Sensations of color show a strong correlation with reflectance, even though the amount of visible light reaching the eye depends on the product of reflectance and illumination. The visual system must achieve this remarkable result by a scheme that does not measure flux. Such a scheme is described as the basis of retinex theory. This theory assumes that there are three independent cone systems, each starting with a set of receptors peaking, respectively, in the long-, middle-, and short-wavelength regions of the visible spectrum. Each system forms a separate image of the world in terms of lightness that shows a strong correlation with reflectance within its particular band of wavelengths. These images are not mixed, but rather are compared to generate color sensations. The problem then becomes how the lightness of areas in these separate images can be independen t of flux. This article describes the mathematics of a lightness scheme that generates lightness numbers, the biologic correlate of reflectance, independent of the flux from objects INDEX HEADINGS: Vision; Color.

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Accepting the first postulate of the retinex theory of color vision that there are three independent lightness-determining mechanisms (one for long waves, one for middle waves, and one for short waves), each operative with less than a millisecond exposure and each served by its own retinal pigment, a basic task of retinex theory becomes the determination of the nature of these mechanisms. Earlier references proposed several workable algorithms. On the basis of experiments described in previous papers (1-3, 5), we start from the first postulate of retinex theory: There are three independent lightness-determining mechanisms-one for long waves, one for middle waves, and one for short waves-each served by its own retinal pigment. A basic task of retinex theory becomes the determination of the nature of these mechanisms.Earlier references proposed several useful algorithms (1)(2)(3)(4)(5). This paper will describe a new and relatively simple alternative technique for the computation of the designator in retinex theory. The designator is the computed numerical measure on one waveband of the lightness seen as part of the whole field of view. Previous retinex techniques have involved some kind of comparison between the flux (on one waveband) coming to the eye from a point on the object and flux (on that same waveband) arriving from points in remote, as well as contiguous, areas. These comparisons involve edges, gradients, thresholds, and pathways, and provide the average of the relationships between a given point and a large number of other points in the field of view. The criteria, as in all retinex theory, were that the value determined be independent of uniformity and intensity of illumination and be achievable with an exposure of <1 msec; i.e., independent of adaptation. Keeping the same criteria, the new technique, instead of utilizing an average of these relationships, compares the flux from the point of interest to an average, weighted in an unusual way, of the fluxes from all points in the field.It is easily shown that this average cannot be a simple average taken over the whole field of view. Fig. 1 in a. R1 reflects 8% of the light falling on it, R2 reflects 30%, and R3 reflects 80%. In b, when the illumination is so adjusted by neutral wedges in the illuminator that the flux to the eye (F1) from R1 equals the flux to the eye (F2) from R2 equals the flux to the eye (F3) from R3, the observer will notice that the black stays black, the grey stays grey, and the white stays white, even though the three measured fluxes to the eye are identical. The circle in b represents a 160 diameter field.falling on it, area 2 reflects 30%, and area 3 reflects 80%, the first will look dark, almost black, the second will be a middle grey, and the third will be almost white. If the illumination is so adjusted by neutral wedges in the illuminator that the flux to the eye from R1 equals the flux to the eye from R2 equals the flux to the eye from R3, the observer will scarcely notice. The nearly black area stays dark, the...

In the Color Vision Symposium at the Academy in April 1958, we showed a series of experiments which demonstrated that "whereas in color-mixing theory the wavelengths of the stimuli and the energy content at each wavelength are significant in determining the sense of color . in images neither the wavelength of the stimulus nor the energy at each wavelength determines the color. This departure from what we expect on the basis of colorimetrv is not a small effect, but is complete (1,2). The initial and most engaging experiment comprised taking two black-and-white photographs of the same scene, one through a red filter and one through a green filter, and projecting these two black-and-white pictures in superposition on the screen to yield a single black-and-white panchromatic image of the scene. When a red filter was placed in the path of the light from the projector that contained the picture taken through a red filter, the whole scene became dramatically colored as if in many respects it were a standard full-color photograph. The first paradox was that the radiation coming to the eye of the observer consisted only of various ratios of red light to white light which should have yielded only a variety of pinks. The second paradox was that the overall ratio of light from the one projector to light from the other projector could be changed markedly without changing the color names of the objects in the colored picture: the colors of the individual objects must be determined bv the ratio of red light to white light, but a change in the overall ratio of red light to white light did not change the colors.In light of the understanding which we now have, this simple experiment, which was a shock to the intuitive understanding of all of us, turns out to be the most sophisticated experiment we could have undertaken.For the flavor of the many experiments described at the Symposium, I refer you to the two papers (1, 2) at that time. Here, I want to turn to the quantitative procedures which we now use. We prepared a laboratory display which we dubbed a "Mondrian" (although it actually is closer to a van Doesburg), utilizing about 100 colored papers. A paper of a given color would appear many times in different parts of the display, each time having a different size and shape and each time being surrounded by a different set of other colored papers. One reason for the design was to prohibit the superposition of afterimages of areas onto other areas (3), and another reason for the design was to obviate explanations of results in terms of the size or shape or surrounding of any given paper.The Mondrian is illuminated by using three 35-mm slide projectors with no slides in the slide holder. The output of each projector/illuminator is controlled independently. An interference filter passing long waves is placed in the path of one projector, a middle wave filter, in the path of the second, and a short-wave filter, in the path of the third (Fig. 1). One may think of these as relating roughly to the three visual pigments. A telescopic p...

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