SYCC explained

sYCC
Long Name:	IEC 61966-2-1 Default YCC encoding transformation for a standard luma-chroma-chroma colour space
Native Name Lang:	English
Status:	Published
Year Started:	1996
Version:	61966-2–1 Amend. 1
Version Date:	2003
Committee:	/: TC 100/TA 2
Base Standards:	IEC 61966 Colour Measurement and Management in Multimedia Systems and Equipment
Abbreviation:	sRGB
Domain:	Color space, color model

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',C _{b',C} _{r'} according to the formulasY' = 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 ^{N-1} (as in the usual two's complement representation of signed integers). Conversely, the encoded integer values are given byY = round (M Y' C _{b} = round (Z + M C _{b')} C _{r} = round (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 ≈ -0 . 50196 ... to +127 / 255 ≈ +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{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' 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{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',G',B' and the CIE 1931 XYZ coordinates. The connection entails the transfer function ("gamma corection") 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') ≈ ( 0 . 0 , 0 . 5 , 0 . 5 ) , which, according to these matrices, has fractional non-linear sRGB coordinate G' ≈ - 0 . 5 x ( 0 . 3341 + 0 . 7141 ) ≈ -0 . 528 , and therefore is not realizable or perceivable. Similarly, the sYCC triplet ( 0 , 0 , 0 ) has R' ≈ -0 . 701 and B' ≈ -0 . 886 .

References

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Notes and References

1. Web site: IEC 61966-2-1:1999. IEC Webstore. International Electrotechnical Commission. 3 March 2017. . The first official specification of sRGB.
2. Web site: 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 . 2003 . 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.