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In a space where Cartesian coordinates represent the excitations of the three cone types involved in color vision, a plane of constant luminance provides a chromaticity diagram in which excitation of each cone type (at constant luminance) is represented by a linear scale (horizontal or vertical), and in which the center-of-gravity rule applies with weights proportional to luminance.
Equations are derived to fit the cone sensitivity values of Smith and Pokorny, which are based mainly upon Judd's modified color matching functions and the spectral sensitivities of normal and dichromatic observers. The equations, which fit Smith and Pokorny's values to within 1 to 3%, are smooth and differentiable. Derivatives of cone sensitivities for an equal luminance spectrum, which are of particular importance for models of chromatic discrimination, have been calculated and are shown graphically.
Contrast-detection thresholds for various combinations of chromaticity and luminance differences were obtained for spatiotemporal square-wave modulation of a yellow field. The results are expressed in terms of excitation of the Vos-Walraven R,G primaries. For every spatiotemporal frequency the thresholds can be approximated by an ellipse in the red-green plane. Large variations were found in the orientation, magnitude, and eccentricity of the discrimination ellipses. It seems that a simple threshold function appears to be sufficient to describe the experimental data. Although the eye does not perceive hue contrast for high spatial frequencies, its sensitivity is not governed mainly by summation of the red and green channels.
We compute the gamut of coordinates in the Commission Internationale de l'Eclairage chromaticity diagram that correspond to positive frequency-limited functions having only three degrees of freedom (a trichromatic system). The results suggest that practical colors are either suitably frequency limited to be represented by three samples or have suitably frequency-limited metamers.
Flicker-photometric spectral sensitivity is measured in the presence and absence of superimposed monochromatic surrounds. Although color appearance depends on surround wavelength, the shape of the flicker-spectral-sensitivity functions are unaffected. These findings indicate both a lack of cone-cone inhibition within the achromatic channel and independence of the achromatic and chromatic channels.
Equiluminous red-green sine-wave gratings were drifted at a uniform rate in the bottom half of a 10-deg field. In the top half of the display was a sinusoidal-luminance grating of the same spatial frequency and 95% contrast that drifted in the opposite direction. Observers, while fixating a point in the display center, adjusted the speed of this upper comparison grating so that it appeared to match the velocity of the chromatic grating below. At low spatial frequencies, equiluminous gratings were appreciably slowed and sometimes stopped even though the individual bars of the grating could be easily resolved. The amount of slowing was proportionally greatest for gratings with slow drift rates. Blue-yellow sine-wave gratings showed similar effects. When luminance contrast was held constant, increasing chrominance modulation caused further decreases in apparent velocity, ruling out the possibility that the slowing was simply due to decreased luminance contrast. Perceived velocity appears to be a weighted average of luminance and chrominance velocity information.
Theory predicts that retinal image size will vary with wavelength. However, this chromatic difference of magnification (CDM) is likely to be very small (< 1% between 400 and 700 nm) under natural viewing conditions. There has been only one attempt to measure CDM experimentally, and the results were inconsistent with optical theory. Using a technique described by Ogle [Research in Binocular Vision, Hafner, New York (1964)], which is sensitive to even small interocular differences in retinal image size, we measured the apparent tilts in the frontoparallel plane induced by interocular differences in wavelength. We obtained the ocular CDM by determining the afocal lens magnification necessary to cancel the apparent frontoparallel plane tilt caused by interocular differences in wavelength. We show that (1) the ocular CDM can be considerably less than theoretical model predictions, (2) the relationship among delta Rx (wavelength-dependent refractive error), CDM, and pupil position is consistent with our theoretical model, (3) CDM increases considerably when an artificial pupil in front of the eye is used, (4) the location of the anterior nodal point of the eye may be inferred from the data, and (5) unlike in the case for delta Rx, large intersubjective differences may exist for CDM. The results suggest caution in the use of artificial pupils experimentally with polychromatic stimuli because of amplification of CDM and concomitant losses of image contrast.
The effects of glaucoma and diabetes on the sensitivities of the opponent and achromatic systems were investigated by measuring thresholds along theoretically defined axes in a three-dimensional color space. Thresholds were measured along two equiluminant chromatic axes and one achromatic axis in patients with diabetes or glaucoma and in glaucoma suspects. The results were compared with measures of sensitivities of short- and middle-wavelength-sensitive-cone pathways [S (Stiles pi 1) and M (Stiles pi 4), respectively] and with measures of hue discrimination by use of the Farnsworth-Munsell 100-hue test. The glaucoma suspects and diabetic patients showed preferential S-cone-pathway sensitivity losses. For glaucoma patients, however, these losses were associated with significant decreases in the sensitivity of the L-M opponent system and with decreased sensitivity to achromatic contrast.
In visual search experiments we examined whether targets that are distinguished from distracting items solely by a contrary change in color can be sought spatially in parallel. Targets under time-varying illumination pop out if they present a contrary luminance signal; targets under space-varying illumination can be detected in parallel when they are isoluminant. The results suggest that neurons with spatially and chromatically opposed receptive fields are active across the central visual field.
There is a growing use of color monitor systems in visual research and a parallel growth in the use of cone-excitation space to define stimuli and to report data. Color specification in monitor systems is accomplished by combination of the phosphor chromaticities. The effect of interobserver variation on color specification is highly dependent on the spectroradiometric properties of the primaries. We review potential sources of biologic variability and its effect on the nominal axes in a cone-excitation diagram for a color monitor system. Variation in preretinal pigment (lens and macular pigment), in the effective optical density and the spectral sensitivity of the visual photopigments, and in the cone weighting used to derive the spectral luminosity function are considered. The consequences of such biological variability are rotation and translation of the axes for a given observer relative to the nominal axes that the observer used for color specification. The importance of such rotations can be viewed within the framework of a particular experimental paradigm.
Subjective transverse chromatic aberration (sTCA) manifest at the fovea was determined for a population of 85 young adults (19-38 years old) by means of a two-dimensional, two-color, vernier alignment technique. The statistical distribution of sTCA was well fitted by a bivariate Gaussian function with mean values that were not significantly different from zero in either the horizontal or the vertical direction. We conclude from this result that a hypothetical, average eye representing the population mean of human eyes with medium-sized pupils is free of foveal sTCA. However, the absolute magnitude of sTCA for any given individual was often significantly greater than zero and ranged from 0.05 to 2.67 arcmin for the red and the blue lights of a computer monitor (mean wavelengths, 605 and 497 nm, respectively). The statistical distribution of the absolute magnitude of sTCA was well described by a Rayleigh probability distribution with a mean of 0.8 arcmin. A simple device useful for population screening in a clinical setting was also tested and gave concordant results. Assuming that sTCA at the fovea is due to decentering of the pupil with respect to the visual axis, we infer from these results that the pupil is, on average, well centered in human eyes. The average magnitude of pupil decentration in individual eyes is less than 0.5 mm, which corresponds to psi = 3 deg for the angle between the achromatic and the visual axes of the eye.
We used a noise masking technique to test the hypothesis that detection is subserved by only two chromatic postreceptoral mechanisms (red-green and blue-yellow) and one achromatic (luminance) mechanism. The task was to detect a 1-c/deg Gaussian enveloped grating presented in a mask of static, spatially low-passed binary or Gaussian distributed noise. In the main experiment, the direction of the test stimulus (termed the signal) was constant in cone contrast space, and the direction of the noise was sampled in equally spaced directions within a plane (the noise plane) in the space. The signal was chosen to coincide with one of the three cardinal directions of three postulated mechanisms. The noise plane was selected to span two of the cardinal directions, including that chosen as the signal direction. As the noise direction was sampled around the noise plane, the signal detection threshold was found to vary in accordance with a linear cosine model, which predicted noise directions yielding maximum and minimum masking of the signal. In the direction of minimum masking (termed a null direction), the noise was found to have no masking effect on the signal. Moreover, the null was not orthogonal to the signal direction but lay instead in one of the cardinal directions. Our findings suggest that detection is mediated by only three mechanisms. In a further experiment we found little or no cross masking between each pair of cardinal directions up to the limit of our noise mask contrasts. This further supports the presence of no more than three independent postreceptoral mechanisms.
We first report Fourier analyses of a collection of 348 daylight spectral power distributions and 1,695 biochrome surface reflectance functions. The power spectra of the daylights are low pass with more than 99% of spectral power below 1 cycle/300 nm and 99.9% below 3 cycles/300 nm. The power spectra of reflectance functions are also low pass with more than 99% of spectral power below 4 cycles/300 nm and 99.9% below 11 cycles/300 nm. Consequently, the resulting color signals are typically low pass with, for our samples, an estimated frequency cutoff of 5 cycles/300 nm. Theoretical and experimental data concerning human chromatic response in the frequency domain show that this limit corresponds to the highest frequency that the color system can resolve. The implications for normal and abnormal human color vision are discussed.
We applied independent component analysis (ICA) to hyperspectral images in order to learn an efficient representation of color in natural scenes. In the spectra of single pixels, the algorithm found basis functions that had broadband spectra and basis functions that were similar to natural reflectance spectra. When applied to small image patches, the algorithm found some basis functions that were achromatic and others with overall chromatic variation along lines in color space, indicating color opponency. The directions of opponency were not strictly orthogonal. Comparison with principal-component analysis on the basis of statistical measures such as average mutual information, kurtosis, and entropy, shows that the ICA transformation results in much sparser coefficients and gives higher coding efficiency. Our findings suggest that nonorthogonal opponent encoding of photoreceptor signals leads to higher coding efficiency and that ICA may be used to reveal the underlying statistical properties of color information in natural scenes.
The development of technology to measure and correct the eye's higher-order aberrations, i.e., those beyond defocus and astigmatism, raises the issue of how much visual benefit can be obtained by providing such correction. We demonstrate improvements in contrast sensitivity and visual acuity in white light and in monochromatic light when adaptive optics corrects the eye's higher-order monochromatic aberrations. In white light, the contrast sensitivity and visual acuity when most monochromatic aberrations are corrected with a deformable mirror are somewhat higher than when defocus and astigmatism alone are corrected. Moreover, viewing conditions in which monochromatic aberrations are corrected and chromatic aberrations are avoided provides an even larger improvement in contrast sensitivity and visual acuity. These results are in reasonable agreement with the theoretical improvement calculated from the eye's optical modulation transfer function.
An exact formalism devoted to the determination of dispersion coefficients is described. The method takes into account two frequent experimental configurations: a solid thin layer on a substrate and a fluid, or solid, layer between a substrate and a superstrate. Introducing the concepts of reduction and reduced finesse, this method is based entirely on the fringes' spectral position of the maxima in the transmittance spectrum. It is found that the chromatic dispersion does not affect the spectral position of the minima in the same way as it does for the maxima. There is no need to get the refractive-index curve, n(lambda), to determine the dispersion coefficients nor to work at multiple incidence angles. Bringing together the possible nonrestrictive approximations, the method becomes easy and simple to implement from a spectrophotometer in tandem with a computer. In addition, the spectrometer does not require ordinate-axis calibration, and knowledge of the substrate's and superstrate's refractive index is not required. Alternatively, the method can be easily used to accurately determine the thickness of thin layers. A numerical example using a thin layer of 2-methyl-4-nitroaniline (MNA) is given.
The spatiochromatic receptive-field structure of neurons in the macaque visual system has been studied almost exclusively with stimuli based on the human foveal cone fundamentals of Smith and Pokorny [Vision Res. 15, 161 (1975)] and generated on cathode ray tube displays. In the current study the artifacts evoked by cone-isolating, spatially structured stimuli due to variations in the eye's preretinal absorption characteristics and axial chromatic aberration are quantified. In addition, the luminance artifacts evoked by nominally isoluminant sinusoidal grating stimuli due to the same factors are quantified. The results indicate that the spatiochromatic stimuli commonly employed to map receptive fields of neurons at eccentricities > 10 deg are especially prone to artifacts and that these artifacts are maximal for the high-contrast S-cone-isolating stimuli that are often used. On the basis of these simulations, a method is introduced that improves spatiochromatic receptive-field estimates by compensating for response contributions from the incompletely silenced cone mosaics during cone-isolating stimulation.
The effects of intensity on chromatic perceptive field size were investigated along the horizontal meridian at 10 degrees temporal eccentricity by manipulating stimulus intensity from 0.3 to 3.3 log trolands. Following light adaptation, observers described the hue and saturation of monochromatic stimuli (440-660 nm, in 10 nm steps) for a series of test sizes (0.098-3 degrees) presented along the time period associated with the cone plateau of the dark-adaptation function. Perceptive field sizes of the four elemental hues (red, green, yellow, and blue) and the saturation component were estimated by three observers at each intensity level for each wavelength. In general, perceptive field sizes of blue and red are the smallest, and yellow and green are the largest. Furthermore, perceptive field sizes of all four hues decrease with increasing stimulus intensity, though the absolute change is largest for green and yellow. The decrease in size with increase in intensity cannot be completely explained in terms of saturation or rod signals and is likely, then, attributable to a cone-based mechanism.