Hat is the correlation between Hunter whiteness (L, a , b) and CIE whiteness (L*, a*, b*)? Can I relate them mathematically?

The HunterLab and CIELAB color spaces to which you are referring (they are more than whiteness metrics) are both computed from CIE XYZ tristimulus values for the sample and the illuminant. To go from one to the other, you would need to invert the first space to compute the sample XYZ values (assuming you know the illuminant values) and then use the normal forward equations for the second model. These could probably be concatenated into one set of equations, but I have never seen that and there would be little benefit.

I would recommend Hunter and Harold's "Measurement of Appearance, 2nd Ed." as a good reference for details on these spaces. More.

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