Geodesic saliency of watershed contours and hierarchical segmentation

The watershed is one of the latest segmentation tools developed in mathematical morphology. In order to prevent its oversegmentation, the notion of dynamics of a minimum, based on geodesic reconstruction, has been proposed. In this paper, we extend the notion of dynamics to the contour arcs. This notion acts as a measure of the saliency of the contour. Contrary to the dynamics of minima, our concept reflects the extension and shape of the corresponding object in the image. This representation is also much more natural, because it is expressed in terms of partitions of the plane, i.e., segmentations. A hierarchical segmentation process is then derived, which gives a compact description of the image, containing all the segmentations one can obtain by the notion of dynamics, by means of a simple thresholding. Finally, efficient algorithms for computing the geodesic reconstruction as well as the dynamics of contours are presented.