sYCC

The three unsigned integers $Y,C\_b,C\_r$ of an sYCC encoded color represent fractional coordinates $Y\text{'},C\_b\text{'},C\_r\text{'}$ according to the formulas

:$Y\text{'}\; =\; Y/M$

:$C\_b\text{'}\; =\; (C\_b\; -\; Z)/M$

:$C\text{'}\_r\; =\; (C\_b\; -\; Z)/M$

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

:$Y\; =\; \backslash mbox\{round\}(M\; Y\text{'}$

:$C\_b\; =\; \backslash mbox\{round\}(Z\; +\; M\; C\_b\text{'})$

:$C\_r\; =\; \backslash mbox\{round\}(Z\; +\; M\; C\_r\text{'})$

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 $Y\text{'}$ ranges from 0 to 1, while the fractional chroma coordinates range from $-128/255\backslash approx-0.50196...$ to $+127/255\backslash approx+0.498039...$.

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

:$$

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

The non-linear fractional sRGB coordinates $R\text{'},G\text{'},B\text{'}$ can be computed from the fractional sYCC coordinates $Y\text{'},C\_b\text{'},C\_r\text{'}$ by inverting the above matrix. The standard gives the approximation

:$$

\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 $N=8$ 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{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 $R\text{'},G\text{'},B\text{'}$ and the CIE 1931 XYZ coordinates. The connection entails the transfer function ("gamma correction") that maps $R\text{'},G\text{'},B\text{'}$ 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 ($R\text{'},G\text{'},B\text{'}$), rather than the linear ones ($R,G,B$), the $Y\text{'}$ 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 $Y\text{'}$ values, and vice-versa.

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

{{cite web|title=IEC 61966-2-1:1999|url=https://webstore.iec.ch/publication/6169|website=IEC Webstore|publisher=International Electrotechnical Commission|access-date=3 March 2017}}. The first official specification of sRGB.

{{cite web |url=https://webstore.iec.ch/publication/6168 |title=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 |date=2003 |publisher=International Electrotechnical Commission}} 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.

{{Color space}}

Category:1996 introductions

Category:Color space

Category:Film and video technology