John Krauskopf

Color discrimination and adaptation

We have measured color discrimination in the isoluminant plane under rigorously controlled adaptation conditions. Two regimes were studied. Under the first regime the observer was adapted to the region of color space in which the discriminations were made. Thresholds for detecting changes along the S-(L + M) axis are a linearly increasing function of the excitation of the S cones. Thresholds for detecting changes along the L-M axis are independent of the locus of adaptation along this axis. The straightness of these functions is inconsistent with the theory that second stage mechanisms are more sensitive in the middle of their operating ranges. No convincing evidence of interactions in the effects of adaptation locus or test stimuli was observed. Under the second regime the observer was adapted to one point in color space and the stimuli to be discriminated were located in other places in color space. Discrimination seems to be limited primarily by mechanisms maximally sensitive to modulation along the isoluminant cardinal axes but evidence suggestive of the operation of higher order mechanisms was also found.

Vernier acuity: effects of chromatic content, blur and contrast.

Offset thresholds were measured for targets whose horizontal profiles were either Gaussian or odd-symmetric Gabor functions. The targets were defined either by variation along the constant B or the constant R & G axes of color space or by luminance variation. Blur was varied in the case of the Gaussian targets by varying the standard deviation of the distribution and in the case of the Gabor functions by varying the spatial frequency of the sinusoidal component. Detection thresholds for all the stimuli were measured. The contrast of the targets used in the measurement of offset thresholds was varied from just above detection threshold to the maximum that could be produced. The offset thresholds obtained with targets of different chromatic composition are nearly identical when blur and contrast relative to detection threshold are held constant. We attribute the slight advantage held by luminance targets over chromatic targets for narrow Gaussians to the detectability of low frequency components of the chromatic targets which are of little use in the assessment of offsets. This conjecture is supported by the complete absence of such an advantage in the case of Gabor targets.

Coherence, cardinal directions and higher-order mechanisms

Our initial purpose was to develop a quantitative method of estimating the cardinal directions of color space. The method is based on the finding that patterns consisting of pairs of drifting gratings modulated along different cardinal axes appear to slip with respect to one another, while the same patterns appear as a single coherent plaid if the modulation directions of the patterns are rotated by 45 deg in color space [Krauskopf & Farell (1990). Nature, 348,328-331]. A forced-choice procedure was used in which observers were asked to choose which of two successively presented patterns appeared less coherent. The patterns consisted of pairs of drifting gratings; the direction of modulation of one of the gratings was fixed and that of the other varied. For example, an estimate of an individuals isoluminant plane could be obtained by fixing the modulation of one grating in the luminance direction and finding the elevation of the modulation of the other grating that resulted in minimum perceived coherence. We found it important to take into consideration individual differences in the tilt of the isoluminant plane in color space and in the detectability of targets in the nominal cardinal directions. When this was done we found that reliable measurements could be made. The method effectively provided quantitative estimates of the cardinal directions. However, the most important result was the inadequacy of the generalization that patterns appear coherent when they share similar components along cardinal directions (Krauskopf & Farell, 1990) to account for the new results. The present results suggest that patterns appear not to cohere to the extent that they fail to stimulate common chromatic mechanisms, but the assumption that these mechanisms are tuned only along cardinal axes can be rejected. Along with other data the results point to the existence of higher-order mechanisms tuned to different isoluminant chromatic directions.

Proximity judgments in color space: tests of a Euclidean color geometry.

We describe two tests of the hypothesis that human judgments of the proximity of colors are consistent with a Euclidean geometry on color matching space. The first test uses proximity judgments to measure the angle between any two intersecting lines in color space. Pairwise estimates of the angles between three lines in a plane were made in order to test the additivity of angles. Three different color proximity tasks were considered. Additivity failed for each of the three proximity tasks. Secondly, we tested a prediction concerning the growth of the variability of judgments of similarity with the distance between the test and reference stimuli. The Euclidean hypothesis was also rejected by this test. The results concerning the growth of variability are consistent with the assumption that observers use a city-block metric when judging the proximity of colored lights.

Relative number of long- and middle-wavelength-sensitive cones in the human fovea

Flicker photometric measurements yield spectral sensitivity curves that are well fitted by sums of the spectral sensitivity curves of long-wavelength-sensitive (L) cones and middle-wavelength-sensitive (M) cones if the L cones are given twice the weight of the M cones. This result has been interpreted as implying that L cones are more numerous than M cones but is also consistent with a different numerical ratio, say, 1:1, and with the assignment of greater weight to the L cone input than to the M cone input by the mechanism subserving flicker photometry. Measurements of temporal sensitivity are presented for lights that modulate the inputs of either only the L cones or only the M cones. Sensitivity to modulation of the L cones is approximately twice that of modulation of the M cones at approximately 30 Hz, but that advantage disappears at approximately 2 Hz. Thus flicker sensitivity is equivocal with regard to cone numerosity. Electrophysiological, anatomical, and psychophysical evidence is reviewed, with particular weight placed on the statistics of color appearance of small, brief, monochromatic lights and on increment thresholds measured on the same observers. It is concluded that, in the central fovea, the ratio of L:M cone numbers is close to unity and may not be so variable as is usually supposed.

Residual eye-movements in macaque and their effects on visual responses of neurons.

We recorded continuously, with high precision, the positions of the eyes in anesthetized macaque monkeys prepared for physiological recording. Most recordings were made after the infusion of muscle relaxant to immobilize the eyes; in some cases we also were able to record eye position for periods before the eyes were immobilized. In all monkeys, the eyes moved continuously by as much as 0.5 deg over a 10-min sampling period. The average distance moved was proportional to the square root of the sampling period, as would be expected from a random walk. The movements had three distinct components: slow drifts, and two rhythms driven by the pulse and respiration. The rhythmic movements occurred only under paralysis: they were not discernible in measurements made before the infusion of muscle relaxant. The movements of the eye in the paralyzed animal can have substantial effects on the measured physiological characteristics of neurons. For excursions in the midrange of those we observed, a neurons sensitivity to a spatial frequency of 10 cycle/deg might be underestimated by as much as a factor of three, depending on the method by which responses were averaged. We show how the effects of eye-movements can be mitigated by appropriate data analysis.

Influence of chromaticity on vernier and stereo acuity.

Vernier offset thresholds for targets modulated in luminance or isoluminantly along the L-M axis were confirmed to be equal for targets whose contrasts were equal multiples of those required for detection. On the other hand, stereoscopic depth thresholds were elevated by a factor of 10 or more for isoluminantly modulated targets. Thresholds for vernier targets are 2 or 3 times larger with a gap of 20 arcmin than for a gap of 1 arcmin for both isoluminant and luminance targets. On the other hand, stereo thresholds decrease by a factor of 2 to 3 for both classes of target over the same range. We consider our results in the light of recent electrophysiological and psychophysical evidence and conclude that our results are consistent with the notion that stereo thresholds are mediated by a single class of mechanism for targets modulated in luminance or isoluminantly. We test and reject the hypothesis that stereopsis is subserved by independent chromatic and luminance mechanisms.

Effect of contrast on detection of motion of chromatic and luminance targets: retina-relative and object-relative movement.

It is now clear, contrary to previous conclusions, that motion may be conveyed by purely chromatic stimuli. The question considered here is how the mechanisms for assessing motion of luminance and chromatic stimuli differ. The dependence on contrast of amplitude thresholds for the perception of oscillatory motion was measured. The targets were Gabor patches modulated either chromatically along the L-M isoluminant axis or in luminance. When single targets were presented, the slope of the function relating log threshold amplitude to log contrast was approximately -0.50 for chromatic targets and 0.00 for luminance targets. When a reference target was present the slopes were approximately -0.50 for both types of target. The results imply that perception of motion of chromatic targets is based on the assessment of changes in relative position of target elements while motion of luminance targets may be signalled either by relative motion of target elements or by local motion of an image relative to the retina.

Adaptation and Color Discrimination

A central problem in color vision is how color discrimination varies over color space. MacAdam (1942) attacked the problem in an elegant set of experiments. He developed a special color mixer which produced a bipartite disc consisting of a fixed half field and a variable half field. Both halves were mixtures of lights derived from the same source and which passed through the same two color selective filters. The experimenter determined the relative amount of the two lights in the fixed half and the observer repeatedly adjusted the relative amount of the lights in the variable half. A large number of color filters sets were selected and trimmed by additional neutral filters so as to produce equally luminous primaries at many different points in the CIE diagram. By using a number of carefully chosen sets of these filters, fixed lights at the same point in the diagram could be obtained with several pairs of filters allowing the matching half of the field to be adjustable along different lines through that point.

A journey in color space

The idea that the first stage in normal daylight vision is characterized by three processes having different spectral sensitivities was established early in the 19th century by Young1 and linked clearly to experimental data on color matching by Maxwell.2 Herings3 notion of opponent processes was grounded in facts of color appearance. A number of “opponent process” theories were developed to account for color appearance, in which the signals from the receptors were combined to form two channels conveying chromatic information and a third carrying achromatic information.4 More recently psychophysical, as opposed to phenomenological, evidence has been advanced in support of the existence of opponent mechanisms.5–12 While these articles provided evidence for the interaction of cone signals, they did not determine in detail the weights of the contributions of the different classes of cones to the second stage (and higher-order) mechanisms. The work discussed here was intended to determine the weights of the second-stage mechanisms by psychophysical means.13 Quantitative reanalysis of the results of habituation experiments demonstrated the existence of higher-order mechanisms that respond to the sums of the signals from second-stage mechanisms.14 Diverse evidence from other psychophysical experiments including detection and discrimination of chromatic pulses,14 and coherence of plaid patterns,15 confirmed the existence of higher-order mechanisms. Single unit recording from striate cortex in monkey revealed cells having the spectral sensitivities implied by the psychophysical results.16 Electrical recording of responses in monkey lateral geniculate nucleus (LGN) revealed single units with weights corresponding to the cardinal directions psychophysically determined.17 LGN cells show no sign of fatigue but units in V1 do.18 They also exhibit the wide range of spectral sensitivities required of higher-order mechanisms. Studies of the influence of the chromatic content of stimuli on vernier acuity and motion thresholds and on temporal modulation sensitivity support the conjecture that, while chromatic stimuli are processed solely by the parvocellular system, luminance stimuli are processed by both magno- and parvocellular neurons. The variation of the relative sensitivity of the L and M cones with temporal frequency, together with analysis of the statistics of color appearance of small, brief, near threshold monochromatic stimuli and data from Stiless increment threshold experiment19 suggest that the numerosity ratio of L:M cones in the normal human fovea is more likely to be 1:1 than 2:1.