Formal connections between lightness algorithms

Abstract

The computational problem underlying color vision is to recover the invariant surface-spectral-reflectance properties of an object. Lightness algorithms, which recover an approximation to surface reflectance in independent wavelength channels, have been proposed as one method to compute color. This paper clarifies and formalizes the lightness problem by proposing a new formulation of the intensity equation on which lightness algorithms are based and by identifying and discussing two basic subproblems of lightness and color computation: spatial decomposition and spectral normalization of the intensity signal. Several lightness algorithms are reviewed, and a new extension (the multiple-scales algorithm) of one of them is proposed. The main computational result is that each of the lightness algorithms may be derived from a single mathematical formula, under different conditions, which, in turn, imply limitations for the implementation of lightness algorithms by man or machine. In particular, the algorithms share certain limitations on their implementation that follow from the physical constraints imposed on the statement of the problem and the boundary conditions applied in its solution.

Lightness, equivalent backgrounds, and anchoring

“…The aim ofthe first process is to define a scale of relative gray values (Arend, 1985;Blake, 1985;Gilchrist, Delman, & Jacobsen, 1983;Horn, 1974;Hurlbert, 1986;Land & McCann, 1971;Whittle & Challands, 1969). The aim of the second process is to "anchor" such a scale to a common reference, so that each surface can be assigned an absolute lightness (Cataliotti & Gilchrist, 1995).…”

“…The aim of the second process is to "anchor" such a scale to a common reference, so that each surface can be assigned an absolute lightness (Cataliotti & Gilchrist, 1995). To date, three means of computing the reference term have been proposed: spaceaverage luminance (Helson, 1943(Helson, , 1964Hurlbert, 1986;Hurlbert & Poggio, 1988;Judd, 1940;Land, 1986;Land, Hubel, Livingstone, Perry, & Burns, 1983), space-average contrast (Brown & MacLeod, 1991), and the highest lu-…”

“…Whereas, ifthe highest luminance is kept constant while the average is varied, colors change only slightly (McCann, 1989(McCann, , 1992. Finally, the main rationale behind averaging, the "gray world" assumption (Hurlbert, 1986), has been challenged by statistical analyses of naturally occurring reflectance spectra (Brown, 1994).…”

A multi-channel approach to brightness coding

“…This important class of brightness models originated from the need to account for lightness constancy and the earliest and best known model in this category is that of Land and McCann (197 I) (for a review of this and other Lightness Integration models see Hurlbert, 1986). Lightness constancy is the apparent constancy of lightness and hue in the context of wide variations in the intensive and spectral content of illumination.…”

Effects of luminance oscillations on simulated lightness discriminations

“…The first assumption is that the object with the highest surface reflectance is white (e.g., Land, 1959bLand, , 1964. The other common assumption is that the space-averaged reflectance of a scene is equal to a neutral surface reflectance, sometimes called the gray world hypothesis (Buchsbaum, 1980;Helson, 1938;Hurlbert, 1986). One proposed mechanism to calculate this space-averaged reflectance is through the integration of the individual reflectances in a scene across eye movements (Cornelissen & Brenner, 1995;D'Zmura & Lennie, 1986;Fairchild & Lennie, 1992).…”