I have a CIELab file that I am looking at with Photoshop. I would like to obtain the mean value of the image's L*, a*, and b* values. However, when I open the Histogram tool and select the individual Lab channels, the displayed mean value is different than then Lab* values displayed by the Info tool, which are correct. For example the mean L* value is listed as 251 when it should be 99 based on the Info tool, the a* mean value is listed as 127 when it is should be -1, and the mean b* value is 128 when it should be 0. The listed values might make sense if PS is taking the mean of the unsigned 8-bit values which I got from this link, instead of the mean of the Lab* values displayed by the Info tool. Is that right? Or, is there a way to convert the incorrect mean Lab* value into the correct mean Lab* value?
Photoshop's histogram provides means(averages) for Lightness, a, and b.
They are not normalized but shown in the LAB PCS space used by ICC profiles which go from 0 to 255 in unsigned, 8 bit values.
To convert these to real Lab* values, divide the lightness reading by 2.55 to get the actual L*. Subtract 128 from the a and b values to get the true, CIE a* and b* values.
If you are interested, the details of conversion of Lab* into the LAB PCS system can be found at www.color.org and is detailed in the specification for ICC profiles.
I don't know for sure but guess that Photoshop's histogram was hard coded for RGB values from 0-255 and they didn't do the work necessary to scale it properly for Lab*. They also scale their histogram 0-255 even for 16 bit RGB spaces.