Reconstructing an Environment from Visibility Information

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Mehrpour, Sahar | 2013

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 45085 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zarei, Alireza
Abstract:
One of the methods to detect an unknown environment, is using the visual information about the environment. In this problem, we have an unknown two-dimensional environment consists of a set of edges and vertices that the geometric positions of vertices is not speciﬁed and only the combinatorial structure of the environment is available. In addition, certain information such as visibility of two vertices in the environment is known. The goal is to recognize the geometric shape of the environment with this information.This problem has many applications in Robotics particularly in dynamic envi- ronment where objects are moving.
In this thesis, we examine this problem in diﬀerent conditions and we provide a polynomial-time algorithm for solving the problem when a visibility graph of a pseudo-triangle is given. We also investigate connecting two pseudo-triangles in pseudo-triangl a special case
Keywords:
Computational Geometry ; Visibility Graph ; Reconstruction From Visibility Information ; Pseudo-Triangle