Reconstructing an Environment from Visibility Information

, M.Sc. Thesis Sharif University of Technology Mehrpour, Sahar (Author) ; Zarei, Alireza (Supervisor)

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...

Characterizing an Environment from Visibility Information

, M.Sc. Thesis Sharif University of Technology Emamy, Zahra Sadat (Author) ; Zarei, Alireze (Supervisor)

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...

Finding the Hamiltonian Cycle Corresponding to the Boundary of a Pseudo-Triangle in its Visibility Graph

, M.Sc. Thesis Sharif University of Technology Farokhi, Soheila (Author) ; Zarei, Alireza (Supervisor)

Abstract

The visibility graph of a simple polygon represents visibility relations between its vertices. Since each vertex in a polygon is visible from the two vertices adjacent to it on the boundary of the polygon, this boundary is analogous to a Hamiltonian cycle in the visibility graph of the polygon. Therefore, visibility graphs are Hamiltonian. Finding this Hamiltonian cycle can be of great help when solving visibility graph recognition problems, in which one should decide whether a given graph is a visibility graph of a simple polygon; and reconstruction problems, which include constructing the polygon corresponding to a given visibility graph. These problems have been solved for the special...