What are the units of color matching functions? In some computer vision book I read lately, the color matching function is invoked without clear definition of its units. I suspect the color matching functions are spectral irradiance or spectral illuminance, i.e. with unit $\mathrm W/\mathrm m^3$ or $\mathrm{lm}/\mathrm m^3$, i.e. $\mathrm W$ or $\mathrm{lm}$ per square meter per wavelength. The inconsistency seems a common problem in books written by engineers. Am I correct?
I know this is only partially a physical question, but I guess physicists are more suitable for answering the question.

Edit: never mind, I figured it ought to be dimensionless. But if I am wrong, please still correct me.  
 A: The CIE standard colorimetric tables give $\bar x(\lambda)$, $\bar y(\lambda)$ and $\bar z(\lambda)$ as pure numbers, normalized so that $\int\bar x(\lambda)d\lambda$ is the same for the three components. 
In the end, it boils down to what units you expect your tristimulus signals $X$, $Y$ and $Z$ to have. For dimensionless $\bar x(\lambda)$, 
$$X=\int I(\lambda)\bar x(\lambda)d\lambda$$
has the units of intensity. This is actually perfectly natural, because it depends directly on $I(\lambda)$ and has not been normalized, so if you double the brightness of the source then $X$ will double as well. To get rid of this, the actual chromaticity variables used are
$$
x=\frac{X}{X+Y+Z}
$$
and similarly for $y$ and $z=1-x-y$. These are naturally dimensionless, do not change with the light intensity, and are independent of what units you give to the color matching functions. If you're matching XYZ colors to other color spaces, it's these functions that matter.
So, the real answer is "it doesn't matter that much".
