Poster on Colour constancy via horizontal cells, page 02

feedforward algorithm

The mean of the light from natural scenes is supposed to bear an information about colour of the illuminant. In such an assumption one of the simplest algorithm of discounting the illumination using the space-averaged signals from retinal cones might look as follows.

X_i^R = S^R ·r_i^R X_i^G = S^G ·r_i^G X_i^B = S^B ·r_i^B
(1)	log X_i^R = log S^R + logr_i^R …
(2)	y^R = ¹/_N ·S log X_i^R – C^R = log S^R + ¹/_N ·S logr_i^R – C^R
Under the gray world assumption, the middle term in (2) is stable in different scenes, and the constant C^R in the algorithm have to be fixed to compensate it. Then the average, y^R, will estimate the light source: y^R = log S^R
(3)	z_i^R = log X_i^R – y^R = log S^R + logr_i^R – log S^R = logr_i^R …
(4)	Z_i^R = exp( z_i^R ) = r_i^R …