7 #include "effect_util.h"
9 #include "white_balance_effect.h"
11 using namespace Eigen;
15 // Temperature is in Kelvin. Formula from http://en.wikipedia.org/wiki/Planckian_locus#Approximation .
16 Vector3d convert_color_temperature_to_xyz(float T)
18 double invT = 1.0 / T;
22 assert(T <= 15000.0f);
25 x = ((-0.2661239e9 * invT - 0.2343580e6) * invT + 0.8776956e3) * invT + 0.179910;
27 x = ((-3.0258469e9 * invT + 2.1070379e6) * invT + 0.2226347e3) * invT + 0.240390;
31 y = ((-1.1063814 * x - 1.34811020) * x + 2.18555832) * x - 0.20219683;
32 } else if (T <= 4000.0f) {
33 y = ((-0.9549476 * x - 1.37418593) * x + 2.09137015) * x - 0.16748867;
35 y = (( 3.0817580 * x - 5.87338670) * x + 3.75112997) * x - 0.37001483;
38 return Vector3d(x, y, 1.0 - x - y);
41 // Assuming sRGB primaries, from Wikipedia.
42 const double rgb_to_xyz_matrix[9] = {
43 0.4124, 0.2126, 0.0193,
44 0.3576, 0.7152, 0.1192,
45 0.1805, 0.0722, 0.9505,
49 * There are several different perceptual color spaces with different intended
50 * uses; for instance, CIECAM02 uses one space (CAT02) for purposes of computing
51 * chromatic adaptation (the effect that the human eye perceives an object as
52 * the same color even under differing illuminants), but a different space
53 * (Hunt-Pointer-Estevez, or HPE) for the actual perception post-adaptation.
55 * CIECAM02 chromatic adaptation, while related to the transformation we want,
56 * is a more complex phenomenon that depends on factors like the viewing conditions
57 * (e.g. amount of surrounding light), and can no longer be implemented by just scaling
58 * each component in LMS space. The simpler way out is to use the HPE matrix,
59 * which is intended to be close to the actual cone response; this results in
60 * the “von Kries transformation” when we couple it with normalization in LMS space.
62 * http://www.brucelindbloom.com/index.html?Eqn_ChromAdapt.html compares
63 * von Kries transformation with using another matrix, the Bradford matrix,
64 * and generally finds that the Bradford method gives a better result,
65 * as in giving better matches with the true result (as calculated using
66 * spectral matching) when converting between various CIE illuminants.
67 * The actual perceptual differences were found to be minor, though.
68 * We use the Bradford tranformation matrix from that page, and compute the
69 * inverse ourselves. (The Bradford matrix is also used in CMCCAT97.)
71 const double xyz_to_lms_matrix[9] = {
72 0.7328, -0.7036, 0.0030,
73 0.4296, 1.6975, 0.0136,
74 -0.1624, 0.0061, 0.9834,
78 * For a given reference color (given in XYZ space), compute scaling factors
79 * for L, M and S. What we want at the output is turning the reference color
80 * into a scaled version of the D65 illuminant (giving it R=G=B in sRGB), or
82 * (sL ref_L, sM ref_M, sS ref_S) = (s d65_L, s d65_M, s d65_S)
84 * This removes two degrees of freedom from our system, and we only need to find s.
85 * A reasonable last constraint would be to preserve Y, approximately the brightness,
86 * for the reference color. Thus, we choose our D65 illuminant's Y such that it is
87 * equal to the reference color's Y, and the rest is easy.
89 Vector3d compute_lms_scaling_factors(const Vector3d &ref_xyz)
91 Vector3d ref_lms = Map<const Matrix3d>(xyz_to_lms_matrix) * ref_xyz;
92 Vector3d d65_lms = Map<const Matrix3d>(xyz_to_lms_matrix) *
93 (ref_xyz[1] * Vector3d(d65_X, d65_Y, d65_Z)); // d65_Y = 1.0.
95 double scale_l = d65_lms[0] / ref_lms[0];
96 double scale_m = d65_lms[1] / ref_lms[1];
97 double scale_s = d65_lms[2] / ref_lms[2];
99 return Vector3d(scale_l, scale_m, scale_s);
104 WhiteBalanceEffect::WhiteBalanceEffect()
105 : neutral_color(0.5f, 0.5f, 0.5f),
106 output_color_temperature(6500.0f)
108 register_vec3("neutral_color", (float *)&neutral_color);
109 register_float("output_color_temperature", &output_color_temperature);
112 std::string WhiteBalanceEffect::output_fragment_shader()
114 return read_file("white_balance_effect.frag");
117 void WhiteBalanceEffect::set_gl_state(GLuint glsl_program_num, const std::string &prefix, unsigned *sampler_num)
119 Vector3d rgb(neutral_color.r, neutral_color.g, neutral_color.b);
120 Vector3d xyz = Map<const Matrix3d>(rgb_to_xyz_matrix) * rgb;
121 Vector3d lms_scale = compute_lms_scaling_factors(xyz);
124 * Now apply the color balance. Simply put, we find the chromacity point
125 * for the desired white temperature, see what LMS scaling factors they
126 * would have given us, and then reverse that transform. For T=6500K,
127 * the default, this gives us nearly an identity transform (but only nearly,
128 * since the D65 illuminant does not exactly match the results of T=6500K);
129 * we normalize so that T=6500K really is a no-op.
131 Vector3d white_xyz = convert_color_temperature_to_xyz(output_color_temperature);
132 Vector3d lms_scale_white = compute_lms_scaling_factors(white_xyz);
134 Vector3d ref_xyz = convert_color_temperature_to_xyz(6500.0f);
135 Vector3d lms_scale_ref = compute_lms_scaling_factors(ref_xyz);
137 lms_scale[0] *= lms_scale_ref[0] / lms_scale_white[0];
138 lms_scale[1] *= lms_scale_ref[1] / lms_scale_white[1];
139 lms_scale[2] *= lms_scale_ref[2] / lms_scale_white[2];
142 * Concatenate all the different linear operations into a single 3x3 matrix.
143 * Note that since we postmultiply our vectors, the order of the matrices
144 * has to be the opposite of the execution order.
146 Matrix3d corr_matrix =
147 Map<const Matrix3d>(rgb_to_xyz_matrix).inverse() *
148 Map<const Matrix3d>(xyz_to_lms_matrix).inverse() *
149 lms_scale.asDiagonal() *
150 Map<const Matrix3d>(xyz_to_lms_matrix) *
151 Map<const Matrix3d>(rgb_to_xyz_matrix);
152 set_uniform_mat3(glsl_program_num, prefix, "correction_matrix", corr_matrix);