E. N. Willmer, W. D. Wright, “Colour sensitivity of the fovea centralis,” Nature 156, 119 (1945); D. R. Williams, D. I. A. MacLeod, M. Hayhoe, “Punctate sensitivity of the blue-sensitive mechanism,” Vision Res. 21, 1357 (1981); F. M. de Monasterio, S. J. Schein, E. P. McCrane, “Staining of blue-sensitive cones of the macaque retina by a fluorescent dye,” Science 213, 1278 (1981).
See K. V. Mardia, J. T. Kent, J. M. Bibby, Multivariate Analysis (Academic, London, 1979), Chap. 8, for a discussion of characteristic vector analysis (also known as principal-components analysis or the Karhunen–Loève decomposition).
E. Krinov, Spectral Reflectance Properties of Natural Formations, Technical translation TT-439 (National Research Council of Canada, Ottawa, 1947); details of the fit of Cohen’s characteristic vectors to the Munsell surface reflectances are given in L. Maloney, “Computational approaches to color constancy,” (Stanford University, Stanford, Calif., 1985).
L. Maloney, “Computational approaches to color constancy,” (Stanford University, Stanford, Calif., 1985).
See Ref. 18, Chap. 4, for details.
D. Brainard, B. Wandell, “An analysis of the retinex theory of color vision,” (Stanford University, Stanford, Calif., 1985).
See P. Sällström, “Colour and physics: some remarks concerning the physical aspects of human colour vision,” (University of Stockholm, Stockholm, 1973).
The computational method that we develop requires only that the ambient light be approximately constant over small local patches of the image. The method is easier to explain if we restrict attention to a region of the image across which the ambient light does not change.
In general the surface reflectance function may depend on the geometry of the scene, the angle of incidence of the light on the surface, and the angle between the surface and the line of sight. We are concerned here with the analysis of a single image drawn from a scene with fixed geometric relations among objects, light sources, and the visual sensor array. Sx(λ) refers to the proportion of light returned from the object toward the sensor array within that fixed geometrical framework.
For a discussion of band-limited functions, see R. Bracewell, The Fourier Transform and Its Application, 2nd ed. (McGraw-Hill, New York, 1978), Chap. 10.
It is not possible to recover E(λ) better than to within a multiplicative constant given only the sensor quantum catches. If, for example, the intensity of the light is doubled to 2E but all reflectances are halved to ½Sx(λ), it is easy to verify that the sensor quantum catches in Eq. (1) are unchanged. When we speak of recovering the ambient light and surface reflectances, we mean recovery up to this unknown mutiplicative constant.