Detecting Weakly Simple Polygons

A closed curve in the plane is weakly simple if it is the limit (in the Fr\'echet metric) of a sequence of simple closed curves. We describe an algorithm to determine whether a closed walk of length n in a simple plane graph is weakly simple in O(n log n) time, improving an earlier O(n^3)-time algorithm of Cortese et al. [Discrete Math. 2009]. As an immediate corollary, we obtain the first efficient algorithm to determine whether an arbitrary n-vertex polygon is weakly simple; our algorithm runs in O(n^2 log n) time. We also describe algorithms that detect weak simplicity in O(n log n) time for two interesting classes of polygons. Finally, we discuss subtle errors in several previously published definitions of weak simplicity.Comment: 25 pages and 13 figures, submitted to SODA 201

Semantic labeling of places

Indoor environments can typically be divided into places with different functionalities like corridors, kitchens, offices, or seminar rooms. We believe that such semantic information enables a mobile robot to more efficiently accomplish a variety of tasks such as human-robot interaction, path-planning, or localization. In this paper, we propose an approach to classify places in indoor environments into different categories. Our approach uses AdaBoost to boost simple features extracted from vision and laser range data. Furthermore,we apply a Hidden Markov Model to take spatial dependencies between robot poses into account and to increase the robustness of the classification. Our technique has been implemented and tested on real robots as well as in simulation. Experiments presented in this paper demonstrate that our approach can be utilized to robustly classify places into semantic categories