Abstract
The paper considers two classes of point location problems found in visual navigation of a mobile robot. The problems we consider are finding the location of a robot using a map of the room where the robot moves and an image taken by a camera carried by the robot. In the first class of problems, vertical edges in the image are given, and a possible location for the robot is investigated by establishing a correspondence between the edges in the images and vertical poles given in the map. In the second class of problems, the possible region for the robot is investigated under the assumption that vertical edges are distinguishable from each other, but only the order in which the edges are found when the image is swept from left to right is given. These problems and their variations are considered from a computational geometry point of view, and efficient algorithms for solving them are given.
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