1. A method for transforming a physically-based characterization of color defined in Euclidean space derived from reflectance spectra and a theoretically defined perceptual space of color appearance defined in Euclidean space in terms of equal perceptual spacing of human judgments of colors comprising: obtaining a physical reflectance spectrum in a selected spectral range of a reflected color of an object; generating a cube root reflectance spectrum of the physical reflectance spectrum; reconstructing the cube root reflectance spectrum by a weighted linear combination of three basis functions, the weights of a linear combination of the basis functions constituting coordinates in a physical Euclidean color space with respect to which Euclidean color space similarities and differences between the physical reflectance spectra and a color characterized in the perceptual space of color appearance can be quantitatively analyzed; and linearly transforming a quantitative characterization of a target color between the physical Euclidean color space and the perceptual space of color appearance by which transformation the target color can be quantitatively compared.