Geodesic reconstruction, saddle zones & hierarchial segmentation - Beucher, Serge (Image analysis and stereology, 2001)
The morphological reconstruction based on geodesic operators, is a powerful tool in mathematical morphology. The general definition of this reconstructionsupposes the use of a marker function f which is not necessarilyrelated to the function g to be built. However, this paper deals with operations where the marker function is defined from given characteristicregions of the initial function f, as it is the case, for instance, for the extrema (maxima or minima) but also for the saddle zones. Firstly, we show that the intuitive definition of a saddle zone is not easy tohandle, especially when digitised images are involved. However, some of these saddle zones (regional ones also called overflow zones) can be defined, this definition providing a simple algorithm to extract them. The second part of the paper is devoted to the use of these overflow zones as markers in imagereconstruction. This reconstruction provides a new function which exhibits a new hierarchy of extrema. This hierarchy is equivalent to the hierarchy produced by the so-called waterfall algorithm. We explain why the waterfall algorithm can be achieved by performing a watershed transform of thefunction reconstructed by its initial watershed lines. Finally, some examples of use of this hierarchical segmentation are described.
Keywords: Geografija; Environment; natural environment; Okolje; Geography; Image Processing, Computer-Assisted; Slika, obdelava z računalnikom; geodesy; geodezija; matematična morfologija