#include <math.h>
#include <assert.h>
+#include <GL/glew.h>
+
+#include <Eigen/LU>
#include "white_balance_effect.h"
#include "util.h"
-#include "opengl.h"
+#include "d65.h"
+
+using namespace Eigen;
namespace {
// Temperature is in Kelvin. Formula from http://en.wikipedia.org/wiki/Planckian_locus#Approximation .
-void convert_color_temperature_to_xyz(float T, float *x, float *y, float *z)
+Vector3d convert_color_temperature_to_xyz(float T)
{
double invT = 1.0 / T;
- double xc, yc;
+ double x, y;
assert(T >= 1000.0f);
assert(T <= 15000.0f);
if (T <= 4000.0f) {
- xc = ((-0.2661239e9 * invT - 0.2343580e6) * invT + 0.8776956e3) * invT + 0.179910;
+ x = ((-0.2661239e9 * invT - 0.2343580e6) * invT + 0.8776956e3) * invT + 0.179910;
} else {
- xc = ((-3.0258469e9 * invT + 2.1070379e6) * invT + 0.2226347e3) * invT + 0.240390;
+ x = ((-3.0258469e9 * invT + 2.1070379e6) * invT + 0.2226347e3) * invT + 0.240390;
}
if (T <= 2222.0f) {
- yc = ((-1.1063814 * xc - 1.34811020) * xc + 2.18555832) * xc - 0.20219683;
+ y = ((-1.1063814 * x - 1.34811020) * x + 2.18555832) * x - 0.20219683;
} else if (T <= 4000.0f) {
- yc = ((-0.9549476 * xc - 1.37418593) * xc + 2.09137015) * xc - 0.16748867;
+ y = ((-0.9549476 * x - 1.37418593) * x + 2.09137015) * x - 0.16748867;
} else {
- yc = (( 3.0817580 * xc - 5.87338670) * xc + 3.75112997) * xc - 0.37001483;
+ y = (( 3.0817580 * x - 5.87338670) * x + 3.75112997) * x - 0.37001483;
}
- *x = xc;
- *y = yc;
- *z = 1.0 - xc - yc;
+ return Vector3d(x, y, 1.0 - x - y);
}
// Assuming sRGB primaries, from Wikipedia.
-static const Matrix3x3 rgb_to_xyz_matrix = {
+const double rgb_to_xyz_matrix[9] = {
0.4124, 0.2126, 0.0193,
0.3576, 0.7152, 0.1192,
0.1805, 0.0722, 0.9505,
};
/*
- * There are several different LMS spaces, at least according to Wikipedia.
- * Through practical testing, I've found most of them (like the CIECAM02 model)
- * to yield a result that is too reddish in practice, possibly because they
- * are intended for different illuminants than what sRGB assumes.
+ * There are several different perceptual color spaces with different intended
+ * uses; for instance, CIECAM02 uses one space (CAT02) for purposes of computing
+ * chromatic adaptation (the effect that the human eye perceives an object as
+ * the same color even under differing illuminants), but a different space
+ * (Hunt-Pointer-Estevez, or HPE) for the actual perception post-adaptation.
+ *
+ * CIECAM02 chromatic adaptation, while related to the transformation we want,
+ * is a more complex phenomenon that depends on factors like the viewing conditions
+ * (e.g. amount of surrounding light), and can no longer be implemented by just scaling
+ * each component in LMS space. The simpler way out is to use the HPE matrix,
+ * which is intended to be close to the actual cone response; this results in
+ * the “von Kries transformation” when we couple it with normalization in LMS space.
*
- * This is the RLAB space, normalized to D65, which means that the standard
- * D65 illuminant (x=0.31271, y=0.32902, z=1-y-x) 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.
+ * http://www.brucelindbloom.com/index.html?Eqn_ChromAdapt.html compares
+ * von Kries transformation with using another matrix, the Bradford matrix,
+ * and generally finds that the Bradford method gives a better result,
+ * as in giving better matches with the true result (as calculated using
+ * spectral matching) when converting between various CIE illuminants.
+ * 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.)
*/
-static const Matrix3x3 xyz_to_lms_matrix = {
- 0.4002, -0.2263, 0.0,
- 0.7076, 1.1653, 0.0,
- -0.0808, 0.0457, 0.9182,
+const double xyz_to_lms_matrix[9] = {
+ 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 LMS-to-XYZ 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.
*/
-static void compute_lms_scaling_factors(float x, float y, float z, float *scale_l, float *scale_m, float *scale_s)
+Vector3d compute_lms_scaling_factors(const Vector3d &ref_xyz)
{
- float l, m, s;
- multiply_3x3_matrix_float3(xyz_to_lms_matrix, x, y, z, &l, &m, &s);
+ Vector3d ref_lms = Map<const Matrix3d>(xyz_to_lms_matrix) * ref_xyz;
+ Vector3d d65_lms = Map<const Matrix3d>(xyz_to_lms_matrix) *
+ (ref_xyz[1] * Vector3d(d65_X, d65_Y, d65_Z)); // d65_Y = 1.0.
- *scale_l = y / l;
- *scale_m = *scale_l * (l / m);
- *scale_s = *scale_l * (l / s);
+ 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);
}
} // namespace
void WhiteBalanceEffect::set_gl_state(GLuint glsl_program_num, const std::string &prefix, unsigned *sampler_num)
{
- float x, y, z;
- multiply_3x3_matrix_float3(rgb_to_xyz_matrix, neutral_color.r, neutral_color.g, neutral_color.b, &x, &y, &z);
-
- float l, m, s;
- multiply_3x3_matrix_float3(xyz_to_lms_matrix, x, y, z, &l, &m, &s);
-
- float l_scale, m_scale, s_scale;
- compute_lms_scaling_factors(x, y, z, &l_scale, &m_scale, &s_scale);
+ Vector3d rgb(neutral_color.r, neutral_color.g, neutral_color.b);
+ Vector3d xyz = Map<const Matrix3d>(rgb_to_xyz_matrix) * rgb;
+ Vector3d lms_scale = compute_lms_scaling_factors(xyz);
/*
* Now apply the color balance. Simply put, we find the chromacity point
* since the D65 illuminant does not exactly match the results of T=6500K);
* we normalize so that T=6500K really is a no-op.
*/
- float white_x, white_y, white_z, l_scale_white, m_scale_white, s_scale_white;
- convert_color_temperature_to_xyz(output_color_temperature, &white_x, &white_y, &white_z);
- compute_lms_scaling_factors(white_x, white_y, white_z, &l_scale_white, &m_scale_white, &s_scale_white);
-
- float ref_x, ref_y, ref_z, l_scale_ref, m_scale_ref, s_scale_ref;
- convert_color_temperature_to_xyz(6500.0f, &ref_x, &ref_y, &ref_z);
- compute_lms_scaling_factors(ref_x, ref_y, ref_z, &l_scale_ref, &m_scale_ref, &s_scale_ref);
-
- l_scale *= l_scale_ref / l_scale_white;
- m_scale *= m_scale_ref / m_scale_white;
- s_scale *= s_scale_ref / s_scale_white;
-
+ Vector3d white_xyz = convert_color_temperature_to_xyz(output_color_temperature);
+ Vector3d lms_scale_white = compute_lms_scaling_factors(white_xyz);
+
+ Vector3d ref_xyz = convert_color_temperature_to_xyz(6500.0f);
+ Vector3d lms_scale_ref = compute_lms_scaling_factors(ref_xyz);
+
+ lms_scale[0] *= lms_scale_ref[0] / lms_scale_white[0];
+ lms_scale[1] *= lms_scale_ref[1] / lms_scale_white[1];
+ lms_scale[2] *= lms_scale_ref[2] / lms_scale_white[2];
+
/*
* Concatenate all the different linear operations into a single 3x3 matrix.
* Note that since we postmultiply our vectors, the order of the matrices
* has to be the opposite of the execution order.
*/
- Matrix3x3 lms_to_xyz_matrix, xyz_to_rgb_matrix;
- invert_3x3_matrix(xyz_to_lms_matrix, lms_to_xyz_matrix);
- invert_3x3_matrix(rgb_to_xyz_matrix, xyz_to_rgb_matrix);
-
- Matrix3x3 temp, temp2, corr_matrix;
- Matrix3x3 lms_scale_matrix = {
- l_scale, 0.0f, 0.0f,
- 0.0f, m_scale, 0.0f,
- 0.0f, 0.0f, s_scale,
- };
- multiply_3x3_matrices(xyz_to_rgb_matrix, lms_to_xyz_matrix, temp);
- multiply_3x3_matrices(temp, lms_scale_matrix, temp2);
- multiply_3x3_matrices(temp2, xyz_to_lms_matrix, temp);
- multiply_3x3_matrices(temp, rgb_to_xyz_matrix, corr_matrix);
-
+ Matrix3d corr_matrix =
+ Map<const Matrix3d>(rgb_to_xyz_matrix).inverse() *
+ Map<const Matrix3d>(xyz_to_lms_matrix).inverse() *
+ lms_scale.asDiagonal() *
+ Map<const Matrix3d>(xyz_to_lms_matrix) *
+ Map<const Matrix3d>(rgb_to_xyz_matrix);
set_uniform_mat3(glsl_program_num, prefix, "correction_matrix", corr_matrix);
}
projects / movit / blobdiff