Attributes of colour images have been found which allow colour and lightness constancy to be computed without prior knowledge of the illumination, even in complex scenes with three -dimensional objects and multiple light sources of different colours. The ratio of surface reflectance colour can be immediately determined between any two image points, however distant. It is possible to determine the number of spectrally independent light sources, and to isolate the effect of each. Reflectance edges across which the illumination remains constant can be correctly identified. In a scene illuminated by multiple distant point sources of distinguishalbe colours, the spatial angle between the sources and their brightness ratios can be computed from the image alone. If there are three or more sources then reflectance constancy is immediately possible without use of additional knowledge. The results are an extension of Edwin Land's Retinex algorithm. They account for previously unexplained data such as Gilchrist's veiling luminances and his single- colour rooms. The validity of the algorithms has been demonstrated by implementing them in a series of computer programs. The computational methods do not follow the edge or region finding paradigms of previous vision mechanisms. Although the new reflectance constancy cues occur in all normal scenes, it is likely that human vision makes use of only some of them. In a colour image all the pixels of a single surface colour lie in a single structure in flux space. The dimension of the structure equals the number of illumination colours. The reflectance ratio between two regions is determined by the transformation between their structures. Parallel tracing of edge pairs in their respective structures identifies an edge of constant illumination, and gives the lightness ratio of each such edge. Enhanced noise reduction techniques for colour pictures follow from the natural constraints on the flux structures.