2.2. Colorspaces

2.2. Colorspaces
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[intro]

Gamma Correction

[to do]

E'_R = f(R)

E'_G = f(G)

E'_B = f(B)

Construction of luminance and color-difference signals

[to do]

E'_Y = Coeff_R E'_R + Coeff_G E'_G + Coeff_B E'_B

(E'_R - E'_Y) = E'_R - Coeff_R E'_R - Coeff_G E'_G - Coeff_B E'_B

(E'_B - E'_Y) = E'_B - Coeff_R E'_R - Coeff_G E'_G - Coeff_B E'_B

Re-normalized color-difference signals

The color-difference signals are scaled back to unity range [-0.5;+0.5]:

K_B = 0.5 / (1 - Coeff_B)

K_R = 0.5 / (1 - Coeff_R)

P_B = K_B (E'_B - E'_Y) = 0.5 (Coeff_R / Coeff_B) E'_R + 0.5 (Coeff_G / Coeff_B) E'_G + 0.5 E'_B

P_R = K_R (E'_R - E'_Y) = 0.5 E'_R + 0.5 (Coeff_G / Coeff_R) E'_G + 0.5 (Coeff_B / Coeff_R) E'_B

Quantization

[to do]

Y' = (Lum. Levels - 1) · E'_Y + Lum. Offset

C_B = (Chrom. Levels - 1) · P_B + Chrom. Offset

C_R = (Chrom. Levels - 1) · P_R + Chrom. Offset

Rounding to the nearest integer and clamping to the range [0;255] finally yields the digital color components Y'CbCr stored in YUV images.

Example 2.1. ITU-R Rec. BT.601 color conversion

Forward Transformation

int ER, EG, EB;         /* gamma corrected RGB input [0;255] */
int Y1, Cb, Cr;         /* output [0;255] */

double r, g, b;         /* temporaries */
double y1, pb, pr;

int
clamp (double x)
{
	int r = x;      /* round to nearest */

	if (r < 0)         return 0;
	else if (r > 255)  return 255;
	else               return r;
}

r = ER / 255.0;
g = EG / 255.0;
b = EB / 255.0;

y1  =  0.299  * r + 0.587 * g + 0.114  * b;
pb  = -0.169  * r - 0.331 * g + 0.5    * b;
pr  =  0.5    * r - 0.419 * g - 0.081  * b;

Y1 = clamp (219 * y1 + 16);
Cb = clamp (224 * pb + 128);
Cr = clamp (224 * pr + 128);

/* or shorter */

y1 = 0.299 * ER + 0.587 * EG + 0.114 * EB;

Y1 = clamp ( (219 / 255.0)                    *       y1  + 16);
Cb = clamp (((224 / 255.0) / (2 - 2 * 0.114)) * (EB - y1) + 128);
Cr = clamp (((224 / 255.0) / (2 - 2 * 0.299)) * (ER - y1) + 128);

Inverse Transformation

int Y1, Cb, Cr;         /* gamma pre-corrected input [0;255] */
int ER, EG, EB;         /* output [0;255] */

double r, g, b;         /* temporaries */
double y1, pb, pr;

int
clamp (double x)
{
	int r = x;      /* round to nearest */

	if (r < 0)         return 0;
	else if (r > 255)  return 255;
	else               return r;
}

y1 = (255 / 219.0) * (Y1 - 16);
pb = (255 / 224.0) * (Cb - 128);
pr = (255 / 224.0) * (Cr - 128);

r = 1.0 * y1 + 0     * pb + 1.402 * pr;
g = 1.0 * y1 - 0.344 * pb - 0.714 * pr;
b = 1.0 * y1 + 1.772 * pb + 0     * pr;

ER = clamp (r * 255); /* [ok? one should prob. limit y1,pb,pr] */
EG = clamp (g * 255);
EB = clamp (b * 255);

Table 2.2. enum v4l2_colorspace

Identifier	Value	Description	Chromaticities^[a]			White Point	Gamma Correction	Luminance E'_Y	Quantization
Identifier	Value	Description	Red	Green	Blue	White Point	Gamma Correction	Luminance E'_Y	Y'	Cb, Cr
`V4L2_COLORSPACE_SMPTE170M`	1	NTSC/PAL according to [SMPTE 170M], [ITU BT.601]	x = 0.630, y = 0.340	x = 0.310, y = 0.595	x = 0.155, y = 0.070	x = 0.3127, y = 0.3290, Illuminant D₆₅	E' = 4.5 I for I ≤0.018, 1.099 I^0.45 - 0.099 for 0.018 < I	0.299 E'_R + 0.587 E'_G + 0.114 E'_B	219 E'_Y + 16	224 P_B,R + 128
`V4L2_COLORSPACE_SMPTE240M`	2	1125-Line (US) HDTV, see [SMPTE 240M]	x = 0.630, y = 0.340	x = 0.310, y = 0.595	x = 0.155, y = 0.070	x = 0.3127, y = 0.3290, Illuminant D₆₅	E' = 4 I for I ≤0.0228, 1.1115 I^0.45 - 0.1115 for 0.0228 < I	0.212 E'_R + 0.701 E'_G + 0.087 E'_B	219 E'_Y + 16	224 P_B,R + 128
`V4L2_COLORSPACE_REC709`	3	HDTV and modern devices, see [ITU BT.709]	x = 0.640, y = 0.330	x = 0.300, y = 0.600	x = 0.150, y = 0.060	x = 0.3127, y = 0.3290, Illuminant D₆₅	E' = 4.5 I for I ≤0.018, 1.099 I^0.45 - 0.099 for 0.018 < I	0.2125 E'_R + 0.7154 E'_G + 0.0721 E'_B	219 E'_Y + 16	224 P_B,R + 128
`V4L2_COLORSPACE_BT878`	4	Broken Bt878 extents^[b], [ITU BT.601]	?	?	?	?	?	0.299 E'_R + 0.587 E'_G + 0.114 E'_B	237 E'_Y + 16	224 P_B,R + 128 (probably)
`V4L2_COLORSPACE_470_SYSTEM_M`	5	M/NTSC^[c] according to [ITU BT.470], [ITU BT.601]	x = 0.67, y = 0.33	x = 0.21, y = 0.71	x = 0.14, y = 0.08	x = 0.310, y = 0.316, Illuminant C	?	0.299 E'_R + 0.587 E'_G + 0.114 E'_B	219 E'_Y + 16	224 P_B,R + 128
`V4L2_COLORSPACE_470_SYSTEM_BG`	6	625-line PAL and SECAM systems according to [ITU BT.470], [ITU BT.601]	x = 0.64, y = 0.33	x = 0.29, y = 0.60	x = 0.15, y = 0.06	x = 0.313, y = 0.329, Illuminant D₆₅	?	0.299 E'_R + 0.587 E'_G + 0.114 E'_B	219 E'_Y + 16	224 P_B,R + 128
`V4L2_COLORSPACE_JPEG`	7	JPEG Y'CbCr, see [JFIF], [ITU BT.601]	?	?	?	?	?	0.299 E'_R + 0.587 E'_G + 0.114 E'_B	256 E'_Y + 16^[d]	256 P_B,R + 128
`V4L2_COLORSPACE_SRGB`	8	[?]	x = 0.640, y = 0.330	x = 0.300, y = 0.600	x = 0.150, y = 0.060	x = 0.3127, y = 0.3290, Illuminant D₆₅	E' = 4.5 I for I ≤0.018, 1.099 I^0.45 - 0.099 for 0.018 < I	n/a
^[a]The coordinates of the color primaries are given in the CIE system (1931) ^[b]The ubiquitous Bt878 video capture chip quantizes E'_Y to 238 levels, yielding a range of Y' = 16 … 253, unlike Rec. 601 Y' = 16 … 235. This is not a typo in the Bt878 documentation, it has been implemented in silicon. The chroma extents are unclear. ^[c]No identifier exists for M/PAL which uses the chromaticities of M/NTSC, the remaining parameters are equal to B and G/PAL. ^[d]Note JFIF quantizes Y'P_BP_R in range [0;+1] and [-0.5;+0.5] to 257 levels, however Y'CbCr signals are still clamped to [0;255].

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