We address the problem of extending topographic maps to color images. A topographic map gives a morphological and a geometrical representation of the information contained in natural images. Two approaches are presented and discussed. The first one is new and consists in defining a total order in IR 3 in accordance with the human visual perception of shapes. This allows defining color topographic maps in the same way that what it has been done for gray-level topographic maps. It has the advantage of leading all properties known in the gray-level case to remain true in the color case. However, the map contains a so huge quantity of data that it has to be drastically simplified. The second approach, based on a so far unpublished result [4], allows building a simplified representation by using the geometry given by the luminance component only. We present experiments, which illustrate the advantages and the drawbacks of each method.