Were they experimentally derived based on color perception from human subjects or can the size of the tolerance ellipsoid for every "color" be mathematically calculated for every point in the 3D space?
Unit colour difference
The so-called tolerance–ellipsoids in LAB space are in effect a complex nonlinear transformation of the Macadam ellipses. This early model quantify boundaries of just visible chromaticity difference in the colour space specified by CIE Standard Observer Tristimulus values. LAB space was later derived from Tristimulus space values by a process of three dimensional non-linear rescaling that seeks to generate (and nearly succeeds in deriving) a unit difference model in which all dimensions of colour change share a an approximately constant unit value. (See also CIE publication 15:2004).
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