SYCC

sYCC

IEC 61966-2-1 Default YCC encoding transformation for a standard luma-chroma-chroma colour space
Abbreviation	sRGB
Status	Published
Year started	1996
First published	October 18, 1999;25 years ago (1999-10-18) [1]
Latest version	61966-2–1 Amend. 1 2003
Organization	IEC [1]
Committee	TC/SC: TC 100/TA 2 [1]
Base standards	IEC 61966 Colour Measurement and Management in Multimedia Systems and Equipment
Domain	Color space, color model
Website	webstore.iec.ch/publication/6169

sYCC is a standard numerical encoding of colors, similar to the CIE YCbCr encoding, ^[2] It uses three coordinates: a luma value ${\displaystyle Y}$, that is roughly proportional to perceived brighness of the color, and two chroma values ${\displaystyle C_{b}}$ and ${\displaystyle C_{r}}$, which are roughly the "blueness" and "redness" of the hue. Each coordinate is represented by an integer with some number ${\displaystyle N}$ of bits, which is interpreted as either unsigned (for ${\displaystyle Y}$) or signed (for ${\displaystyle C_{b}}$ and ${\displaystyle C_{r}}$).

The space is defined by Annex F of the International Electrotechnical Commission (IEC) standard 61966-2-1 Amendment 1 (2003), as a linear transformation of the non-linear sRGB color space defined by the same document.

The official conversion from sYCC to sRGB may result in negative R, G, or B values; meaning that not all sYCC triplets represent colors that can be displayed on a computer screen, printed, or even perceived by the human eye.

sYCC definition

The three unsigned integers ${\displaystyle Y,C_{b},C_{r}}$ of an sYCC encoded color represent fractional coordinates ${\displaystyle Y',C_{b}',C_{r}'}$ according to the formulas ^[2]

${\displaystyle Y'=Y/M}$

${\displaystyle C_{b}'=(C_{b}-Z)/M}$

${\displaystyle C'_{r}=(C_{b}-Z)/M}$

where the scale factor ${\displaystyle M=2^{N}-1}$ is the maximum unsigned ${\displaystyle N}$-bit integer, and the offset ${\displaystyle Z}$ is ${\displaystyle 2^{N-1}}$ (as in the usual two's complement representation of signed integers). Conversely, the encoded integer values are given by

${\displaystyle Y={\mbox{round}}(MY'}$

${\displaystyle C_{b}={\mbox{round}}(Z+MC_{b}')}$

${\displaystyle C_{r}={\mbox{round}}(Z+MC_{r}')}$

with the resulting values clipped to the range ${\displaystyle 0..M}$.

In particular, for ${\displaystyle N=8}$ (which is the normal bit size), one gets ${\displaystyle M=255}$ and ${\displaystyle Z=128}$. Thus the fractional luma ${\displaystyle Y'}$ ranges from 0 to 1, while the fractional chroma coordinates range from ${\displaystyle -128/255\approx -0.50196...}$ to ${\displaystyle +127/255\approx +0.498039...}$.

The standard specifies that these fractional values ${\displaystyle Y',C_{b}',C_{r}'}$ are related to the non-linear fractional sRGB coordinates ${\displaystyle R',G',B'}$ by a linear transformation, described by the matrix product

${\displaystyle {\begin{bmatrix}Y'\\C_{b}'\\C_{r}'\end{bmatrix}}={\begin{bmatrix}+0.2990&+0.5870&+0.1140\\-0.1687&-0.3313&+0.5000\\+0.5000&-0.4817&-0.0813\end{bmatrix}}{\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}}$

This correspondence is the same as the RGB to YCC mapping specified by the old TV standard ITU-R BT.601-5, except that the coefficients of ${\displaystyle Y'}$ are here defined with four decimal digits instead of just three. ^[2]

The non-linear fractional sRGB coordinates ${\displaystyle R',G',B'}$ can be computed from the fractional sYCC coordinates ${\displaystyle Y',C_{b}',C_{r}'}$ by inverting the above matrix. The standard gives the approximation

${\displaystyle {\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}={\begin{bmatrix}+1.0000&0.0000&+1.4020\\+1.0000&-0.3441&-0.7141\\+1.0000&+1.7720&0.0000\end{bmatrix}}{\begin{bmatrix}Y'\\C_{b}'\\C_{r}'\end{bmatrix}}}$

which is expected to be accurate enough for ${\displaystyle N=8}$ bits per component. For bit sizes greater than 8, the standard recommends using a more accurate inverse. It states that the following matrix with 6 decimal digits is accurate enough for ${\displaystyle N=16}$:

${\displaystyle {\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}={\begin{bmatrix}+1.000000&+0.000037&+1.401988\\+1.000000&-0.344113&-0.714104\\+1.000000&+1.771978&+0.000135\end{bmatrix}}{\begin{bmatrix}Y'\\C_{b}'\\C_{r}'\end{bmatrix}}}$

The same standard specifies the relation between the non-linear fractional coordinates ${\displaystyle R',G',B'}$ and the CIE 1931 XYZ coordinates. The connection entails the transfer function ("gamma corection") that maps ${\displaystyle R',G',B'}$ to the linear R, G, B coordinates, and then a 3D linear transformation that relates these to the CIE ${\displaystyle X,Y,Z}$.

Since the linear transformation from sRGB to sYCC is defined in terms of non-linear (gamma-encoded) values (${\displaystyle R',G',B'}$), rather than the linear ones (${\displaystyle R,G,B}$), the ${\displaystyle Y'}$ component of sYCC is not the CIE Y coordinate, not even a function of it alone. That is, two colors with the same CIE Y value may have different sYCC ${\displaystyle Y'}$ values, and vice-versa.

Particular values

The integer encoded sYCC triplet ${\displaystyle (0,0,0)}$ represents the color black whereas ${\displaystyle (255,0,0)}$ is white (more precisely, the CIE illuminant D65). More generally, triplets ${\displaystyle (Y,0,0)}$, for ${\displaystyle Y}$ in 0..255, represent shades of gray.

Note that the 8-bit integer sYCC triplet ${\displaystyle (Y,Cb,Cr)=(0,255,255)}$ has fractional coordinates ${\displaystyle (Y',Cb',Cr')\approx (0.0,0.5,0.5)}$, which, according to these matrices, has fractional non-linear sRGB coordinate ${\displaystyle G'\approx -0.5\times (0.3341+0.7141)\approx -0.528}$, and therefore is not realizable or perceivable. Similarly, the sYCC triplet ${\displaystyle (0,0,0)}$ has ${\displaystyle R'\approx -0.701}$ and ${\displaystyle B'\approx -0.886}$.

References

1. "IEC 61966-2-1:1999". IEC Webstore. International Electrotechnical Commission. Retrieved 3 March 2017.. The first official specification of sRGB.
2. "IEC 61966-2-1:1999 Multimedia systems and equipment – Colour measurement and management – Part 2-1: Colour management – Default RGB colour space – sRGB: Amendment 1". International Electrotechnical Commission. 2003. Replaces the version IEC 61966-2-1:1999, introducing the sYCC encoding for YCbCr color spaces, an extended-gamut RGB encoding bg-sRGB, and a CIELAB transformation.