From: Steinar H. Gunderson
Date: Sat, 3 Nov 2012 16:39:11 +0000 (+0100)
Subject: When correcting for white balance, move the D65 normalization into compute_lms_scalin...
XGitTag: 1.0~211
XGitUrl: https://git.sesse.net/?p=movit;a=commitdiff_plain;h=181fca60b28290c92207cfb40e27113e4f5f021c;ds=sidebyside
When correcting for white balance, move the D65 normalization into compute_lms_scaling_factors() instead of folding it into the LMS matrix. This makes much more sense, and should be equivalent.

diff git a/white_balance_effect.cpp b/white_balance_effect.cpp
index f185228..8a495fb 100644
 a/white_balance_effect.cpp
+++ b/white_balance_effect.cpp
@@ 67,41 +67,34 @@ double rgb_to_xyz_matrix[9] = {
* The actual perceptual differences were found to be minor, though.
* We use the Bradford tranformation matrix from that page, and compute the
* inverse ourselves. (The Bradford matrix is also used in CMCCAT97.)
 *
 * We normalize the Bradford fundamentals to D65, which means that the standard
 * D65 illuminant (x=0.31271, y=0.32902, z=1yx) gives L=M=S under this
 * transformation. This makes sense because sRGB (which is used to derive
 * those XYZ values in the first place) assumes the D65 illuminant, and so the
 * D65 illuminant also gives R=G=B in sRGB. (We could also have done this
 * step separately in XYZ space, but we'd have to do it to all colors we
 * wanted scaled to LMS.)
*/
const double xyz_to_lms_matrix[9] = {
 0.8951 / d65_X, 0.7502 / d65_X, 0.0389 / d65_X,
 0.2664, 1.7135, 0.0685,
 0.1614 / d65_Z, 0.0367 / d65_Z, 1.0296 / d65_Z,
+ 0.7328, 0.7036, 0.0030,
+ 0.4296, 1.6975, 0.0136,
+ 0.1624, 0.0061, 0.9834,
};
/*
 * For a given reference color (given in XYZ space),
 * compute scaling factors for L, M and S. What we want at the output is equal L, M and S
 * for the reference color (making it a neutral illuminant), or sL ref_L = sM ref_M = sS ref_S.
 * This removes two degrees of freedom for our system, and we only need to find fL.
+ * For a given reference color (given in XYZ space), compute scaling factors
+ * for L, M and S. What we want at the output is turning the reference color
+ * into a scaled version of the D65 illuminant (giving it R=G=B in sRGB), or
+ *
+ * (sL ref_L, sM ref_M, sS ref_S) = (s d65_L, s d65_M, s d65_S)
*
+ * This removes two degrees of freedom from our system, and we only need to find s.
* A reasonable last constraint would be to preserve Y, approximately the brightness,
 * for the reference color. Since L'=M'=S' and the Y row of the LMStoXYZ matrix
 * sums to unity, we know that Y'=L', and it's easy to find the fL that sets Y'=Y.
+ * for the reference color. Thus, we choose our D65 illuminant's Y such that it is
+ * equal to the reference color's Y, and the rest is easy.
*/
Vector3d compute_lms_scaling_factors(const Vector3d &xyz)
+Vector3d compute_lms_scaling_factors(const Vector3d &ref_xyz)
{
 Vector3d lms = Map(xyz_to_lms_matrix) * xyz;
 double l = lms[0];
 double m = lms[1];
 double s = lms[2];

 double scale_l = xyz[1] / l;
 double scale_m = scale_l * (l / m);
 double scale_s = scale_l * (l / s);
+ Vector3d ref_lms = Map(xyz_to_lms_matrix) * ref_xyz;
+ Vector3d d65_lms = Map(xyz_to_lms_matrix) *
+ (ref_xyz[1] * Vector3d(d65_X, d65_Y, d65_Z)); // d65_Y = 1.0.
+
+ double scale_l = d65_lms[0] / ref_lms[0];
+ double scale_m = d65_lms[1] / ref_lms[1];
+ double scale_s = d65_lms[2] / ref_lms[2];
return Vector3d(scale_l, scale_m, scale_s);
}