1. A method of populating cells in a look-up table (LUT) which maps from input color values in a source color space to corresponding output color values in a destination color space, wherein the LUT includes cells corresponding to first input color values within a spectrum locus and second input color values outside the spectrum locus, wherein the method comprises: using a computer to determine whether cells in the LUT correspond to the first input color values within the spectrum locus or to the second input color values outside the spectrum locus; for cells determined to correspond to the first input color values, all of which are within the spectrum locus, calculating first output color values in the destination color space using a color transform, wherein the color transform is constructed based on device profiles for the source and for the destination which are defined based on user's selection, and populating corresponding cells of the LUT based on the calculated first output color values; training an artificial neural network using the calculated first output color values; and for cells determined to correspond to the second input color values outside the spectrum locus, calculating second output color values in the destination color space using outputs of the trained neural network, and populating corresponding cells based on the calculated second output color values; wherein the neural network is a feed-forward neural network with at least three layers including an input layer, at least one hidden layer having 12 or more neurons, and an output layer; wherein the neural network is trained on fewer than all cells within the spectrum locus; and wherein the neural network is trained primarily on cells near an edge of the spectrum locus, and fewer than all cells at an interior of the spectrum locus.