Retinex theory

The trichromatic theory, subsequendy confirmed by the existence of the three sets of cones, must be combined with the opponent theory, which is involved in the retinal pathway. A third approach, the appearance theory (2) or the retinex theory, must be added to explain color constancy and other effects. As one example of this last, consider an area perceived as red in a multicolored object such as a Mondrian painting when illuminated with white... 

Land and McCann (1971) then developed a computational theory for color constancy, the retinex theory. In their experiments, they used a stimulus similar to the famous paintings... 

Figure 1.1 A Mondrian image similar to the one used by Land to develop his retinex theory. Land used colored sheets of paper and arranged them randomly. The resulting image reminded him of the abstract paintings that were drawn by the Dutch artist Piet Mondrian. This is why this stimulus is called a Mondrian image.

Figure 1.2 Spectral transmittances of the filters. The filters were placed in front of the projectors which were used to illuminate the Mondrian image. (Reproduced from Land EH and McCann JJ 1971 Lightness and retinex theory. Journal of the Optical Society of America 61(1), 1-11, by permission from The Optical Society of America.)...

Land and McCann (1971) came to the conclusion that color perception involves structures of the retina as well as the visual cortex. On the basis of these experiments, Land and McCann developed a computational theory of color constancy, the retinex theory. Land later developed additional versions of his retinex theory. The retinex theory of color vision is discussed in detail in Chapter 7. 

Figure 2.20 The transformation performed by the color opponency mechanism may be a simple rotation of the coordinate system. In this case, the mechanism for color constancy may operate on the rotated coordinates. (Reprinted from Vision Res., Vol. 26, No. 1, Edwin H. Land, Recent advances in retinex theory, pp. 7-21, Copyright 1986, with permission from Elsevier.)...

Figure 7.4 Computation of the sequential product along a path on the Mondrian. The rectangles of the Mondrian are symbolized at the top. The reflectance is shown in percent inside each rectangle. Pairs of detectors are spread along the path. These pairs of detectors are used to compute the ratio of the measured luminance. A ratio of 1.0 is assumed for the beginning of the path. Whenever this ratio becomes larger than 1.0, it is reset to 1.0. After the rectangle with a reflectance of 1.0 is passed, the sequential product outputs the reflectance of the rectangle (Reproduced from Land EH and McCann JJ 1971 Lightness and retinex theory. Journal of the Optical Society of America, 61(1), 1-11 by permission from The Optical Society of America.)...

To handle nonuniform illumination, a threshold must be applied to each ratio along the path. If the logarithm of the ratio is larger than the threshold, it is reset to zero. In this case, the output color in Land s retinex theory is calculated as follows (Land 1983 Land et al. 1983). Let (x) be a step function. 

This formulation is similar to Land s alternative version of his retinex theory where each term of the sum computes... 

The computed output color is independent of the illuminant. The retinex theory of color vision was also analyzed in depth by Brainard and Wandell (1992). Brainard and Wandell experimented with color Mondrians consisting of nine colored patches. They found that the retinex algorithm does not correctly predict color appearance when the composition of the Mondrian is varied. The results of Brainard and Wandell could be due to the use of infinite path lengths for the retinex algorithm. The effect of the path length on the retinex algorithm is discussed by (Ciurea and Funt 2004). 

The real-time neural system developed by Moore et al. (1991) is also based on the retinex theory. This holds for the original implementation and the extension proposed by Moore et al. In the extended version, a smoothed version of the derivative of the input image is used to modulate the blurred version of the input image before it is subtracted from the input image. 

The scaling is done uniformly over all three bands red, green, and blue. Thus, we only need to consider the simple version, which is another variant of Land s retinex theory. 

The algorithm of Rahman et al. (1999) is another extension of Land s retinex theory (Land 1986a). The adjustment is done for a number of different scales. The results are added together using a set of weights. Since each intermediate output is independent of the color of the illuminant, the combined output computed by the algorithm of Rahman et al. will also be independent of the color of the illuminant. 

Brainard DH and Wandell BA 1992 Analysis of the retinex theory of color vision In Color (eds. Healey GE, Shafer SA and Wolff LB), pp. 208-218. Jones and Bartlett Publishers, Boston. 

Land EH 1974 The retinex theory of colour vision. Proceedings of the Royal Institution of Great Britain 47, 23-58. 

Land EH 1983 Recent advances in retinex theory and some implications for cortical computations color vision and the natural image. Proceedings of the National Academy of Sciences of the United States of America 80, 5163-5169. 

Land EH 1986b Recent advances in retinex theory. Vision Research 26(1), 7-21. 

Land EH and McCann JJ 1971 Lightness and retinex theory. Journal of the Optical Society of America 61(1), 1-11. 

McCann JJ, McKee SP and Taylor TH 1976 Quantitative studies in retinex theory. Vision Research 16, 445-458. 

Young RA 1987 Color vision and the retinex theory. Science 238, 1731-1732. 

Reprinted from Vision Res., Vol. 26, No. 1, Edwin H. Fand, Recent advances in retinex theory, pp. 7-21, Copyright 1986, with permission from Elsevier... 

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