Theoretical Analysis of Color Constancy Algorithms

We start with a theoretical analysis of the algorithms. Before we address each algorithm in turn, let us define a suitable stimulus. We assume that a sample is placed on a uniform background. Let Rp be the reflectance of the sample and let R g be the reflectance of the background. Let L be the vector that describes the intensity of the illuminant for the three primaries red, green, and blue. Then, the color cp = cr, cg, ci,]T of the sample (as measured by the sensor) is given by 

These are the two colors measured by the image sensor. In practice, intermediate colors also occur at the boundary of the patch however, this shall not be our concern here. This input stimulus is processed by a color constancy algorithm. In the following text, we will calculate the output color for each algorithm in turn. 

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In this case, the output color o = [or, og, 0, ]T of the sample will be 

If the reflectance of the sample is equivalent to the reflectance of the background, then all input pixels will be equivalent. If we divide the pixel color by the maximum, then we again obtain an output value of [1, 1, l]r. Therefore, the output will be achromatic. 

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