2 * Image Library -- Color Spaces
4 * (c) 2006 Pavel Charvat <pchar@ucw.cz>
6 * This software may be freely distributed and used according to the terms
7 * of the GNU Lesser General Public License.
12 #include "sherlock/sherlock.h"
14 #include "images/images.h"
15 #include "images/color.h"
17 struct color color_black = { .color_space = COLOR_SPACE_GRAYSCALE };
18 struct color color_white = { .c = { 255 }, .color_space = COLOR_SPACE_GRAYSCALE };
21 color_put_grayscale(byte *dest, struct color *color)
23 switch (color->color_space)
25 case COLOR_SPACE_GRAYSCALE:
26 dest[0] = color->c[0];
29 dest[0] = rgb_to_gray_func(color->c[0], color->c[1], color->c[2]);
37 color_put_rgb(byte *dest, struct color *color)
39 switch (color->color_space)
41 case COLOR_SPACE_GRAYSCALE:
42 dest[0] = dest[1] = dest[2] = color->c[0];
45 dest[0] = color->c[0];
46 dest[1] = color->c[1];
47 dest[2] = color->c[2];
55 color_put_color_space(byte *dest, struct color *color, uns color_space)
59 case COLOR_SPACE_GRAYSCALE:
60 color_put_grayscale(dest, color);
63 color_put_rgb(dest, color);
70 /********************* EXACT CONVERSION ROUTINES **********************/
72 /* Reference whites */
73 #define COLOR_ILLUMINANT_A 0.44757, 0.40744
74 #define COLOR_ILLUMINANT_B 0.34840, 0.35160
75 #define COLOR_ILLUMINANT_C 0.31006, 0.31615
76 #define COLOR_ILLUMINANT_D50 0.34567, 0.35850
77 #define COLOR_ILLUMINANT_D55 0.33242, 0.34743
78 #define COLOR_ILLUMINANT_D65 0.31273, 0.32902
79 #define COLOR_ILLUMINANT_D75 0.29902, 0.31485
80 #define COLOR_ILLUMINANT_9300K 0.28480, 0.29320
81 #define COLOR_ILLUMINANT_E (1./3.), (1./3.)
82 #define COLOR_ILLUMINANT_F2 0.37207, 0.37512
83 #define COLOR_ILLUMINANT_F7 0.31285, 0.32918
84 #define COLOR_ILLUMINANT_F11 0.38054, 0.37691
87 color_illuminant_d50[2] = {COLOR_ILLUMINANT_D50},
88 color_illuminant_d65[2] = {COLOR_ILLUMINANT_D65},
89 color_illuminant_e[2] = {COLOR_ILLUMINANT_E};
91 /* RGB profiles (many missing) */
92 const struct color_space_info
93 color_adobe_rgb_info = {"Adobe RGB", {{0.6400, 0.3300}, {0.2100, 0.7100}, {0.1500, 0.0600}, {COLOR_ILLUMINANT_D65}}, {0.45, 0.45, 0, 0, 0}},
94 color_apple_rgb_info = {"Apple RGB", {{0.6250, 0.3400}, {0.2800, 0.5950}, {0.1550, 0.0700}, {COLOR_ILLUMINANT_D65}}, {0.56, 0.56, 0, 0, 0}},
95 color_cie_rgb_info = {"CIE RGB", {{0.7350, 0.2650}, {0.2740, 0.7170}, {0.1670, 0.0090}, {COLOR_ILLUMINANT_E}}, {0.45, 0.45, 0, 0, 0}},
96 color_color_match_rgb_info = {"ColorMatch RGB", {{0.6300, 0.3400}, {0.2950, 0.6050}, {0.1500, 0.0750}, {COLOR_ILLUMINANT_D50}}, {0.56, 0.56, 0, 0, 0}},
97 color_srgb_info = {"sRGB", {{0.6400, 0.3300}, {0.3000, 0.6000}, {0.1500, 0.0600}, {COLOR_ILLUMINANT_D65}}, {0.45, 0.42, 0.055, 0.003, 12.92}};
99 #define CLIP(x, min, max) (((x) < (min)) ? (min) : ((x) > (max)) ? (max) : (x))
104 a[0] = CLIP(a[0], 0, 1);
105 a[1] = CLIP(a[1], 0, 1);
106 a[2] = CLIP(a[2], 0, 1);
110 correct_gamma_simple(double dest[3], double src[3], const struct color_space_gamma_info *info)
112 dest[0] = pow(src[0], info->simple_gamma);
113 dest[1] = pow(src[1], info->simple_gamma);
114 dest[2] = pow(src[2], info->simple_gamma);
118 invert_gamma_simple(double dest[3], double src[3], const struct color_space_gamma_info *info)
120 dest[0] = pow(src[0], 1 / info->simple_gamma);
121 dest[1] = pow(src[1], 1 / info->simple_gamma);
122 dest[2] = pow(src[2], 1 / info->simple_gamma);
126 correct_gamma_detailed(double dest[3], double src[3], const struct color_space_gamma_info *info)
128 for (uns i = 0; i < 3; i++)
129 if (src[i] > info->transition)
130 dest[i] = (1 + info->offset) * pow(src[i], info->detailed_gamma) - info->offset;
132 dest[i] = info->slope * src[i];
136 invert_gamma_detailed(double dest[3], double src[3], const struct color_space_gamma_info *info)
138 for (uns i = 0; i < 3; i++)
139 if (src[i] > info->transition * info->slope)
140 dest[i] = pow((src[i] + info->offset) / (1 + info->offset), 1 / info->detailed_gamma);
142 dest[i] = src[i] / info->slope;
146 apply_matrix(double dest[3], double src[3], double matrix[9])
148 dest[0] = src[0] * matrix[0] + src[1] * matrix[1] + src[2] * matrix[2];
149 dest[1] = src[0] * matrix[3] + src[1] * matrix[4] + src[2] * matrix[5];
150 dest[2] = src[0] * matrix[6] + src[1] * matrix[7] + src[2] * matrix[8];
154 color_invert_matrix(double dest[9], double matrix[9])
156 double *i = dest, *m = matrix;
157 double a0 = m[4] * m[8] - m[5] * m[7];
158 double a1 = m[3] * m[8] - m[5] * m[6];
159 double a2 = m[3] * m[7] - m[4] * m[6];
160 double d = 1 / (m[0] * a0 - m[1] * a1 + m[2] * a2);
164 i[1] = -d * (m[1] * m[8] - m[2] * m[7]);
165 i[4] = d * (m[0] * m[8] - m[2] * m[6]);
166 i[7] = -d * (m[0] * m[7] - m[1] * m[6]);
167 i[2] = d * (m[1] * m[5] - m[2] * m[4]);
168 i[5] = -d * (m[0] * m[5] - m[2] * m[3]);
169 i[8] = d * (m[0] * m[4] - m[1] * m[3]);
173 mul_matrices(double r[9], double a[9], double b[9])
175 r[0] = a[0] * b[0] + a[1] * b[3] + a[2] * b[6];
176 r[1] = a[0] * b[1] + a[1] * b[4] + a[2] * b[7];
177 r[2] = a[0] * b[2] + a[1] * b[5] + a[2] * b[8];
178 r[3] = a[3] * b[0] + a[4] * b[3] + a[5] * b[6];
179 r[4] = a[3] * b[1] + a[4] * b[4] + a[5] * b[7];
180 r[5] = a[3] * b[2] + a[4] * b[5] + a[5] * b[8];
181 r[6] = a[6] * b[0] + a[7] * b[3] + a[8] * b[6];
182 r[7] = a[6] * b[1] + a[7] * b[4] + a[8] * b[7];
183 r[8] = a[6] * b[2] + a[7] * b[5] + a[8] * b[8];
186 /* computes conversion matrix from a given color space to CIE XYZ */
188 color_compute_color_space_to_xyz_matrix(double matrix[9], const struct color_space_chromacity_info *space)
190 double wX = space->white[0] / space->white[1];
191 double wZ = (1 - space->white[0] - space->white[1]) / space->white[1];
193 a[0] = space->prim1[0]; a[3] = space->prim1[1]; a[6] = 1 - a[0] - a[3];
194 a[1] = space->prim2[0]; a[4] = space->prim2[1]; a[7] = 1 - a[1] - a[4];
195 a[2] = space->prim3[0]; a[5] = space->prim3[1]; a[8] = 1 - a[2] - a[5];
196 color_invert_matrix(b, a);
197 double ra = wX * b[0] + b[1] + wZ * b[2];
198 double rb = wX * b[3] + b[4] + wZ * b[5];
199 double rc = wX * b[6] + b[7] + wZ * b[8];
200 matrix[0] = a[0] * ra;
201 matrix[1] = a[1] * rb;
202 matrix[2] = a[2] * rc;
203 matrix[3] = a[3] * ra;
204 matrix[4] = a[4] * rb;
205 matrix[5] = a[5] * rc;
206 matrix[6] = a[6] * ra;
207 matrix[7] = a[7] * rb;
208 matrix[8] = a[8] * rc;
211 /* computes matrix to join transofmations with different reference whites */
213 color_compute_bradford_matrix(double matrix[9], const double source[2], const double dest[2])
215 /* cone response matrix and its inversion */
216 static double r[9] = {
217 0.8951, 0.2664, -0.1614,
218 -0.7502, 1.7135, 0.0367,
219 0.0389, -0.0685, 1.0296};
220 //static double i[9] = {0.9870, -0.1471, 0.1600, 0.4323, 0.5184, 0.0493, -0.0085, 0.0400, 0.9685};
222 color_invert_matrix(i, r);
223 double aX = source[0] / source[1];
224 double aZ = (1 - source[0] - source[1]) / source[1];
225 double bX = dest[0] / dest[1];
226 double bZ = (1 - dest[0] - dest[1]) / dest[1];
227 double x = (r[0] * bX + r[1] + r[2] * bZ) / (r[0] * aX + r[1] + r[2] * aZ);
228 double y = (r[3] * bX + r[4] + r[5] * bZ) / (r[3] * aX + r[4] + r[5] * aZ);
229 double z = (r[6] * bX + r[7] + r[8] * bZ) / (r[6] * aX + r[7] + r[8] * aZ);
231 m[0] = i[0] * x; m[1] = i[1] * y; m[2] = i[2] * z;
232 m[3] = i[3] * x; m[4] = i[4] * y; m[5] = i[5] * z;
233 m[6] = i[6] * x; m[7] = i[7] * y; m[8] = i[8] * z;
234 mul_matrices(matrix, m, r);
238 color_compute_color_spaces_conversion_matrix(double matrix[9], const struct color_space_chromacity_info *src, const struct color_space_chromacity_info *dest)
240 double a_to_xyz[9], b_to_xyz[9], xyz_to_b[9], bradford[9], m[9];
241 color_compute_color_space_to_xyz_matrix(a_to_xyz, src);
242 color_compute_color_space_to_xyz_matrix(b_to_xyz, dest);
243 color_invert_matrix(xyz_to_b, b_to_xyz);
244 if (src->white[0] == dest->white[0] && src->white[1] == dest->white[1])
245 mul_matrices(matrix, a_to_xyz, xyz_to_b);
248 color_compute_bradford_matrix(bradford, src->white, dest->white);
249 mul_matrices(m, a_to_xyz, bradford);
250 mul_matrices(matrix, m, xyz_to_b);
256 srgb_to_xyz_exact(double xyz[3], double srgb[3])
258 static double matrix[9] = {
259 0.41248031, 0.35756952, 0.18043951,
260 0.21268516, 0.71513904, 0.07217580,
261 0.01933501, 0.11918984, 0.95031473};
263 invert_gamma_detailed(srgb_lin, srgb, &color_srgb_info.gamma);
264 apply_matrix(xyz, srgb_lin, matrix);
265 xyz_to_srgb_exact(srgb_lin, xyz);
270 xyz_to_srgb_exact(double srgb[3], double xyz[3])
272 static double matrix[9] = {
273 3.24026666, -1.53704957, -0.49850256,
274 -0.96928381, 1.87604525, 0.04155678,
275 0.05564281, -0.20402363, 1.05721334};
277 apply_matrix(srgb_lin, xyz, matrix);
279 correct_gamma_detailed(srgb, srgb_lin, &color_srgb_info.gamma);
284 xyz_to_luv_exact(double luv[3], double xyz[3])
286 double sum = xyz[0] + 15 * xyz[1] + 3 * xyz[2];
288 luv[0] = luv[1] = luv[2] = 0;
291 double var_u = 4 * xyz[0] / sum;
292 double var_v = 9 * xyz[1] / sum;
293 if (xyz[1] > 0.008856)
294 luv[0] = 116 * pow(xyz[1], 1 / 3.) - 16;
296 luv[0] = (116 * 7.787) * xyz[1];
297 luv[1] = luv[0] * (13 * (var_u - 4 * REF_WHITE_X / (REF_WHITE_X + 15 * REF_WHITE_Y + 3 * REF_WHITE_Z)));
298 luv[2] = luv[0] * (13 * (var_v - 9 * REF_WHITE_Y / (REF_WHITE_X + 15 * REF_WHITE_Y + 3 * REF_WHITE_Z)));
299 /* intervals [0..100], [-134..220], [-140..122] */
305 luv_to_xyz_exact(double xyz[3], double luv[3])
307 double var_u = luv[1] / (13 * luv[0]) + (4 * REF_WHITE_X / (REF_WHITE_X + 15 * REF_WHITE_Y + 3 * REF_WHITE_Z));
308 double var_v = luv[2] / (13 * luv[0]) + (9 * REF_WHITE_Y / (REF_WHITE_X + 15 * REF_WHITE_Y + 3 * REF_WHITE_Z));
309 double var_y = (luv[0] + 16) / 116;
310 double pow_y = var_y * var_y * var_y;
311 if (pow_y > 0.008856)
314 var_y = (var_y - 16 / 116) / 7.787;
316 xyz[0] = -(9 * xyz[1] * var_u) / ((var_u - 4) * var_v - var_u * var_v);
317 xyz[2] = (9 * xyz[1] - 15 * var_v * xyz[1] - var_v * xyz[0]) / (3 * var_v);
321 /***************** OPTIMIZED SRGB -> LUV CONVERSION *********************/
323 u16 srgb_to_luv_tab1[256];
324 u16 srgb_to_luv_tab2[9 << SRGB_TO_LUV_TAB2_SIZE];
325 u32 srgb_to_luv_tab3[20 << SRGB_TO_LUV_TAB3_SIZE];
328 srgb_to_luv_init(void)
330 DBG("Initializing sRGB -> Luv table");
331 for (uns i = 0; i < 256; i++)
335 t = pow((t + 0.055) * (1 / 1.055), 2.4);
338 srgb_to_luv_tab1[i] = CLAMP(t * 0xfff + 0.5, 0, 0xfff);
340 for (uns i = 0; i < (9 << SRGB_TO_LUV_TAB2_SIZE); i++)
342 double t = i / (double)((9 << SRGB_TO_LUV_TAB2_SIZE) - 1);
344 t = 1.16 * pow(t, 1 / 3.) - 0.16;
346 t = (1.16 * 7.787) * t;
347 srgb_to_luv_tab2[i] =
348 CLAMP(t * ((1 << SRGB_TO_LUV_TAB2_SCALE) - 1) + 0.5,
349 0, (1 << SRGB_TO_LUV_TAB2_SCALE) - 1);
351 for (uns i = 0; i < (20 << SRGB_TO_LUV_TAB3_SIZE); i++)
353 srgb_to_luv_tab3[i] = i ? (13 << (SRGB_TO_LUV_TAB3_SCALE + SRGB_TO_LUV_TAB3_SIZE)) / i : 0;
358 srgb_to_luv_pixels(byte *dest, byte *src, uns count)
362 srgb_to_luv_pixel(dest, src);
369 /************************ GRID INTERPOLATION ALGORITHM ************************/
371 struct color_grid_node *srgb_to_luv_grid;
372 struct color_interpolation_node *color_interpolation_table;
374 /* Returns volume of a given tetrahedron multiplied by 6 */
376 tetrahedron_volume(uns *v1, uns *v2, uns *v3, uns *v4)
378 int a[3], b[3], c[3];
379 for (uns i = 0; i < 3; i++)
381 a[i] = v2[i] - v1[i];
382 b[i] = v3[i] - v1[i];
383 c[i] = v4[i] - v1[i];
386 a[0] * (b[1] * c[2] - b[2] * c[1]) -
387 a[1] * (b[0] * c[2] - b[2] * c[0]) +
388 a[2] * (b[0] * c[1] - b[1] * c[0]);
389 return (result > 0) ? result : -result;
393 interpolate_tetrahedron(struct color_interpolation_node *n, uns *p, const uns *c)
396 for (uns i = 0; i < 4; i++)
398 v[i][0] = (c[i] & 0001) ? (1 << COLOR_CONV_OFS) : 0;
399 v[i][1] = (c[i] & 0010) ? (1 << COLOR_CONV_OFS) : 0;
400 v[i][2] = (c[i] & 0100) ? (1 << COLOR_CONV_OFS) : 0;
402 ((c[i] & 0001) ? 1 : 0) +
403 ((c[i] & 0010) ? (1 << COLOR_CONV_SIZE) : 0) +
404 ((c[i] & 0100) ? (1 << (COLOR_CONV_SIZE * 2)) : 0);
406 uns vol = tetrahedron_volume(v[0], v[1], v[2], v[3]);
407 n->mul[0] = ((tetrahedron_volume(p, v[1], v[2], v[3]) << 8) + (vol >> 1)) / vol;
408 n->mul[1] = ((tetrahedron_volume(v[0], p, v[2], v[3]) << 8) + (vol >> 1)) / vol;
409 n->mul[2] = ((tetrahedron_volume(v[0], v[1], p, v[3]) << 8) + (vol >> 1)) / vol;
410 n->mul[3] = ((tetrahedron_volume(v[0], v[1], v[2], p) << 8) + (vol >> 1)) / vol;
412 for (j = 0; j < 4; j++)
415 for (uns i = 0; i < 4; i++)
417 n->ofs[i] = n->ofs[j];
421 interpolation_table_init(void)
423 DBG("Initializing color interpolation table");
424 struct color_interpolation_node *n = color_interpolation_table =
425 xmalloc(sizeof(struct color_interpolation_node) << (COLOR_CONV_OFS * 3));
427 for (p[2] = 0; p[2] < (1 << COLOR_CONV_OFS); p[2]++)
428 for (p[1] = 0; p[1] < (1 << COLOR_CONV_OFS); p[1]++)
429 for (p[0] = 0; p[0] < (1 << COLOR_CONV_OFS); p[0]++)
432 static const uns tetrahedrons[5][4] = {
433 {0000, 0001, 0010, 0100},
434 {0110, 0111, 0100, 0010},
435 {0101, 0100, 0111, 0001},
436 {0011, 0010, 0001, 0111},
437 {0111, 0001, 0010, 0100}};
438 if (p[0] + p[1] + p[2] <= (1 << COLOR_CONV_OFS))
440 else if ((1 << COLOR_CONV_OFS) + p[0] <= p[1] + p[2])
442 else if ((1 << COLOR_CONV_OFS) + p[1] <= p[0] + p[2])
444 else if ((1 << COLOR_CONV_OFS) + p[2] <= p[0] + p[1])
448 interpolate_tetrahedron(n, p, tetrahedrons[index]);
453 typedef void color_conv_func(double dest[3], double src[3]);
456 conv_grid_init(struct color_grid_node **grid, color_conv_func func)
460 struct color_grid_node *g = *grid = xmalloc((sizeof(struct color_grid_node)) << (COLOR_CONV_SIZE * 3));
461 double src[3], dest[3];
462 for (uns k = 0; k < (1 << COLOR_CONV_SIZE); k++)
464 src[2] = k * (255 / (double)((1 << COLOR_CONV_SIZE) - 1));
465 for (uns j = 0; j < (1 << COLOR_CONV_SIZE); j++)
467 src[1] = j * (255/ (double)((1 << COLOR_CONV_SIZE) - 1));
468 for (uns i = 0; i < (1 << COLOR_CONV_SIZE); i++)
470 src[0] = i * (255 / (double)((1 << COLOR_CONV_SIZE) - 1));
472 g->val[0] = CLAMP(dest[0] + 0.5, 0, 255);
473 g->val[1] = CLAMP(dest[1] + 0.5, 0, 255);
474 g->val[2] = CLAMP(dest[2] + 0.5, 0, 255);
482 srgb_to_luv_func(double dest[3], double src[3])
484 double srgb[3], xyz[3], luv[3];
485 srgb[0] = src[0] / 255.;
486 srgb[1] = src[1] / 255.;
487 srgb[2] = src[2] / 255.;
488 srgb_to_xyz_exact(xyz, srgb);
489 xyz_to_luv_exact(luv, xyz);
490 dest[0] = luv[0] * 2.55;
491 dest[1] = luv[1] * (2.55 / 4) + 128;
492 dest[2] = luv[2] * (2.55 / 4) + 128;
496 color_conv_init(void)
498 interpolation_table_init();
499 conv_grid_init(&srgb_to_luv_grid, srgb_to_luv_func);
503 color_conv_pixels(byte *dest, byte *src, uns count, struct color_grid_node *grid)
507 color_conv_pixel(dest, src, grid);
514 /**************************** TESTS *******************************/
520 conv_error(u32 color, struct color_grid_node *grid, color_conv_func func)
522 byte src[3], dest[3];
523 src[0] = color & 255;
524 src[1] = (color >> 8) & 255;
525 src[2] = (color >> 16) & 255;
526 color_conv_pixel(dest, src, grid);
527 double src2[3], dest2[3];
528 for (uns i = 0; i < 3; i++)
532 for (uns i = 0; i < 3; i++)
533 err += (dest[i] - dest2[i]) * (dest[i] - dest2[i]);
537 typedef void test_fn(byte *dest, byte *src);
540 func_error(u32 color, test_fn test, color_conv_func func)
542 byte src[3], dest[3];
543 src[0] = color & 255;
544 src[1] = (color >> 8) & 255;
545 src[2] = (color >> 16) & 255;
547 double src2[3], dest2[3];
548 for (uns i = 0; i < 3; i++)
552 for (uns i = 0; i < 3; i++)
553 err += (dest[i] - dest2[i]) * (dest[i] - dest2[i]);
558 test_grid(byte *name, struct color_grid_node *grid, color_conv_func func)
560 double max_err = 0, sum_err = 0;
562 for (uns i = 0; i < count; i++)
564 double err = conv_error(random_max(0x1000000), grid, func);
565 max_err = MAX(err, max_err);
568 DBG("%s: error max=%f avg=%f", name, max_err, sum_err / count);
570 die("Too large error in %s conversion", name);
574 test_func(byte *name, test_fn test, color_conv_func func)
576 double max_err = 0, sum_err = 0;
578 for (uns i = 0; i < count; i++)
580 double err = func_error(random_max(0x1000000), test, func);
581 max_err = MAX(err, max_err);
584 DBG("%s: error max=%f avg=%f", name, max_err, sum_err / count);
586 die("Too large error in %s conversion", name);
593 test_func("func sRGB -> Luv", srgb_to_luv_pixel, srgb_to_luv_func);
595 test_grid("grid sRGB -> Luv", srgb_to_luv_grid, srgb_to_luv_func);
599 byte *a = xmalloc(3 * CNT), *b = xmalloc(3 * CNT);
600 for (uns i = 0; i < 3 * CNT; i++)
601 a[i] = random_max(256);
603 for (uns i = 0; i < TESTS; i++)
604 memcpy(b, a, CNT * 3);
605 DBG("memcpy time=%d", (uns)get_timer());
607 for (uns i = 0; i < TESTS; i++)
608 srgb_to_luv_pixels(b, a, CNT);
609 DBG("direct time=%d", (uns)get_timer());
611 for (uns i = 0; i < TESTS; i++)
612 color_conv_pixels(b, a, CNT, srgb_to_luv_grid);
613 DBG("grid time=%d", (uns)get_timer());