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 R³ in accordance with the human visual percept ion of shapes. This allows one to define color topographic maps in the same way as 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 huge quantity of data that it has to be drastically simplified. The second approach allows one to build a simplified representation by using the geometry given by the luminance component only. We present experiments which illustrate the advantages and drawbacks of each of the method