SYCC

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

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 $Y,C_b,C_r$ of an sYCC encoded color represent fractional coordinates $Y^{\prime },{C_b}^{\prime },{C_r}^{\prime }$ according to the formulas

$Y^{\prime }=Y/M$

${C_b}^{\prime }=(C_b-Z)/M$

$C{\text{'}}_r=(C_b-Z)/M$

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

$Y=\text{round}(M{Y}^{\prime }$

$C_b=\text{round}(Z+M{C_b}^{\prime })$

$C_r=\text{round}(Z+M{C_r}^{\prime })$

with the resulting values clipped to the range $0..M$.

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

The standard specifies that these fractional values $Y^{\prime },{C_b}^{\prime },{C_r}^{\prime }$ are related to the non-linear fractional sRGB coordinates $R^{\prime },G^{\prime },B^{\prime }$ by a linear transformation, described by the matrix product

$\left[\begin{array}{c}{Y}^{\prime }\\ {C_b}^{\prime }\\ {C_r}^{\prime }\end{array}\right]=\left[\begin{array}{ccc}+0.2990& +0.5870& +0.1140\\ -0.1687& -0.3313& +0.5000\\ +0.5000& -0.4817& -0.0813\end{array}\right]\left[\begin{array}{c}{R}^{\prime }\\ G^{\prime }\\ B^{\prime }\end{array}\right]$

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 $Y^{\prime }$ are here defined with four decimal digits instead of just three.

The non-linear fractional sRGB coordinates $R^{\prime },G^{\prime },B^{\prime }$ can be computed from the fractional sYCC coordinates $Y^{\prime },{C_b}^{\prime },{C_r}^{\prime }$ by inverting the above matrix. The standard gives the approximation

$\left[\begin{array}{c}{R}^{\prime }\\ G^{\prime }\\ B^{\prime }\end{array}\right]=\left[\begin{array}{ccc}+1.0000& 0.0000& +1.4020\\ +1.0000& -0.3441& -0.7141\\ +1.0000& +1.7720& 0.0000\end{array}\right]\left[\begin{array}{c}{Y}^{\prime }\\ {C_b}^{\prime }\\ {C_r}^{\prime }\end{array}\right]$

which is expected to be accurate enough for $N=8$ 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 $N=16$:

$\left[\begin{array}{c}{R}^{\prime }\\ G^{\prime }\\ B^{\prime }\end{array}\right]=\left[\begin{array}{ccc}+1.000000& +0.000037& +1.401988\\ +1.000000& -0.344113& -0.714104\\ +1.000000& +1.771978& +0.000135\end{array}\right]\left[\begin{array}{c}{Y}^{\prime }\\ {C_b}^{\prime }\\ {C_r}^{\prime }\end{array}\right]$

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

Since the linear transformation from sRGB to sYCC is defined in terms of non-linear (gamma-encoded) values ($R^{\prime },G^{\prime },B^{\prime }$), rather than the linear ones ($R,G,B$), the $Y^{\prime }$ 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 $Y^{\prime }$ values, and vice-versa.

Particular values

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

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