Curved Line of Constant Illumination

The solution to this problem is also clear. We need to calculate the local curvature of the illuminant for each processing element. Then, we can average the values along the line of constant illumination even if the shape of the change of the illuminant is curved. The curvature K of a point (x, y) on a surface F(x, y) is defined as (Bronstein et al. 2001) 

if we have an estimate of the illuminant, we can compute the local curvature for each 

The sign of the curvature K tells us on which side of the curve the center of the curvature lies. If K 0, then the center of the curvature lies on the positive side of the curve normal. It lies on the negative side of the curve normal if K 0. If K = 0, then the line of constant illumination is really a straight line. 

By substituting the first equation into the second equation, we can solve for x. 

COMPUTING ANISOTROPIC LOCAL SPACE AVERAGE COLOR 

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