The colors seen behind transparent filters.

How do the colors and lightnesses of surfaces seen to lie behind a transparent filter depend on the chromatic properties of the filter? A convergence model developed in prior work (D'Zmura et al, 1997 Perception 26 471-492; Chen and D'Zmura, 1998 Perception 27 595-608) suggests that the visual system interprets a filter's transformation of color in terms of a convergence in color space. Such a convergence is described by a color shift and a change in contrast. We tested the model using an asymmetric matching task. Observers adjusted, in computer graphic simulation, the color of a surface seen behind a transparent filter in order to match the color of a surface seen in plain view. The convergence model fits the color-matching results nearly as well as a more general affine-transformation model, even though the latter has many more parameters. Other models, including von Kries scaling, did not perform as well. These results suggest that the color constancy revealed in this task is described best by a model that takes into account both color shifts and changes in contrast.

Color appearance of surfaces viewed through fog.

How do the colors of surfaces seen through fog depend on the chromatic properties of the fog? Prior work (e.g. Chen and D'Zmura, 1998 Perception 27 595-608) shows that the colors of surfaces seen through a transparent filter can be described by a convergence model. The convergence model takes into account color shift and change in contrast. Whether the convergence model can also be applied to fog was tested experimentally with an asymmetric matching task. In computer graphic simulation, observers adjusted the color of a surface seen through fog in order to match the color of a surface seen in the absence of fog. The convergence model fits the data well. The results suggest that the color constancy revealed in this task with fog is described best by a model that takes into account both shift in color and change in contrast.

Test of a convergence model for color transparency perception.

Models of color transparency suggest that a region in which colors of surfaces converge in color space will appear transparent. The convergence is described by a transparency parameter alpha and a target of convergence. To test such models psychophysically, observers were presented a display with four colored areas. The colors of three of the areas were chosen in advance by the experimenter. The task of the observer was to choose the color of the fourth area to make a central region appear transparent. Settings for the fourth color were collected for a total of twenty-four color combinations chosen from three planes in color space. Observers' settings agreed well with the model, which predicts that choices for the fourth color lie along a line segment in color space that is parameterized by alpha. The results suggest further that color discriminability and color opponency also influence transparency judgment.

Spectral bandwidths for the detection of color.

The spectral properties of human color detection mechanisms were measured using a noise masking technique that minimizes the possibility of off-axis looking and artifactually narrow estimates of bandwidth. Observers were induced to use a single detection mechanism throughout a spectral bandwidth measurement by using sectored noise to mask a time-varying signal of fixed chromatic properties. Sectored noise draws samples from sectors of variable width in the color plane, centered on the signal axis. Contrast thresholds for equiluminant signals that appeared yellow, orange, red and violet were found to depend on the power of the noise, projected along the chromatic axis of the signal, but not on the sector width of the noise. These results are consistent with the activity of spectrally broadband, linear detection mechanisms that are tuned to the signal color directions tested.

Dependence of color on context in a case of cortical color vision deficiency.

Color constancy depends on sensitivity to change in both illumination spectral properties and object position. We investigated this latter form of color constancy by asking a cerebral achromatopsic to name the colors of papers that were presented atop black, gray or white backgrounds under identical illumination. Comparison of color names across background conditions reveals poor constancy, characterized by a contrasting of foreground and background values that is not corrected by proper anchoring.

Color search and visual field segregation.

Visual search for targets that combine color and shape features that are shared by distracting items can be conducted spatially in parallel. Experimental results show that parallel search for color/shape conjunctions is possible when the shapes chosen let observers segregate the spatially interspersed items into figure and ground and when, within the figure, the target differs from other items by a distinguishing color feature. Results of experiments that manipulate stimulus color suggest that adaptive mechanisms of color discrimination are used to detect targets within such a figure.

Color transparency.

Observation suggests that the chromatic changes which elicit an impression of transparency include translations and convergences in color space. Neither rotations nor shears in color space lead to perceived transparency. Results of matching experiments show that equiluminous translations, which cannot be generated by episcotister or filter models, give rise to the perception of transparency. This implies that systematic luminance change is not needed for transparency to be perceived. These results were used for the development of a method for detecting a transparent overlay within a color image and for separating the overlay from the underlying surfaces. The method tests for the coherence of chromatic change along contours through X-junctions to help detect the contour of a transparent region. The algorithm tests locally for translation and convergence to detect a transparent region. It estimates globally the chromatic parameters of the transparent overlay in order to separate the overlay from the underlying surfaces.

Spatial pooling of contrast in contrast gain control.

We report psychophysical measurements of spatial pooling functions for contrast gain control. We use a nulling technique to measure the dependence of contrast induction on the spatial frequency of a sinusoidal contrast modulation. This dependence on spatial frequency, when transformed, provides the profile of a spatial pooling function. The measured profiles are fitted well by Gaussians. We confirm earlier results that the area over which spatial pooling takes place depends on the scale of the modulated pattern. We also find that pooling functions are similar for achromatic and isoluminant stimuli.

Contrast gain control: a bilinear model for chromatic selectivity.

We report the results of psychophysical experiments on color contrast induction. In earlier work [Vision Res. 34, 3111 (1994)], we showed that modulating the spatial contrast of an annulus in time induces an apparent modulation of the contrast of a central disk, at isoluminance. Here we vary the chromatic properties of disk and annulus systematically in a study of the interactions among the luminance and the color-opponent channels. Results show that induced contrast depends linearly on both disk and annulus contrast, at low and moderate contrast levels. This dependence leads us to propose a bilinear model for color contrast gain control. The model predicts the magnitude and the chromatic properties of induced contrast. In agreement with experimental results, the model displays chromatic selectivity in contrast gain control and a negligible effect of contrast modulation at isoluminance on the appearance of achromatic contrast. We show that the bilinear model for chromatic selectivity may be realized as a feed-forward multiplicative gain control. Data collected at high contrast levels are fit by embellishing the model with saturating nonlinearities in the contrast gain control of each color channel.

Color contrast induction.

We report the results of psychophysical experiments on the intensive, spatial, temporal and chromatic properties of color contrast induction. Modulating the contrast of an annulus induces an apparent modulation of the color contrast of a central disk, at isoluminance. Results of varying the size of the annulus suggest that mechanisms which control contrast gain are spatially localized. Results of varying the orientations of disk and annulus patterns, with peak spatial frequencies at about 2 c/deg, suggest that the mechanisms are spatially isotropic. Results of varying the rate at which annulus contrast is modulated shows that mechanisms which mediate contrast induction have a low-pass temporal sensitivity that cuts off at about 8 Hz. Results of an experiment on the interocular transfer of color contrast induction suggest that the induction has a cortical locus. Finally, the results of varying the chromatic properties of disk and annulus suggest that the underlying mechanisms are partially, but not fully, chromatically selective.

Color constancy. III. General linear recovery of spectral descriptions for lights and surfaces.

We present a color-constancy algorithm that uses quantum-catch data from reflected lights to recover surface reflectance functions and illuminant spectral power distributions. The algorithm recovers both surface and light-source spectral properties simultaneously. The method works in all situations that were handled by the earlier two-stage algorithms of Maloney and Wandell [J. Opt. Soc. Am. A 3, 29 (1986)] and D'Zmura and Iverson [J. Opt. Soc. Am. A 9, 490 (1992); 10, 2148, 2166 (1993); 11, 1970 (1994)]. In addition, the method handles problems that lie outside the scope of earlier algorithms. Using this method, a trichromatic visual system can recover, when provided adequate information, spectral descriptions of arbitrarily high accuracy for lights and surfaces. We determine conditions under which bilinear models can be used to recover color properties uniquely with the new procedure, and we formulate an algorithm for checking whether a particular bilinear model provides perfect color constancy. This research extends our analysis of linear methods for color constancy begun earlier [J. Opt. Soc. Am. A 10, 2148, 2166 (1993)].

Criteria for color constancy in trichromatic bilinear models.

We examine conditions under which the spectral properties of lights and surfaces may be recovered by a trichromatic visual system that uses bilinear models. We derive criteria for perfect recovery, formulated in terms of invariant properties of model matrices, for situations in which either two or three lights are shown sequentially on a set of surfaces.

Detection of contrary chromatic change.

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.

Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces.

Changing a scene's illuminant causes the chromatic properties of reflected lights to change. This change in the lights from surfaces provides spectral information about surface reflectances and illuminants. We examine conditions under which these properties may be recovered by using bilinear models. Necessary conditions that follow from comparing the number of equations and the number of unknowns in the recovery procedure are not sufficient for unique recovery. Necessary and sufficient conditions follow from demanding a one-to-one relationship between quantum catch data and sets of lit surfaces. We present an algorithm for determining whether spectral descriptions of lights and surfaces can be recovered uniquely from reflected lights.

Color constancy. II. Results for two-stage linear recovery of spectral descriptions for lights and surfaces.

Our analysis of color constancy in a companion paper [J. Opt. Soc. Am A 10, 2148 (1993)] provided an algorithm that lets one test how well linear color constancy schemes work. Here we present the results of applying the algorithm to a large parametric class of color constancy problems involving bilinear models that relate photoreceptoral spectral sensitivities, surface reflectance functions, and illuminant spectral power distributions. These results, supported by simulation and further analysis, provide a detailed classification of two-stage linear methods for recovering the spectral properties of reflectances and illuminants from reflected lights.

Color in visual search.

Colored targets pop out of displays under conditions in which the standard red-green, yellow-blue and black-white mechanisms cannot directly mediate detection. Experimental evidence suggests that observers possess chromatic detection mechanisms tuned to intermediate hues such as orange as well as to hues characterizing the standard color-opponent mechanisms and that these mechanisms, as a group, form a fine-grained representation of hue within the central visual field. Spatially-parallel search is mediated by a single such mechanism that is spectrally sensitive to the target chromaticity but insensitive to the distractor chromaticities; different mechanisms are used to detect a single target in a way that depends on distractor chromaticities.

Mechanisms of color vision.

We review the physiological and psychophysical research on mechanisms of color vision. Psychophysical work has led to the formulation of explicit theories of the early stages of color vision. The principal postulates of these theories have been confirmed by physiologists (e.g., the existence of three classes of receptors and second-stage mechanisms in which the signals from these receptors are compared), but some important features of the psychophysical scheme have found limited physiological support. One such issue is the absence of the unitary "achromatic" mechanism required by psychophysicists. We know a good deal less about the chromatic analyses that occur beyond these early stages. Although physiologists have devoted much effort to the study of cortical mechanisms, little of this work has been guided by clear ideas of the tasks performed by them. The provision of color constancy and the ability to segment scenes are perhaps the foremost concerns of chromatic mechanisms, and recent psychophysical work bearing on these problems offers physiologists clearer guidance on what to seek with their electrodes.

Mechanisms of color constancy.

We develop a model of how the visual system finds the colors of objects that have unknown shapes and positions. The model relies on mechanisms of light adaptation, coupled with eye movements, to recover three descriptors of surface reflectance that are represented in the signals of an achromatic mechanism and two color-opponent mechanisms. These descriptors are transformed to yield estimates of hue, the dimension of surface color that is independent of object shape and viewing geometry.

Shared pathways for rod and cone vision.

We have used heterochromatic gratings falling on 10 deg temporal retina to measure the spatial contrast sensitivities of the isolated rod and cone systems in the mesopic range. As the level of illumination was raised within this range, the contrast sensitivity of the rod system increased, reaching a peak of about 50 (and providing an acuity of 6 c/deg) at 20 scot. td, whereupon the rod system began to saturate. Over most of the mesopic range the sensitivity of the cone system was lower than that of the rod system, although it provided better acuity (up to 15 c/deg). Within the range of spatial frequencies capable of exciting both rod and cone systems, a grating that excited only rods was indistinguishable from a grating of the same spatial frequency that excited only cones. Moreover, contrast adaptation to gratings that excited either rods or cones raised threshold for gratings that excited rods or cones. From these results we conclude that signals from rods and cones travel together in pathways subserving the detection of low spatial frequencies, while only signals from cones travel in pathways subserving the detection of high spatial frequencies.