WATERSHED OF A CONTINUOUS FUNCTION

The notion of watershed, used in morphological segmentation, has only a digital definition. In this paper, we propose to extend this definit ion to the continuous plane. Using this continuous definition, we pres ent the watershed differences with classical edge detectors. We then e xhibit a metric in the plane for which the watershed is a skeleton by influence zones and show the lower semicontinuous behaviour of the ass ociated skeleton. This theoretical approach suggests an algorithm for solving the eikonal equation: \\del f\\ = g. Finally, we end with some new watershed algorithms, which present the advantage of allowing the use of markers and/or anchor points, thus opening the way towards gre y-tone skeletons.