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 brightness 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 $Y',C_b',C_r'$ according to the formulas
:$Y' = Y/M$
:$C_b' = (C_b - Z)/M$
:$C'_r = (C_b - Z)/M$
where the scale factor $M = 2^N - 1$ is the maximum unsigned $N$-bit integer, and the offset $Z$ is $2^$ (as in the usual two's complement representation of signed integers). Conversely, the encoded integer values are given by
:$Y = \mbox(M Y'$
:$C_b = \mbox(Z + M C_b')$
:$C_r = \mbox(Z + M C_r')$
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 $Y'$ 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 $Y',C_b',C_r'$ are related to the non-linear fractional sRGB coordinates $R',G',B'$ by a linear transformation, described by the matrix product
:$\begin Y' \\ C_b' \\ C_r' \end = \begin +0.2990 & +0.5870 & +0.1140 \\ -0.1687 & -0.3313 & +0.5000 \\ +0.5000 & -0.4817 & -0.0813 \end \begin R' \\ G' \\ B' \end$
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 $Y'$ are here defined with four decimal digits instead of just three.

The non-linear fractional sRGB coordinates $R',G',B'$ can be computed from the fractional sYCC coordinates $Y',C_b',C_r'$ by inverting the above matrix. The standard gives the approximation
:$\begin R' \\ G' \\ B' \end = \begin +1.0000 & 0.0000 & +1.4020 \\ +1.0000 & -0.3441 & -0.7141 \\ +1.0000 & +1.7720 & 0.0000 \end \begin Y' \\ C_b' \\ C_r' \end$
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 $N=16$:
:$\begin R' \\ G' \\ B' \end = \begin +1.000000 & +0.000037 & +1.401988 \\ +1.000000 & -0.344113 & -0.714104 \\ +1.000000 & +1.771978 & +0.000135 \end \begin Y' \\ C_b' \\ C_r' \end$

The same standard specifies the relation between the non-linear fractional coordinates $R',G',B'$ and the CIE 1931 XYZ coordinates. The connection entails the transfer function ("gamma correction") that maps $R',G',B'$ 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 ($R',G',B'$), rather than the linear ones ($R,G,B$), the $Y'$ 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 $Y'$ 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 $(Y',Cb',Cr')\approx(0.0,0.5,0.5)$, which, according to these matrices, has fractional non-linear sRGB coordinate $G' \approx - 0.5\times(0.3341 + 0.7141) \approx -0.528$, and therefore is not realizable or perceivable. Similarly, the sYCC triplet $(0,0,0)$ has $R'\approx -0.701$ and $B'\approx -0.886$.

References

. The first official specification of sRGB.

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.

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