本文详细介绍了不同色彩空间（如YCbCr、YUV等）与RGB之间的转换公式，并提供了从RGB到HSL及HSV颜色模型的算法实现。适用于图像处理、视频编码等领域。
[ITU 601: YCbCr <-> RGB]
0 <= Y, R, G, B <= 1
-0.5 <= Cb, Cr <= 0.5
Y = 0.299 * R + 0.587 * G + 0.114 * B
Cb = -0.169 * R - 0.331 * G + 0.500 * B
Cr = 0.500 * R - 0.419 * G - 0.081 * B
R = Y + 0.000 * Cb + 1.403 * Cr
G = Y - 0.344 * Cb - 0.714 * Cr
B = Y + 1.773 * Cb + 0.000 * Cr
[ITU 601 Revision: YCbCr <-> RGB]
0 <= Y, Cb, Cr, R, G, B <= 255
Y = 0.299 * R + 0.587 * G + 0.114 * B
Cb = -0.169 * R - 0.331 * G + 0.499 * B + 128
Cr = 0.499 * R - 0.418 * G - 0.0813 * B + 128
R = Y + 0.000 * (Cb – 128) + 1.402 * (Cr – 128)
G = Y - 0.344 * (Cb – 128) - 0.714 * (Cr – 128)
B = Y + 1.772 * (Cb - 128) + 0.000 * (Cr – 128)
[ITU 709: YCbCr <-> RGB]
0 <= Y, R, G, B <= 1
-0.5 <= Cb, Cr <= 0.5
Y = 0.2215 * R + 0.7154 * G + 0.0721 * B
Cb = -0.1145 * R - 0.3855 * G + 0.5000 * B
Cr = 0.5016 * R - 0.4556 * G - 0.0459 * B
R = Y + 0.0000 * Cb + 1.5701 * Cr
G = Y - 0.1870 * Cb - 0.4664 * Cr
B = Y - 1.8556 * Cb + 0.0000 * Cr
[EBU: YUV <-> RGB]
0 <= Y, R, G, B <= 1
-0.436 <= U <= 0.436
-0.615 <= V <= 0.615
Y = 0.299 * R + 0.587 * G + 0.114 * B
U = 0.493 * (B - Y) = -0.147 * R - 0.289 * G + 0.436 * B
V = 0.877 * (R - Y) = 0.615 * R - 0.515 * G - 0.100 * B
R = Y + 0.000 * U + 1.140 * V
G = Y - 0.396 * U - 0.581 * V
B = Y + 2.029 * U + 0.000 * V
[RGB <-> HSL]
Algorithm RGB -> HSL
0 <= R, G, B <= 1
0 <= H <= 360
0 <= S, L <= 1
max = MAX( R, G, B )
min = MIN( R, G, B )
1) max = min
h = 0
2) max = R
h = (60 * (G - B) / (max - min) + 360 ) mod 360
3) max = G
h = 60 * (B - R) / (max - min) + 120
4) max = B
h = 60 * (R - G) / (max - min) + 240
L = (max + min) / 2
1) max = min
s = 0;
2) L <= 0.5
s = (max - min) / (max + min) = (max - min) / (2 * L)
3) L > 0.5
s = (max - min) / (2 - (max + min)) = (max - min) / (2 - 2 * L)
Algorithm HSL -> RGB
0 <= R, G, B <= 1
0 <= H < 360
0 <= S, L <= 1
1) L < 0.5
Q = L * (L + S)
2) L >= 0.5
Q = L + S - (L * S)
P = 2 * L - Q
Hk = H / 360
Tr = Hk + 1.0 / 3.0
Tg = Hk
Tb = Hk - 1.0 / 3.0
1) Tr < 0
Tr = Tr + 1.0
2) Tr > 1.0
Tr = Tr - 1.0
3) Tg < 0
Tg = Tg + 1.0
4) Tg > 1.0
Tg = Tg - 1.0
5) Tb < 0
Tb = Tb + 1.0
6) Tb > 1.0
Tb = Tb - 1.0
1) Tr < 1.0 / 6.0
Tr = P + ((Q - P) * 6 * Tr)
2) 1.0 / 6.0 <= Tr < 0.5
Tr = Q
3) 0.5 <= Tr < 2.0 / 3.0
Tr = P + ((Q- P) * 6 * (2.0 / 3.0 - Tr))
4) otherwise
Tr = P
5) Tg < 1.0 / 6.0
Tg = P + ((Q - P) * 6 * Tg)
6) 1.0 / 6.0 <= Tg < 0.5
Tg = Q
7) 0.5 <= Tg < 2.0 / 3.0
Tg = P + ((Q- P) * 6 * (2.0 / 3.0 - Tg))
8) otherwise
Tg = P
9) Tb < 1.0 / 6.0
Tb = P + ((Q - P) * 6 * Tb)
10) 1.0 / 6.0 <= Tb < 0.5
Tb = Q
11) 0.5 <= Tb < 2.0 / 3.0
Tb = P + ((Q- P) * 6 * (2.0 / 3.0 - Tb))
12) otherwise
Tb = P
[RGB <-> HSV]
Algorithm RGB -> HSV
0 <= R, G, B <= 1
0 <= H <= 360
0 <= S, V <= 1
max = MAX( R, G, B )
min = MIN( R, G, B )
1) max = min
h = 0
2) max = R
h = (60 * (G - B) / (max - min) + 360 ) mod 360
3) max = G
h = 60 * (B - R) / (max - min) + 120
4) max = B
h = 60 * (R - G) / (max - min) + 240
1) max = 0
S = 0
2) otherwise
S = (max - min) / max = 1 - (min / max)
V = max
Algorithm HSV -> RGB
0 <= R, G, B <= 1
0 <= H < 360
0 <= S, V <= 1
Hi = INT(H /60.0) mod 6
F = H / 60.0 - INT(H /60.0)
P = V * (1 - S)
Q = V * (1 - F * S)
T = V * (1 - (1 - F) * S)
1) Hi = 0
R = V
G = T
B = P
2) Hi = 1
R = Q
G = V
B = P
3) Hi = 2
R = P
G = V
B = T
4) Hi = 3
R = P
B = Q
G = V
5) Hi = 4
R = T
G = P
B = V
6) Hi = 5
R = V
G = P
B = Q
[The implementation for converter]
#define I_MACRO_BEGIN do {
#define I_MACRO_END } while ( 0 )
#define CLIP( v, min, max ) /
I_MACRO_BEGIN /
if ( (v) < (min) ) /
(v) = (min); /
else if ( (v) > (max) ) /
(v) = (max); /
I_MACRO_END
// r, g, b, y, u, v are [0, 255]
// Cb = u
// Cr = v
#define ITU601_REV_RGB2YUV444( r, g, b, y, u, v ) /
I_MACRO_BEGIN /
(y) = (int) (0.299 * (r) + 0.587 * (g) + 0.114 * (b) + 0.5); /
(u) = (int) (-0.169 * (r) - 0.331 * (g) + 0.499 * (b) + 128.5); /
(v) = (int) (0.499 * (r) - 0.418 * (g) - 0.0813 * (b) + 128.5); /
CLIP( y, 0, 255 ); /
CLIP( u, 0, 255 ); /
CLIP( v, 0, 255 ); /
I_MACRO_END
// r, g, b, y, u, v are [0, 255]
// Cb = u
// Cr = v
#define ITU601_REV_YUV4442RGB( y, u, v, r, g, b ) /
I_MACRO_BEGIN /
(r) = (int) ((y) + 1.402 * ((v) - 128) + 0.5); /
(g) = (int) ((y) - 0.344 * ((u) - 128) - 0.714 * ((v) - 128) + 0.5); /
(b) = (int) ((y) + 1.772 * ((u) - 128) + 0.5); /
CLIP( r, 0, 255 ); /
CLIP( g, 0, 255 ); /
CLIP( b, 0, 255 ); /
I_MACRO_END
// r, g, b, y are [0, 1]
// u, v are [-0.5, 0.5]
// Cb = u
// Cr = v
#define ITU601_RGB2YUV444( r, g, b, y, u, v ) /
I_MACRO_BEGIN /
(y) = 0.299 * (r) + 0.587 * (g) + 0.114 * (b); /
(u) = -0.169 * (r) - 0.331 * (g) + 0.500 * (b); /
(v) = 0.500 * (r) - 0.419 * (g) - 0.081 * (b); /
CLIP( y, 0, 1.0 ); /
CLIP( u, -0.5, 0.5 ); /
CLIP( v, -0.5, 0.5 ); /
I_MACRO_END
// r, g, b, y are [0, 1]
// u, v are [-0.5, 0.5]
// Cb = u
// Cr = v
#define ITU601_YUV4442RGB( y, u, v, r, g, b ) /
I_MACRO_BEGIN /
(r) = (y) + 1.403 * (v); /
(g) = (y) - 0.344 * (u) - 0.714 * (v); /
(b) = (y) + 1.773 * (u); /
CLIP( r, 0, 1.0 ); /
CLIP( g, 0, 1.0 ); /
CLIP( b, 0, 1.0 ); /
I_MACRO_END
// r, g, b, y are [0, 1]
// u, v are [-0.5, 0.5]
// Cb = u
// Cr = v
#define ITU709_RGB2YUV444( r, g, b, y, u, v ) /
I_MACRO_BEGIN /
(y) = 0.2215 * (r) + 0.7154 * (g) + 0.0721 * (b); /
(u) = -0.1145 * (r) - 0.3855 * (g) + 0.500 * (b); /
(v) = 0.5016 * (r) - 0.4556 * (g) - 0.0459 * (b); /
CLIP( y, 0, 1.0 ); /
CLIP( u, -0.5, 0.5 ); /
CLIP( v, -0.5, 0.5 ); /
I_MACRO_END
// r, g, b, y are [0, 1]
// u, v are [-0.5, 0.5]
// Cb = u
// Cr = v
#define ITU709_YUV4442RGB( y, u, v, r, g, b ) /
I_MACRO_BEGIN /
(r) = (y) + 1.5701 * (v); /
(g) = (y) - 0.1870 * (u) - 0.4664 * (v); /
(b) = (y) - 1.8556 * (u); /
CLIP( r, 0, 1.0 ); /
CLIP( g, 0, 1.0 ); /
CLIP( b, 0, 1.0 ); /
I_MACRO_END
// r, g, b are [0, 1]
// h is [0, 360)
// s is [0, 1]
// l is [0, 1]
#define RGB2HSL( r, g, b, h, s, l ) /
I_MACRO_BEGIN /
if ( (r) == (g) && (g) == (b) ) /
{ /
(h) = 0; /
(s) = 0; /
(l) = (g); /
} /
else /
{ /
float _max; /
float _min; /
if ( (r) > (g) ) /
{ /
_min = (g) > (b) ? (b) : (g); /
if ( (r) > (b) ) /* r is max */ /
{ /
_max = (r); /
(h) = ((int) (60.0 * ((g) - (b)) / ((r) - _min) + 0.5) + 360) % 360; /
} /
else /* b is max */ /
{ /
_max = (b); /
(h) = (int) (60.0 * ((r) - (g)) / ((b) - _min) + 0.5) + 240; /
} /
} /
else /* (r) <= (g) */ /
{ /
_min = (r) > (b) ? (b) : (r); /
if ( (g) > (b) ) /* g is max */ /
{ /
_max = (g); /
(h) = (int) (60.0 * ((b) - (r)) / ((g) - _min) + 0.5) + 120; /
} /
else /* b is max */ /
{ /
_max = (b); /
(h) = (int) (60.0 * ((r) - (g)) / ((b) - _min) + 0.5) + 240; /
} /
} /
(l) = 0.5 * (_max + _min); /
if ( (l) > 0.5 ) /
{ /
(s) = (float) (_max - _min) / (2.0 - (_max + _min)); /
} /
else /
{ /
(s) = (float) (_max - _min) / (float) (_max + _min); /
} /
} /
I_MACRO_END
#define II_HSL2RGB( p, q, tc ) /
I_MACRO_BEGIN /
if ( (tc) < 1.0 / 6.0 ) /
{ /
(tc) = (p) + ((q) - (p)) * 6.0 * (tc); /
} /
else if ( (tc) < 1.0 / 2.0 ) /
{ /
(tc) = (q); /
} /
else if ( (tc) < 2.0 / 3.0 ) /
{ /
(tc) = (p) + ((q) - (p)) * 6.0 * (2.0 / 3.0 - (tc)); /
} /
else /
{ /
(tc) = (p); /
} /
I_MACRO_END
// h is [0, 360)
// s is [0, 1]
// l is [0, 1]
// r, g, b are [0, 1]
#define HSL2RGB( h, s, l, r, g, b ) /
I_MACRO_BEGIN /
float _p; /
float _q; /
float _hk; /
float _tr; /
float _tg; /
float _tb; /
assert( (h) < 360 ); /
if ( (l) < 0.5 ) /
{ /
_q = (l) * (1 + (s)); /
} /
else /
{ /
_q = (l) + (s) - (l) * (s); /
} /
_p = 2.0 * (l) - _q; /
_hk = (float) (h) / 360.0; /
_tr = _hk + 1.0 / 3.0; /
if ( _tr < 0 ) /
_tr += 1.0; /
else if ( _tr > 1.0 ) /
_tr -= 1.0; /
_tg = _hk; /
if ( _tg < 0 ) /
_tg += 1.0; /
else if ( _tg > 1.0 ) /
_tg -= 1.0; /
_tb = _hk - 1.0 / 3.0; /
if ( _tb < 0 ) /
_tb += 1.0; /
else if ( _tb > 1.0 ) /
_tb -= 1.0; /
II_HSL2RGB( _p, _q, _tr ); /
II_HSL2RGB( _p, _q, _tg ); /
II_HSL2RGB( _p, _q, _tb ); /
(r) = _tr; /
(g) = _tg; /
(b) = _tb; /
I_MACRO_END
// r, g, b are [0, 1]
// h is [0, 360)
// s is [0, 1]
// v is [0, 1]
#define RGB2HSV( r, g, b, h, s, v ) /
I_MACRO_BEGIN /
if ( (r) == (g) && (g) == (b) ) /
{ /
(h) = 0; /
(s) = 0; /
(v) = (g); /
} /
else /
{ /
float _max; /
float _min; /
if ( (r) > (g) ) /
{ /
_min = (g) > (b) ? (b) : (g); /
if ( (r) > (b) ) /* r is max */ /
{ /
_max = (r); /
(h) = ((int) (60.0 * ((g) - (b)) / ((r) - _min) + 0.5) + 360) % 360; /
} /
else /* b is max */ /
{ /
_max = (b); /
(h) = (int) (60.0 * ((r) - (g)) / ((b) - _min) + 0.5) + 240; /
} /
} /
else /* (r) <= (g) */ /
{ /
_min = (r) > (b) ? (b) : (r); /
if ( (g) > (b) ) /* g is max */ /
{ /
_max = (g); /
(h) = (int) (60.0 * ((b) - (r)) / ((g) - _min) + 0.5) + 120; /
} /
else /* b is max */ /
{ /
_max = (b); /
(h) = (int) (60.0 * ((r) - (g)) / ((b) - _min) + 0.5) + 240; /
} /
} /
(v) = _max; /
if ( _max == 0 ) /
{ /
(s) = 0; /
} /
else /
{ /
(s) = (float) (_max - _min) / (float) _max; /
} /
} /
I_MACRO_END
// h is [0, 360)
// s is [0, 1]
// v is [0, 1]
// r, g, b are [0, 255]
#define HSV2RGB( h, s, v, r, g, b ) /
I_MACRO_BEGIN /
int _hi; /
float _f; /
float _p; /
float _q; /
float _t; /
assert( (h) < 360 ); /
_hi = ((int) (h) / 60) % 6; /
_f = (float) (h) / 60.0 - (int) ((int) (h) / 60); /
_p = (v) * (1.0 - (s)); /
_q = (v) * (1.0 - _f * (s)); /
_t = (v) * (1.0 - (1.0 - _f) * (s)); /
switch ( _hi ) /
{ /
case 0: /
(r) = (v); /
(g) = (_t); /
(b) = (_p); /
break; /
case 1: /
(r) = (_q); /
(g) = (v); /
(b) = (_p); /
break; /
case 2: /
(r) = (_p); /
(g) = (v); /
(b) = (_t); /
break; /
case 3: /
(r) = (_p); /
(g) = (_q); /
(b) = (v); /
break; /
case 4: /
(r) = (_t); /
(g) = (_p); /
(b) = (v); /
break; /
case 5: /
(r) = (v); /
(g) = (_p); /
(b) = (_q); /
break; /
} /
I_MACRO_END
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