Functional experiment design for the analysis of colour changes in granite using new L*a*b* functional colour coordinates

We propose a functional data approach to evaluating colour changes in stone that is based on applying a functional experiment design to the tristimulus curves resulting from the product of the power spectral distribution of the source, the stone reflectance curve and the matching colour functions of the standard observer. The proposed method was applied to an analysis of colour changes in granite after the application of different desalination treatments. The results were compared with those obtained by the classical analysis of variance applied to the colorimetric coordinates L^*a^*b^*. The granite RGB and XYZ colour coordinate systems were obtained by integrating the respective tristimulus curves. The L^*a^*b^* coordinates, however, were obtained directly by transforming the XYZ coordinates, as no corresponding tristimulus functions have been proposed to date. With a view to comparing the results for these functional and scalar methods for a uniform colour measurement system, these functions, whose integral coincides with the L^*a^*b^* values, have been deduced and proposed for the first time. The results obtained demonstrate the usefulness of the additional information supplied by the functional approach. However, this information does not replace that produced by the scalar approach for the scalar coordinates, and so it is recommended to use both approaches. The new tristimulus functions associated with the L^*a^*b^* coordinates are perfectly interpretable in a way analogous to the coordinates themselves, i.e., as the degree of luminosity (L^*), the green-red relative position (a^*) and the blue-yellow relative position (b^*), except that they are interpreted for each infinitesimal wavelength interval. A brief introduction to the colour measurement problem and to functional statistical techniques is provided for readers coming from different disciplines.