The Node-Relation-Structure NRS Representing Indoor Spaces Using the Node-Relation-Structure

Copyright © 2010 Open Geospatial Consortium 19 7 Related Work Substantial work has already been done in the area of indoor navigation. In the following, we give a brief over- view of current developments on specific systems and underlying information structures needed in order to support location services and route planning in indoor environments. The OntoNav system [3] describes a semantic indoor navigation system. It proposes an indoor navigation ontol- ogy which provides semantic descriptions of the constituent elements of navigation paths such as obstacles, exits, and passages. Furthermore, specific user capabilitieslimitations are modeled allowing for a user-centric navigation paradigm and the application of reasoning functionality. In the field of mobile robot navigation, Kulyukin et al. [4] present an indoor navigation system for assisting the visually impaired. The system is designed as a tool to help visually impaired customers navigate a typical gro- cery store using a robot shopping cart. For localization, the system relies on RFID tags deployed at various locations in the store. In order to simplify complex spatial relationships between 3D objects in built environment, Lee [6] introduces a topological data model, the Node-Relation-Structure NRS. The NRS is a dual graph representing the connec- tivity relationships between 3D entities by Poincaré Duality. In the context of emergency response, Lee et al. [7] show the use of this simplified NRS representation of the indoor environment for routing purposes. Within the REWERSE project, Lorenz et al. [2, 17] provide an approach for the automated partitioning of the building interior not only into rooms, but also into smaller parts, so called cells. The internal structure of the building is hence represented as a hierarchical graph enabling localization and route planning on different levels of detail. The partitioning is based on the automatic cell-and-portal decomposition of polygonal scenes proposed by Lefebvre and Hornus [5]. Liao et al. [13] propose an approach to track moving objects and their identity in indoor environments. Based on a Voronoi graph providing a natural discretization of the environment, the locations of people are estimated using noisy, sparse information collected by id-sensors such as infrared and ultrasound badge systems. Kolodziej [9] provides a comprehensive overview and discussion of existing technologies and systems in the context of indoor navigation. Various approaches and algorithms for indoor localization using different kinds of sensor systems are described, which form the basis for Location Based Services LBS.

7.1 Representing Indoor Spaces Using the Node-Relation-Structure

It is assumed that for realizing navigation systems, built environments are represented geometrically in Euclide- an space, particularly in IR 3 . Therefore, a building can be described using geometric and topological representa- tions defined in ISO 19107 [1].

7.1.1 The Node-Relation-Structure NRS

Network structure has been used to abstract geographical features such as roads or streams. According to the scale of topographic map, area features e.g. cities, buildings are represented as nodes and roads are shown as edges in the network [24]. Lee [6] adopted the network structure concept to represent topological relationships, e.g., adjacency and connectivity relationships, among 3D objects. In the network-based topological representa- tion, 2D or 3D geographical features are represented as nodes, and the topological relationships among the features are represented as edges, which is called Node-Relation Structure NRS [6]. The NRS is a dual graph structure derived based on three elements, which are Poincaré Duality, graph-theoretical formalisms, and a hierarchical network structure [6]. Lee utilized the NRS to develop Combinatorial Data Mode CDM, which is a logical data model to abstract, simplify, and represent the complex topological relationships among 3D spatial units in indoor environments, such as rooms within a building [6]. The CDM can be used to find spatial neigh- bors of a particular feature or spatial unit in a building. As answer to the question “Which other 3D objects are located on top or under a particular 3D object?” will provide information about its neighbors, the CDM can be very useful in environmentally oriented analyses such as noise or air pollution and emergency situations in micro-spatial environments. In order to implement network-based analysis such as optimal routing, allocation, tracing and spatial analysis in the CDM, the logical network model needs to be complemented by a geometric Copyright © 2010 Open Geospatial Consortium 20 network model that accurately represents these geometric properties. A 3D network data model, called Geomet- ric Network Model GNM, is developed by transforming the CDM, representing the connectivity relationships among 3D objects. A Straight Medial Axis Transformation Algorithm S-MAT is applied to perform one key step in this transformation [25].

7.1.2 Poincaré Duality