their study of the distinctness of borders formed between equally saturated, psychologically unique fields. For both subjects of that exborders were formed periment, very indistinct between red-yellow and blue-green pairs, whereas the other four possible combinations all formed borders of much greater distinctness. Boynton and Greenspon (1972) tried to explain their results in terms of the brain-element model described in the introduction to this paper, We have already indicated that the brainelement model cannot survive the evidence of the

present paper. Unlike Kotlka and Harrower. however, Boynton and Greenspon did provide physical specification of their stimuli, which permits a re-analysis. When their chromaticities are plotted, the “melting” pairs fall close to tritanopic confusion lines; the other six pairs do not. Because stimuli that fall along tritanopic confusion lines are equivalent to one another for the formation of borders. it would be predicted that the other four pairs would form borders about equally distinct to one another; this was the obtained result. From the results of these three experiments it must be concluded that border distinctness at the MDB setting depends upon the differential activity of R and G cones only. Because of this, the scaled distinctness of borders at MDB cannot be related to saturation differences (Kaiser et al.. 1971; Boynton and Greenspon, 1972) nor can the distinctness measure alone be used as an index of color differences because, for normal observers, the B cones presumably contribute to the perception of both hue and saturation. in the fovea1 region, it has been shown that there is a paucity of B cones (Wald, 1967) and, although their contribution to color vision is important. they seem to contribute very little to brightness whittle* 1974). Because observers could clearly identify the color of hemifields in these experiments, and because these fietds were relatively large compared to the B conefree area, we conclude that their lack of contribution to border perception at equal luminance is probably due to their poor spatial resolution characteristics, not to their functional absence in the fovea1 region. Several investigators have studied the spatial resolution capacities of short-wavelength-sensitive cones. Brindley (1953, 1954) isolated blue cones by chromatic adaptation with long-wave light and showed that they have a higher Weber fraction than other cones, that complete spatial summation occurs up to 12 min of visual angle (compared to about 3 min for R and G cones), and that visual resolving power by B cones alone is very poor. Stiles (1949) confirmed these results. Green (1968) using a two-color increment-threshold method, measured the contrast sensitivity of the various n mechanisms as a function of spatial frequency. His results also suggest that the resolution properties of the short-wavelength-sensitive cones are poorer than those of the long-wavelength-sensitive mechanisms. Kelly (1974) also found that the short wavelen~h-sensitive mechanism has lower spatial resolution capabilities. The temporal, as well as the spatial properties of B cones, must enter into the results that are obtained in studies of border distinctness. Here again the inferiority of the B cone system is not difficult to document. Because the illumination falling on the retina is continually changing, whether during attempted fixation (due to residual eye movement), or when the normal kinds of saccadic eye movements are permitted, the resolution of contour for any appreciable period of time is greatly aided by the fresh excitation of receptors that results. Buck, Frome and Boynton (1977) have specifically investigated the fading of chromatic borders as a function of border distinctness at MDB; the correlation between the percentage of time visible and border distinctness is so high that

695

Chromatic border perception

fading time can be used as a valid index of border distinctness. Pi&on (1952) reported investigations where equiluminois lights were alternated in rapid sequence and the rate at which perceptual fusion occurred was measured (chromatic and brightness flicker fusion). He found the flicker-fusion threshold to be highest for long wavelength lights and lowest for short-wavelength lights. Brindley, DuCroz and Rushton (1966) confirmed this result utilizing a square-wave flickering light superimposed on a steady background, a modification of the two-color increment threshold technique of Stiles. Green (1969) has also found that the shortwavelength-sensitive cones have reduced temporal sensitivity. His experimental methodology was similar to that of Brindley et al., with the modification that sinusoidally flickering stimuli were used. Mollon and Krauskopf (1973), using a reaction-time paradigm, found that response time to detection of near-threshold blue targets was longer than that to near-threshold red targets. Also, using the two-color increment threshold method, they concluded that Stiles’ bluesensitive color mechanism, x1, has sluggish temporal characteristics. Kelly (1974) also found that the shortwavelength-sensitive cones have poorer temporal response characteristics. His experimental methodology was similar to that of Green (1969) in that sinusoidally flickering lights superimposed on steady-state backgrounds were employed. Boynton and Baron (1975) have provided electrophysiological evidence in support of the notion that the responses from B cones, isolated by selective chromatic adaptation, are more sluggish than R and G cone responses.

the additive luminance signals. When compared to the longwave cones, everything about B cones is different. There are far fewer of them, especially in the central retina, and therefore an occasional B cone has no important deleterious effect upon the mosaic of R and G cones upon which the perception of fine detail depends. When B cones operate in isolation, they can mediate vision only of very low acuity. Contours in small fields like those of our experiments cannot even be seen in response to very large differential B cone stimulation associated with the two halves of the field. In addition, the B cones are temporally sluggish so that eye movements cannot much enhance their ability to mediate the perception of contour. Far from being associated with “interlaced mosaics of chromatic elements somewhere in the brain”, the phenomenon of the minimally distinct border is to be associated with only one variable-the ratio of R to G cone activation. At constant luminance, which is what the MDB operation defines, border distinctness corresponds very simply to the difference between the level of stimulation of R (or G) cones from the two halves of the field. Acknowledgements-This work was supported by Grant EY 01541 from the National Eye Institute. We wish to thank Mary Hayhoe, Drs Donald MacLeod. Roger Shepard and Arne Valberg for their contributions to our thinking about this subject.

REFERENCES Relation

to electrophysiological

studies

The results of the experiments reported here, and the interpretation that we have placed upon them, are fully consistent with existing physiological evidence regarding the dual role of the excitatory red center and inhibitory green surround cells (and the converse of these). Such cells, which seem equally as important for contour formation as for signalling color, were first observed by Wiesel and Hubel (1966) in single-unit recordings from the lateral geniculate nucleus. Ingling and Drum (1973) have given a detailed exposition of correlations between psychophysical and electrophysiological data, with a special emphasis on the relation between the red-green chromatic units and what their behavior implies for the formation of contour. They show why such units, when they signal contour at equal luminance, might not be expected to elicit contrast enhancement by lateral inhibition, whereas borders that include luminance differences would. Conclusion

The results of the experiments described here are consistent, overall, with the following view. R and G cones feed quickly into opponent color pathways whose function is equally as much to transmit information about contour as hue. These cones are numerous upon the retina, with especially high density in the central fovea, as is required for pickup devices in a high acuity system. The visual mechanisms fed by R and G cones have a brisk temporal responsiveness, especially those parts of it which carry Y.R.IR/6-F

Boynton R. M. and Kaiser P. K. (1968) Vision: The Additivity Law made to work for heterochromatic photometry with bipartite fields. Science 161, 366368. Boynton -R. M. (1973) Implications of the minimallydistinct border. J. opt. Sot. Am. 63. 1037-1043. Boynton R. M. and dreenspon T. S. (1972) The distinctness of borders formed between equally saturated psychologically unique fields. Vision Rex 12, 495-507. Boynton R. M. and Baron W. S. (1975) Sinusoidal characteristics of primate cones in response to heterochromatic stimuli. J. opt. Sot. Am. 65, 1091-1100. Boynton R. M. and Wagner G. (1972) Color differences assessed by the minimally-distinct border method. In Color Metrics (Edited by Vos J. J., Friele R. C. and Walraven P. L.). Proceedings of the Helmholtz Memorial Symposium on color metrics, pp. 2635. AIC/Holland, Soesterberg. Brindley G. S. (1953) The effects of colour vision to adaptation of very bright lights. J. Physiol., Lond. 122, 332-350.

Brindley G. S. (1954) The summative areas of human colorreceptive mechanisms at threshold. J. Physiol.. Lond. 124, 40%408.

Brindley G. S.. DuCroz J. J. and Rushton W. A. H. (1966) The flicker fusion frequency of the blue-sensitive mechanism of color vision. J. Physiol.. Lond. 183, 497-500. Brown W. R. J. and MacAdam D. L. (1949) Visual sensitivities to combined chromaticity and luminance differences. J. opt. Sot. Am. 39, 808-834. Buck S.. Frome F. and Boynton R. M. (1977) Initial dis-

tinctness and subsequent fading of chromatic borders, J. opt. Sot. Am. 67. i 12&1128.Carroll J. D. (1972) Individual differences in multidimensional scaling. In’ Multidimensional Scaling: Theory and Applications in the Behavioral Sciences. Vol. I (Edited

696

BRIAN W. TANSLEYand R. M.

by Shepard R. M., Romney A. K. and Nerlove S.). Seminar Press, New York. Carroll J. D. and Chang J. L. (1969) How to U.W INWSCAL. A computer program for canonical decomposition of N-wry tables and individual differences in multidimensional sealing. Vol. 1, pp. 105-155. Bell Laboratories, Murray Hill.

NJ. De Valois R. L. (1966) Neural processing of visual information. In Fronriers qf Physiologicof Ps~~chology (Edited by Russell R. W.), pp. 51-91. Academic Press, New York. Granger E. M. (1975) Specification of color image quaiity. Doctoral dissertation. Institute of Optics, University of Rochester. N.Y. Green D. G. (1968) The contrast sensitivity of the color mechanisms of the human eye. J. Physiol., Lond. 1%. 415-429. Green D. G. (1969) Sinusoidal flicker characteristics of the color-sensitive mechanisms of the eye. Vision Res. 9, 591-601.

Guild J. (1925) A trichromatic calorimeter suitable for stand~di~ation work. Trans. opt. Sot. 27, 105-129. Guth S. L., Donley N. J. and Marocco R. T. (1969) On luminance additivity and related topics. Vision Res. 9, 537-576. Hecht S. (1949) Brightness, visual acuity, and colour blindness. Documenta ophth. 3, 289-306. Horst G. J. C. van der and Bouman M. A. (1967) On searching for Mach-band type phenomena in color vision. Vision Res. 7, 1027-1029. Ingling C. R. and Drum B. A. (1973) Retinal receptive fields: correlations between psychophysics and electrophysiology. Vision Res. 13, 1151-l 163. Kaiser P. K. (1971) Minimally distinct border as preferred psychophysical criterion in visual heterochromatic photometry. J. opt. Sot. Am. 61. 966-971. Kaiser P. K. and Greenspon T. S. (1971) Brightness difference and its relation to the distinctness of a border. J. opt. Sot. Am. 61. 962-965.

Kaiser P. K., Hertberg P. and Boynton R. M. (1971) Chromatic border distinctness and its relation to saturation. Vision Res. 11, 953-968. Kelly D. H. (1972) Flicker. in Handbook of Sensory Physiology, VII/4 (Edited by Jameson D. and Hurvich L.). pp. 273-302. Springer-Verlag, New York. Kelly D. H. (1973) Lateral inhibition in human color mechanisms. J. Physiol., Lond. 228, 55-72. Kelly D. H. (1974) Spatio-temporal frequency characteristics of color-vision mechanisms. J. opt. Sot. Am. 64, 983-990.

KoRka K. (1935) Principles of Gestalt Psychology. Harcourt, Brace & Co., New York. Koflka K. and Harrower M. R. (1931) Color and arganitation I. Psych. Forsch. 15, 145-275 and 193. Kruskal J. B. and Carmone F. (1969) How to use M-DScale (version SM) and other useful information. Bell Laboratories Technical Report. Kruskal J. B., Young F. W. and Seery J. B. (1969) HOW to use K YST, a very j?e.xible progr~ to do multidimensional scaling and un~ld~ng. Bell Laboratories Technical Report. MacAdam D. L. (1942) Visual sensitivities to color differences in daylight. J. opt. Sot. Am. 32, 247-274. MacAdam D. L. (1949) Color discrimination and the influence of color contrast on visual acuity. Revue Opt. thPor. instrum. 28, 161. McCree K. J. (1960) Color confusion produced by voluntary fixation. Optica Acta 7, 281-290. Middleton W. E. K. and Sanders C. L. (1953) An improved sphere paint. Ilfum. Engr., N.Y: 48, 254-256. Mellon J. D. and Krauskopf J. (1973) Reaction time as a measure of the temporal response properties of individual color mechanisms. Vision Res. 13, 27-40.

BOWTON

Piiron H. (19.52)The sensations: Their Functions. Processes and Mechanisms. Miller, London. Pokorny J., Smith V. C. and Katz I. (1973) Derivation of the photopigment absorption spectra in anomalous trichromats. J. opt. Sot. Am. 63, 232-237. Shepard R. M. (1962) The analysis of proximities: multidimensional scaling with an unknown distance function 1. Psychomerrika 27, 125-140. Shepard R. N. (1965) Approximation to uniform gradients of generalization by monotone transformations of scale. In Stimulus Gener&zotion (Edited by Mostofsky D. J.). Stanford University Press, Stanford. CA. Shepard R. M. (1974) Representation of structure in similarity data: problems and prospects. Psyc~zometr~~a 39. 373-421.

Spence I. and Graef J. (1973) How to use M-SPACE, a program for the determination of the underlying dimensionality of an empirically obtained matrix of proximities. University of Western Ontario Research Bulletin 257, London, Ontario. Spence 1. and Graef J. (1974) The determination of the underlying dimensionality of an empiri~lly obtained matrix of proximities. Multio. Beh. Res. 9, 33 i-342. Stiles W. S. (1949) Increment thresholds and mechanisms of colour vision. Documenta ophch. 3, 138-163. Tansley B. W. (1976) Psychophysical studies of the contributions of chromatic mechanisms to the visual perception of borders. Doctoral dissertation, University of Rochester. N.Y. Tansley B. W. and Boynton, R. M. (f976) A single line predicts the distinctness of borders by different colors. Science 191, 954-957. Torgerson W. S. (1967) Theory and methods qf scaling. Wiley, New York. Valberg A. (1974) Color indirection: dependence on luminance, purity, and dominant or complimentary wavelength of inducing stimuli. J. opt. Sot. itm. 64, 1531-1540. Valberg A. and Tansley B. W. (1977) A tritanopic purity difference function accounts for border distinctness at the MDB-point. J. opr. Sot. Am. 67. 133&1336. Vos J. J. and Walraven P. L. (1971) On the derivation of the fovea1 receptor primaries. Vision Res. 11, 799-818. Wagenaar W. A. and Padmos P. (1971) Quantitative interpretation of stress in Kruskal’s multidimensional scaling technique Br. J. math. stat. Psych. 24, 101-110. Wagner G. and Boynton R. M. (1972) A comparison of four methods of heterochromatic photometry. J. opt. Sot. Am. 62, 1508-1515.

Wald G. (1967) Blue-blindness in the normal fovea. J. opf. Sot. Am. 57, 1289-1301.

Walraven P. L. (1966) A zone theory of color vision. Farbe 15. 1339-I 343. Walraven P. L. (1974) A closer look at the tritanopic convergence point. Vision Res. 14, 1339-1343. Ward-F. and Boynton R. M. (1974) Scaling of large chromatic differences. Vision Res. 14. 943-949. Westheimer G. (1966) The MaxwAlian view. Vision Res. 6, 669-682.

Wetherall W. 3. (1961) The design of visual calorimeters presenting a new monvariant calorimeter. M.Sc. thesis. University of Rochester, N.Y. Whittle P. (1973) The brightness of colored flashes on backgrounds of various colors and luminances. Vision Res. 13, 621-638.

Whittle P. (1974) Intensity discrimination between flashes which do not differ in brightness: some new measures on the “blue” cones. vision Res, 14, 599-601. Wiesel T. N. and Hubel D. H. (1966) Spatiat and chromatic interactions in the lateral geniculate body of the rhesus monkey. J. Neurophysiol. 29, 1115-1156. Wyszecki G. and Stiles W. S. (1967) Color science. Wiley, New York.

Chromatic border perception APPENDIX

In order to determine the dimensionatity of the most appropriate solution of the multidimensional scaling results in experiment 3, a technique suggested by Spence and Graef (1974) was tried. Their algorithm, similar to the one orooosed bv Wanenaar and Padmos (1971) utilizes the iesuits of an extensive set of synthetically produced dissimilarity matrices. The technique is based on the results of an extensive Monte Carlo experiment and is basically an attempt to find the set of Monte Carlo data, for some given dimensionality, that best fits the obtained stress values. This program utilizes the stress values from sohitions from five dimensions through one dimension.” The results of this anaIysis essentially confirmed our suspicion that the correct solution is probably one-dimensional in nature. In order to develop a model based upon the responses of R and G cones only, we tested the assumption that the subjective distinctness scale could be considered as an interval scale. If this assumption can be made, the use of metric multidimensional scaling can be justified. Although the variability within a particular condition in an experiment was quite small, the judgment of border distinctness is subject to the same measurement uncertainties as any other subjective rating task. To check on the validity of the use of the metric regression options of the KYST algorithm, the data from experiment 3 were analyzed by use of both the interval-scale assumption (metric) and weaker ordinal-scale assumption (nonmetric). Equivalence of the obtained configurations for these two analyses unequivocally demonstrates that the metric assumption can be made. Even when constrained only to mo,notonicity, the Shepard diagram exhibits a high degree of linearity, with only slight deviations near the extremes, as noted earlier. The stress (formula 1) was identical to 2 or 3 decimal places in both the two- and three-dimensional solutions 3 We thank Dr. Ian Spence of the University of Western Ontario for providing us with a copy of M-SPACE.

691

for the metric and nonmetric analyses. Finally, to exclude the possibility that the two analyses had found configurations that were equally good fits to the data, but that were different in structure, we used the CONGRU program to rotate the nonmetric three-dimensional configuration into maximum congruence with the metric one. The correlation measure obtained from this procedure was 0.999. Therefore, because the nonmetric and metric assumptions resulted in virtually identical configurations, it is safe to assume that the border distinctness ratings made in this study are on an interval scale. It is of some interest to examine the KYST configurations obtained for each of the three observers separately. For this task, an algorithm called INDSCAL. described by Carroll and Chang (1969) was used. The INDSCAL model differs from the KYST procedure most notably in that the dimensions of the former are not arbitrarily assignable, as in the latter. Although Carroll (1972) suggested that the algorithm is robust with respect to violations of the metric constraints, his qualification that having many different subjects “helps” in this regard would have been of little comfort with the present study which employs data from only three observers. (The demonstration that the data were interval in nature was therefore necessary, because it was a prerequisite for the meaningful use of the INDSCAL analysis of the three observers’ mean distinctness ratings.) The INDSCAL analysis revealed some interesting individual differences in the border ratings of each observer. The solution accounted for different proportions of the variance of the individual’s ratings but, more importantly, the distribution of this variance over the dimensions indicated some qualitative differences in the observations underlying the ratings. The data of two observers, BT and RB, were always better represented than the data of the third observer, TS, regardless of the dimensionality of the solution. This information from the INDSCAL analysis simply reflects the fact that BT and RB were more experienced at making these judgments than TS.