Subtract space average color

Another possibility is to subtract space average color in order to adjust the colors of the image (Ebner 2003a). This method of color constancy was also used by Moore et al. (1991). 

If we subtract this vector from the current color, we move local space average color back to the gray vector. This is visualized in Figure 11.6. Let C = [cr, c . cb T be the color of the input pixel. Thus, output colors can be calculated by subtracting the component of local space average color, which is perpendicular to the gray vector. 

Figure 11.5 For these images, output pixels were calculated by subtracting the component of local space average color, which is perpendicular to the gray vector, from the current pixel color.

That is, we project both colors onto the plane with r + g + b = 1. We can calculate the component perpendicular to the gray vector by projecting local space average color onto the gray vector and subtracting the resulting vector from local space average color. 

Figure 11.8 The color of the current pixel c, and local space average color a are projected onto the plane r + g + b = 1. Let c and a be the normalized points. Now, normalized local space average color is projected onto the gray vector w. The projection is subtracted from a, which gives us ax- The component ax is orthogonal to the gray vector w. This component is subtracted from the color of the current pixel that gives us the normalized output color 6. Finally, the output color is scaled back to the intensity of the input pixel.

Given the maximum deviation between local space average color and the pixel intensity, the output pixels are calculated as follows. First, local space average color is subtracted from the current intensity. Then, the deviation dj is used to rescale the difference. Henceforth, we drop the coordinate of the current processing element. 

The algorithm described in Section 11.2 subtracts the component of local space average color that is orthogonal to the gray vector from the color of the input pixel. Let cp be the color of the input pixel and let a be the local space average color. Let c = [cr,cg, cj,] be the average value of the components of a pixel, i.e. a denotes the average value of... 

The algorithm described in Section 11.5 subtracts local space average color from the color of the input pixel. Each channel is then scaled by a factor that depends on the maximum... 

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