Characterizing an Environment from Visibility Information

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Emamy, Zahra Sadat | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46240 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zarei, Alireze
Abstract:
Using visual information of an environment is the immediate way of detecting and identifying an unknown environment. These information maybe obtained using straight visibility detecting sensors. One of the formal models of these visual information is the visibility graph which have a vertex for each vertex (corner point) of the environment and two vertices have an edge whenever their corresponding corners see each other. Then, the problem is to characterize such a graph and reconstruct the target environment with equivalent visibility graph. Despite existence of plenty of research results, these are open problems in computational geometry and rigid results exist only for limited special cases.
In this thesis, we consider the problem of identify a pseudo-triangulation
of the target environment from it’s visibility graph. We propose several
methods for identify a triangulation and extend this result to obtain a pseudotriangulation
Keywords:
Computational Geometry ; Visibility Graph ; Pseudo-Triangle ; Characterization From Visibility