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Technical Report Details

Date 21-6-2013
Number DIBRIS-TR-13-04
Title Morphologically correct elimination of flat edges and triangles from a triangulated terrain
Authors Paola Magillo, Leila De Floriani, Federico Iuricich
Bibtex Entry
E-mail paola.magillo@unige.it
Link ftp://ftp.disi.unige.it/person/MagilloP/pub.html
Abstract Modeling the morphology of a terrain is a relevant issue in several applications, such as terrain analysis and understanding, hydrological simulation, environmental modeling. Morphological models of terrains are rooted in Morse theory, which is defined for smooth functions. In real applications, discrete terrain models are used. Morse theory has been transposed into a discrete setting under the assumption that no two adjacent vertices have the same elevation, i.e., the terrain has no flat edges. As flat edges occur in real terrains, algorithms must deal with them. For some algorithms, the only solution is perturbing the data points as a preprocessing, while other algorithms can manage flat edges internally. However, data perturbation leads to over-segmentation, and the results of existing segmentation algorithms, based on different approach, often differ considerably in the presence of flat edges. Here, we propose a preprocessing method to eliminate flat edges from a TIN in a morphologically consistent way, i.e., maxima and minima of the terrain are preserved. Moreover, segmentation produced by different algorithms are much more similar, and (almost) equal on terrains prof which flat edges have been eliminated with our method, than on the original terrains with flat edges. This last result confirms the correctness of our approach.
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