Involved people : Gilles Bertrand, Michel Couprie, Petr Dokládal.
We proposed an original approach of the concept of watershed, a traditional concept from the framework of mathematical morphology having many applications in image segmentation. Our approach is based on the introduction of a "mono-dimensional" topology for the functions from Z 2 into Z, and more generally for weighted graphs. This enables us to define precisely, from the topological point of view, a watershed transformation. Moreover, we proposed an effective algorithm to operate this transformation, and gave examples of applications to the segmentation of graylevel images [ CB97 ].
The H-minima operator is also a tool from the framework of mathematical morphology. He makes it possible to filter a graylevel image according to a criterion based on the "depth" of the regional minima : if a minimum has a depth lower than a threshold H, then it is eliminated, if not it is retained and can be used as marker for a later stage of segmentation.
The direct application of the H-minima operator is limited to the cases where one wishes to segment the image into two classes of pixels (object/background), the object and the background can each consist of several connected components. To apply this operator to a multi-class problem of segmentation, where the areas to be segmented can possibly touch each other, one uses classically a gradient operator. However, the discrete gradients are delicate to use, in particular fine details of the original image can be lost.
We proposed H-minima operator acting on a weighted graph which allows the direct resolution of multi-class problems of segmentation, without using a gradient operator [ DB99 ]. This allows us to segment fine structures which would be lost with the use of the traditional approach (fig. 12).
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