3D indoor topological modelling based on homotopy continuation

Abstract

Indoor navigation is important for various applications such as disaster management, building modelling and safety analysis. In the last decade, the indoor environment has been a focus of extensive research that includes the development of indoor data acquisition techniques, three-dimensional (3D) data modelling and indoor navigation. 3D indoor navigation modelling requires a valid 3D geometrical model that can be represented as a cell complex: a model without any gap or intersection such that the two cells, a room and corridor, should perfectly touch each other. This research is to develop a method for 3D topological modelling of an indoor navigation network using a geometrical model of an indoor building environment. To reduce the time and cost of the surveying process, a low-cost non-contact range-based surveying technique was used to acquire indoor building data. This technique is rapid as it requires a shorter time than others, but the results show inconsistencies in the horizontal angles for short distances in indoor environments. The rangefinder was calibrated using the least squares adjustment and a polynomial kernel. A method of combined interval analysis and homotopy continuation was developed to model the uncertainty level and minimize error of the non-contact range-based surveying techniques used in an indoor building environment. Finally, a method of 3D indoor topological building modelling was developed as a base for building models which include 3D geometry, topology and semantic information. The developed methods in this research can locate a low-cost, efficient and affordable procedure for developing a disaster management system in the near-future.