Modeling and generalization of discrete Morse terrain decompositions

We address the problem of morphological analysis ofreal terrains. We describe a morphological model for
a terrain by considering extensions of Morse theory to
the discrete case. We propose a two-level model of the
morphology of a terrain based on a graph joining the
critical points of the terrain through integral lines. We
present a new set of generalization operators specific
for discrete piece-wise linear terrain models, which are
used to reduce noise and the size of the morphological
representation. We show results of our approach on real
terrains.