Topographic Maps of Color Images

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 IR3 in accordance with the human visual perception of shapes. This allows to define color topographic maps in the same way that what it has been done for graylevel topographic maps. It has the advantage of leading all properties known in the gray-level case to remain true in the color case. But 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 The second approach, based on a so far unpublished result [4], allows to build a simplified representation by using the geometry given by the luminance component only.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.