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In a paper on morphological image segmentation, Najman and Schmitt (1996) introduce the powerful concept of edge dynamics. In this communication, we show that the method that they propose to compute the edge dynamics gives erroneous results for certain spatial configurations, and we propose a new algorithm which always yields correct edge dynamics. The reply presents in detail the algorithm of the watershed, which have been sketched in the original article and criticized in the comment. First, the formal definition of the flooding list, the key data structure of the algorithm, is given. Then, the construction of this flooding list and of the watershed are described and proved.