## CIE (1931) XYZ vs xyY

### CIE (1931) XYZ vs xyY

|Recently purcased the book "Illumination and Color in Computer Generated
|Imagery" by Roy Hall.  Great book.  In this book, he gives the color
|coordinates of each square of the Macbeth ColorChecker(r) chart using
|CIE 1931 XYZ coordinates.  I ran out & bought one of these charts at
|my local camera store, and started writing a program to calibrate my
|computer's display.  The chart came with a leaflet which lists the
|color coordinates of each square on the chart, but it contains different
|numbers!  It also claims to be using the CIE 1931 system, but the three
|columns are labelled " x y Y " instead of " X Y Z ".  Anybody know what's
|going on here?

The "x y Y" system is a normalized form of the
"X Y Z" color coordinate space.

X
x = ---------
X + Y + Z

Y
y = ---------
X + Y + Z

Note that  x + y <= 1.0 in this system, and that the
locus x = 1/3, y = 1/3 exhibits equal energy contribution
from each part of the visible spectrum. The Y component
in both systems represents the luminosity function, which
is a measure of perceived brightness independent of color.
Because the "x y Y" system is normalized, Y can be scaled
to any arbitrary reference value.

--
,u,    Bruce Becker   Toronto, Ontario

`\o\-e  UUCP: ...!uunet!mnetor!becker!bdb
_< /_        "I still have my phil-os-o-phy" - Meredith Monk

xyY and XYZ are two slightly different color coodinate systems.
Fortunately, there's a simple transformation. I'll show it now, but
you ought to check a good book on color like Wyszecki&Stiles "Colour Science"
(John Wiley and Sons, 1967).

Y = Y;  x = X/(X+Y+Z); y = Y/(X+Y+Z)

or backwards:

X = (x/y)*Y;  Y=Y;  Z=((1-x-y)/y)*Y

As for interpretation, XYZ values represent the amounts of three
specially defined hypothetical primaries (not physically realizable).
The Y primary was specifically defined to be roughly the human monochromatic
response, so a color image given in XYZ, can be shown in Black and White
by just mapping Y to intensity.

xyY is a kind of normalized form, where Y is that same monochromatic
intensity and x and y are chormatic coordinates which don't include
the intensity. This is useful when defining a color without knowing
the intensity as just (x,y).

The book I mentioned gives all the background you'll need to understand
color science. There are many other wild and wacky color spaces out there.
Some are non-linear and are much better at modeling human color vision.

I hope I helped....