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

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  of an sYCC encoded color represent fractional coordinates  according to the formulas

where the scale factor  is the maximum unsigned  -bit integer, and the offset  is  (as in the usual two's complement  representation of signed integers). Conversely, the encoded integer values are given by

with the resulting values clipped to the range .

In particular, for  (which is the normal bit size), one gets  and .  Thus the fractional luma  ranges from 0 to 1, while the fractional chroma coordinates range from  to .

The standard specifies that these fractional values  are related to the non-linear fractional sRGB coordinates  by a linear transformation, described by the matrix product

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  are here defined with four decimal digits instead of just three.

The non-linear fractional sRGB coordinates  can be computed from the fractional sYCC coordinates  by inverting the above matrix. The standard gives the approximation

which is expected to be accurate enough for  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 :

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

Since the linear transformation from sRGB to sYCC is defined in terms of non-linear (gamma-encoded) values (), rather than the linear ones (), the  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  values, and vice-versa.

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

Note that the 8-bit integer sYCC triplet  has fractional coordinates , which, according to these matrices, has fractional non-linear sRGB coordinate , and therefore is not realizable or perceivable.  Similarly, the sYCC triplet  has  and .

References

1996 introductions
Color space
Film and video technology