The Segment Maxima Method for calculating gamut boundary descriptors of both colons reproduction media and colour images is introduced. Methods for determining the gamut boundary along a given line of mapping used by gamut mapping algorithms are then described whereby these methods use the Gamut Boundary Descriptor obtained using the Segment Maxims Method. Throughout the article, the focus is both on colons reproduction media and colour images as well as on the suitability of the methods for use in gamut mapping.