On the dichromatic object-colour palette.

The object- and light-colour palettes prove to be different for both trichromats and dichromats. This explains why there is no consensus on what colours dichromats see, since, until now, studies of dichromatic vision have mainly focused on the light-colour palette. By contrast, this study concentrates on the dichromatic object-colour palette, assuming that it is as much determined by optimal reflectances as the trichromatic palette.

On Counting Metamers.

Objects reflecting lights, which invoke the identical responses of the photoreceptors, are called metameric. Metameric objects match each other in color. Assuming all the reflecting objects equiprobable, the probability density distribution on the set of all the classes of mutually metameric objects is evaluated.

The Achromatic Object-Colour Manifold is Three-Dimensional.

When in shadow, the achromatic object colours appear different from when they are in light. This immediate observation was quantitatively confirmed by Logvinenko and Maloney (2006, Perception & Psychophysics, 68, 76-83) who, using multidimensional scaling (MDS), showed the two-dimensionality of achromatic object colours. As their experiments included only cast shadows, a question arises: is this also the case for attached shadows? Recently, Madigan and Brainard (2014) argued in favour of the negative answer.

The color cone.

While the notion of a color cone can be found in writings of Maxwell, Helmholtz, Grassmann, and other scientists of the nineteenth century, it has not been clearly defined as yet. In this paper, the color cone is understood as the set of points in the cone excitation space produced by all possible lights. The spectral curve representing all the monochromatic lights is shown not to entirely belong to the color cone boundary, since its ends turn into the color cone interior.

Rethinking Colour Constancy.

Colour constancy needs to be reconsidered in light of the limits imposed by metamer mismatching. Metamer mismatching refers to the fact that two objects reflecting metameric light under one illumination may reflect non-metameric light under a second; so two objects appearing as having the same colour under one illuminant can appear as having different colours under a second. Yet since Helmholtz, object colour has generally been believed to remain relatively constant.

How metamer mismatching decreases as the number of colour mechanisms increases with implications for colour and lightness constancy.

Metamer mismatching has been previously found to impose serious limitations on colour constancy. The extent of metamer mismatching is shown here to be considerably smaller for trichromats than for dichromats, and maximal for monochromats. The implications for achromatic colour perception are discussed.

The geometric structure of color.

Color is commonly described in terms of the three perceptual attributes-hue, saturation, and brightness-of which only hue has a qualitative nature, saturation and brightness being of a quantitative nature. A possible reason for such a phenomenological structure of the color manifold, and its geometric representation, are discussed.

Metamer mismatching.

A new algorithm for calculating the metamer mismatch volumes that arise in colour vision and colour imaging is introduced. Unlike previous methods, the proposed method places no restrictions on the set of possible object reflectance spectra. As a result of such restrictions, previous methods have only been able to provide approximate solutions to the mismatch volume.

Unique hues as revealed by unique-hue selecting versus partial hue-matching.

Unique hues are usually defined as those that cannot be introspectively reduced to any other hue. According to a major dogma of color science, there are four unique hues: yellow, blue, red, and green. Yet only 55 of the 173 inexperienced observers who participated in our experiment selected exactly four Munsell papers that, according to their judgment, had a unique hue.

Color constancy investigated via partial hue-matching.

Each hue is believed to be made up of the four component hues (yellow, blue, red, and green). A hue consisting of just one component hue is called unitary (or unique). A new technique--partial hue-matching--has been used to reveal the component and unitary hues for a sample of 32 Munsell papers, which were illuminated by neutral, yellow, blue, green, and red lights and assessed by four normal trichromatic observers.

A test for psychometric function shift.

A nonparametric, small-sample-size test for the homogeneity of two psychometric functions against the left- and right-shift alternatives has been developed. The test is designed to determine whether it is safe to amalgamate psychometric functions obtained in different experimental sessions. The sum of the lower and upper p-values of the exact (conditional) Fisher test for several 2 × 2 contingency tables (one for each point of the psychometric function) is employed as the test statistic.

Colour constancy as measured by least dissimilar matching.

Although asymmetric colour matching has been widely used in experiments on colour constancy, an exact colour match between objects lit by different chromatic lights is impossible to achieve. We used a modification of this technique, instructing our observers to establish the least dissimilar pair of differently illuminated coloured papers. The stimulus display consisted of two identical sets of 22 Munsell papers illuminated independently by neutral, yellow, blue, green and red lights.

Partial hue-matching.

It is widely believed that color can be decomposed into a small number of component colors. Particularly, each hue can be described as a combination of a restricted set of component hues. Methods, such as color naming and hue scaling, aim at describing color in terms of the relative amount of the component hues.

Lightness constancy and illumination discounting.

Contrary to the implication of the term "lightness constancy", asymmetric lightness matching has never been found to be perfect unless the scene is highly articulated (i.e., contains a number of different reflectances).

Hue manifold.

It is generally accepted that hues can be arranged so as to make a circle. The circular representation of hue has been supported by multidimensional scaling, which allows for the representation of a set of colored papers as a configuration in a Euclidean space where the distances between the papers correspond to the perceptual dissimilarities between them. In particular, when papers of various hues are evenly illuminated, they are arranged in a one-dimensional circular configuration.

Material and lighting hues of object colour.

Observers can easily differentiate between a pigmented stain and the white surface that it lies on. The same applies for a colour shadow cast upon the same surface. Although the difference between these two kinds of colour appearance (referred to as material and lighting hues) is self-evident even for inexperienced observers, it is not one that has been captured by any colour appearance model thus far.

Material and lighting dimensions of object colour.

The dimensionality of the object colour manifold was studied using a multidimensional scaling technique, which allows for the representation of a set of coloured papers as a configuration in a Euclidean space where the distance between papers corresponds to the perceptual dissimilarities between them. When the papers are evenly illuminated they can be arranged as a three-dimensional configuration. This is in line with the generally accepted view that the object colour space is three-dimensional.

An object-color space.

Putting aside metaphorical meanings of the term, color space is understood as a vector space, where lights having the same color (i.e., subjectively indistinguishable) are represented as a point.

A scaling analysis of the snake lightness illusion.

Logvinenko and Maloney (2006) measured perceived dissimilarities between achromatic surfaces placed in two scenes illuminated by neutral lights that could differ in intensity. Using a novel scaling method, they found that dissimilarities between light surface pairs could be represented as a weighted linear combination of two dimensions, "surface lightness" (a perceptual correlate of the difference in the logarithm of surface albedo) and "surface brightness" (which corresponded to the differences of the logarithms of light intensity across the scenes). Here we attempt to measure the contributions of these dimensions to a compelling lightness illusion (the "snake illusion").

Dissimilarity of yellow-blue surfaces under neutral light sources differing in intensity: separate contributions of light intensity and chroma.

Observers viewed two side-by-side arrays each of which contained three yellow Munsell papers, three blue, and one neutral Munsell. Each array was illuminated uniformly and independently of the other. The neutral light source intensities were 1380, 125, or 20 lux.

Evidence for the existence of colour mechanisms producing unique hues as derived from a colour illusion based on spatio-chromatic interactions.

When its spatial frequency is high enough, a grid of grey horizontal strips presented on a coloured background may change its neutral colour. It was found that some background colours induce a strong illusion and some no illusion at all. The effect of the background colour on the illusion was studied for the spatial frequencies of 0.

The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching.

In asymmetric lightness matching tasks, observers sometimes report that they cannot achieve satisfactory matches between achromatic surfaces under different neutral illuminants. The surfaces appear different, yet no further adjustment of either surface improves the match. There are evident difficulties in interpreting data from a task that the observer cannot always do, and these difficulties likely affect the interpretation of a large number of previous studies.

An effect of luminance contrast on high-spatial-frequency tritanopia.

Luminance contrast was found to affect high-spatial-frequency tritanopia despite the S-cone coordinates of the stimuli being kept constant. This proves that a traditional account of artificial tritanopias based on the spatial resolution differences between the S-cone channel and the M- and L-cone channels is not applicable here. We suggest that the lack of spatial resolution in one of the post-receptor (rather than receptor) spatio-chromatic channels could be a cause of high-spatial-frequency tritanopia.

One blue colour channel or two?

Contrary to the general belief that the yellow-blue mechanism has lower spatial resolution than the red-green mechanism, it has been recently claimed that both mechanisms have similar spatial sensitivity (McKeefry et al, 2001 Vision Research 41 245-255). Studying high-spatial-frequency tritanopia (a colour illusion based on spatio-chromatic interactions in human vision), we found strong evidence for the existence of two blue mechanisms-with low and high spatial-frequency resolution. If confirmed, this may resolve the apparent paradox concerning spatial resolution of the yellow-blue mechanism.