Qualitative Spatial Reasoning about Relative Orientation --- A Question of Consistency ---

Abstract. After the emergence of Allen s Interval Algebra Qualitative Spatial Reasoning has evolved into a fruitful field of research in artificial intelligence with possible applications in geographic information systems (GIS) and robot navigation Qualitative Spatial Reasoning abstracts from the detailed metric description of space using rich mathematical theories and restricts its language to a finite, often rather small, set of relations that fulfill certain properties. This approach is often deemed to be cognitively adequate . A major question in qualitative spatial reasoning is whether a description of a spatial situation given as a constraint network is consistent. The problem becomes a hard one since the domain of space (often R2 ) is infinite. In contrast many of the interesting problems for constraint satisfaction have a finite domain on which backtracking methods can be used. But because of the infinity of its domains these methods are generally not applicable to Qualitative Spatial Reasoning. Anyhow the method of path consistency or rather its generalization algebraic closure turned out to be helpful to a certain degree for many qualitative spatial calculi. The problem regarding this method is that it depends on the existence of a composition table, and calculating this table is not an easy task. For example the dipole calculus (operating on oriented dipoles) DRAf has 72 base relations and binary composition, hence its composition table has 5184 entries. Finding all these entries by hand is a hard, long and error-prone task. Finding them using a computer is also not easy, since the semantics of DRAf in the Euclidean Plane, its natural domain, rely on non-linear inequalities. This is not a special problem of the DRAf calculus. In fact, all calculi dealing with relative orientation share the property of having semantics based on non-linear inequalities in the Euclidean plane. This not only makes it hard to find a composition table, it also makes it particularly hard to decide consistency for these calculi. As shown in [79] algebraic closure is always just an approximation to consistency for these calculi, but it is the only method that works fast. Methods like Gröbner reasoning can decide consistency for these calculi but only for small constraint networks. Still finding a composition table for DRAf is a fruitful task, since we can use it analyze the properties of composition based reasoning for such a calculus and it is a starting point for the investigation of the quality of the approximation of consistency for this calculus. We utilize a new approach for calculating the composition table for DRAf using condensed semantics, i.e. the domain of the calculus is compressed in such a way that only finitely many possible configurations need to be investigated. In fact, only the configurations need to be investigated that turn out to represent special characteristics for the placement of three lines in the plane. This method turns out to be highly efficient for calculating the composition table of the calculus. Another method of obtaining a composition table is borrowing it via a suitable morphism. Hence, we investigate morphisms between qualitative spatial calculi. Having the composition table is not the end but rather the beginning of the problem. With that table we can compute algebraically closed refinements of constraint networks, but how meaningful is this process? We know that all constraint networks for which such a refinement does not exist are inconsistent, but what about the rest? In fact, they may be consistent or not. If they are all consistent, then we can be happy, since algebraic closure would decide consistency for the calculus at hand. We investigate LR, DRAf and DRAfp and show that for all these calculi algebraic closure does not decide consistency. In fact, for the LR calculus algebraic closure is an extremely bad approximation of consistency. For this calculus we introduce a new method for the approximation of consistency based on triangles, that performs far better than algebraic closure. A major weak spot of the field of Qualitative Spatial Reasoning is the area of applications. It is hard to refute the accusation of qualitative spatial calculi having only few applications so far. As a step into the direction of scrutinizing the applicability of these calculi, we examine the performance of DRA and OPRA in the issue of describing and navigating street networks based on local observations. Especially for OPRA we investigate a factorization of the base relations that is deemed cognitively adequate . Whenever possible we use real-world data in these investigations obtained from OpenStreetMap

Algebraic Properties of Qualitative Spatio-Temporal Calculi

Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent do the qualitative calculi proposed meet these demands? The literature provides various answers to the first question but only few facts about the second. In this paper we identify the minimal requirements to binary spatio-temporal calculi and we discuss the relevance of the according axioms for representation and reasoning. We also analyze existing qualitative calculi and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia

Geospatial images in the acquisition of spatial knowledge for wayfinding

Geospatial images such as maps and aerial photographs are important sources of spatial knowledge that people use for wayfinding. The rapid development of geodata acquisition and digital graphics has recently led to rather complete geographic coverage of both traditional and novel types of geospatial images. Divergent types of geospatial images vary in their support of human acquisition of spatial knowledge. However evaluative studies about the acquisition of spatial knowledge from the diversity of geospatial images have been rare. In this article we review a variety of literature about the acquisition of spatial knowledge while paying particular attention to the role of geospatial images. Based on the literature we present a framework of image parameters that characterize the acquisition of spatial knowledge from geospatial images: vantage point number of visible vertical features and visual realism. With the help of the framework we evaluate commonly used geospatial images. In concordance with the previous experiments our evaluation shows that the different types of geospatial images have large differences in the types of spatial knowledge they support and to what extent. However further experimentation is needed in order to better understand the human cognitive needs for geospatial images and to develop more useful geospatial images for wayfinding

Automated generation of geometrically-precise and semantically-informed virtual geographic environnements populated with spatially-reasoning agents

La Géo-Simulation Multi-Agent (GSMA) est un paradigme de modélisation et de simulation de phénomènes dynamiques dans une variété de domaines d'applications tels que le domaine du transport, le domaine des télécommunications, le domaine environnemental, etc. La GSMA est utilisée pour étudier et analyser des phénomènes qui mettent en jeu un grand nombre d'acteurs simulés (implémentés par des agents) qui évoluent et interagissent avec une représentation explicite de l'espace qu'on appelle Environnement Géographique Virtuel (EGV). Afin de pouvoir interagir avec son environnement géographique qui peut être dynamique, complexe et étendu (à grande échelle), un agent doit d'abord disposer d'une représentation détaillée de ce dernier. Les EGV classiques se limitent généralement à une représentation géométrique du monde réel laissant de côté les informations topologiques et sémantiques qui le caractérisent. Ceci a pour conséquence d'une part de produire des simulations multi-agents non plausibles, et, d'autre part, de réduire les capacités de raisonnement spatial des agents situés. La planification de chemin est un exemple typique de raisonnement spatial dont un agent pourrait avoir besoin dans une GSMA. Les approches classiques de planification de chemin se limitent à calculer un chemin qui lie deux positions situées dans l'espace et qui soit sans obstacle. Ces approches ne prennent pas en compte les caractéristiques de l'environnement (topologiques et sémantiques), ni celles des agents (types et capacités). Les agents situés ne possèdent donc pas de moyens leur permettant d'acquérir les connaissances nécessaires sur l'environnement virtuel pour pouvoir prendre une décision spatiale informée. Pour répondre à ces limites, nous proposons une nouvelle approche pour générer automatiquement des Environnements Géographiques Virtuels Informés (EGVI) en utilisant les données fournies par les Systèmes d'Information Géographique (SIG) enrichies par des informations sémantiques pour produire des GSMA précises et plus réalistes. De plus, nous présentons un algorithme de planification hiérarchique de chemin qui tire avantage de la description enrichie et optimisée de l'EGVI pour fournir aux agents un chemin qui tient compte à la fois des caractéristiques de leur environnement virtuel et de leurs types et capacités. Finalement, nous proposons une approche pour la gestion des connaissances sur l'environnement virtuel qui vise à supporter la prise de décision informée et le raisonnement spatial des agents situés

Schematisation in Hard-copy Tactile Orientation Maps

This dissertation investigates schematisation of computer-generated tactile orientation maps that support mediation of spatial knowledge of unknown urban environments. Computergenerated tactile orientation maps are designed to provide the blind with an overall impression of their surroundings. Their details are displayed by means of elevated features that are created by embossers and can be distinguished by touch. The initial observation of this dissertation states that only very little information is actually transported through tactile maps owing to the coarse resolution of tactual senses and the cognitive effort involved in the serial exploration of tactile maps. However, the differences between computer-generated, embossed tactile maps and manufactured, deep-drawn tactile maps are significant. Therefore the possibilities and confines of communicating information through tactile maps produced with embossers is a primary area of research. This dissertation has been able to demonstrate that the quality of embossed prints is an almost equal alternative to traditionally manufactured deep-drawn maps. Their great advantage is fast and individual production and (apart from the initial procurement costs for the printer)low price, accessibility and easy understanding without the need of prior time-consuming training. Simplification of tactile maps is essential, even more so than in other maps. It can be achieved by selecting a limited number from all map elements available. Qualitative simplification through schematisation may present an additional option to simplification through quantitative selection. In this context schematisation is understood as cognitively motivated simplification of geometry and synchronised maintenance of topology. Rather than further reducing the number of displayed objects, the investigation concentrates on how the presentation of different forms of streets (natural vs. straightened) and junctions (natural vs. prototypical) affects the transfer of knowledge. In a second area of research, a thesis establishes that qualitative simplification of tactile orientation maps through schematisation can enhance their usability and make them easier to understand than maps that have not been schematised. The dissertation shows that simplifying street forms and limiting them to prototypical junctions does not only accelerate map exploration but also has a beneficial influence on retention performance. The majority of participants that took part in the investigation selected a combination of both as their preferred display option. Tactile maps that have to be tediously explored through touch, uncovering every detail, complicate attaining a first impression or an overall perception. A third area of research is examined, establishing which means could facilitate map readersâ options to discover certain objects on the map quickly and without possessing a complete overview. Three types of aids are examined: guiding lines leading from the frame of the map to the object, position indicators represented by position markers at the frame of the map and coordinate specifications found within a grid on the map. The dissertation shows that all three varieties can be realised by embossers. Although a guiding line proves to be fast in size A4 tactile maps containing only one target object and few distracting objects, it also impedes further exploration of the map (similar to the grid). In the following, advantages and drawbacks of the various aids in this and other applications are discussed. In conclusion the dissertation elaborates on the linking points of all three examinations. They connect and it is argued that cognitively motivated simplification should be a principle of construction for embossed tactile orientation maps in order to support their use and comprehension. A summary establishes the recommendations that result from this dissertation regarding construction of tactile orientation maps considering the limitations through embosser constraints. Then I deliberate how to adapt schematisation of other maps contingent to intended function, previous knowledge of the map reader, and the relation between the time in which knowledge is acquired and the time it is employed. Closing the dissertation, I provide an insight into its confines and deductions and finish with a prospective view to possible transfers of the findings to other applications, e.g. multimedia or interactive maps on pin-matrix displays and devices

Hierarchical Graphs as Organisational Principle and Spatial Model Applied to Pedestrian Indoor Navigation

In this thesis, hierarchical graphs are investigated from two different angles – as a general modelling principle for (geo)spatial networks and as a practical means to enhance navigation in buildings. The topics addressed are of interest from a multi-disciplinary point of view, ranging from Computer Science in general over Artificial Intelligence and Computational Geometry in particular to other fields such as Geographic Information Science. Some hierarchical graph models have been previously proposed by the research community, e.g. to cope with the massive size of road networks, or as a conceptual model for human wayfinding. However, there has not yet been a comprehensive, systematic approach for modelling spatial networks with hierarchical graphs. One particular problem is the gap between conceptual models and models which can be readily used in practice. Geospatial data is commonly modelled - if at all - only as a flat graph. Therefore, from a practical point of view, it is important to address the automatic construction of a graph hierarchy based on the predominant data models. The work presented deals with this problem: an automated method for construction is introduced and explained. A particular contribution of my thesis is the proposition to use hierarchical graphs as the basis for an extensible, flexible architecture for modelling various (geo)spatial networks. The proposed approach complements classical graph models very well in the sense that their expressiveness is extended: various graphs originating from different sources can be integrated into a comprehensive, multi-level model. This more sophisticated kind of architecture allows for extending navigation services beyond the borders of one single spatial network to a collection of heterogeneous networks, thus establishing a meta-navigation service. Another point of discussion is the impact of the hierarchy and distribution on graph algorithms. They have to be adapted to properly operate on multi-level hierarchies. By investigating indoor navigation problems in particular, the guiding principles are demonstrated for modelling networks at multiple levels of detail. Complex environments like large public buildings are ideally suited to demonstrate the versatile use of hierarchical graphs and thus to highlight the benefits of the hierarchical approach. Starting from a collection of floor plans, I have developed a systematic method for constructing a multi-level graph hierarchy. The nature of indoor environments, especially their inherent diversity, poses an additional challenge: among others, one must deal with complex, irregular, and/or three-dimensional features. The proposed method is also motivated by practical considerations, such as not only finding shortest/fastest paths across rooms and floors, but also by providing descriptions for these paths which are easily understood by people. Beyond this, two novel aspects of using a hierarchy are discussed: one as an informed heuristic exploiting the specific characteristics of indoor environments in order to enhance classical, general-purpose graph search techniques. At the same time, as a convenient by- product of this method, clusters such as sections and wings can be detected. The other reason is to better deal with irregular, complex-shaped regions in a way that instructions can also be provided for these spaces. Previous approaches have not considered this problem. In summary, the main results of this work are: • hierarchical graphs are introduced as a general spatial data infrastructure. In particular, this architecture allows us to integrate different spatial networks originating from different sources. A small but useful set of operations is proposed for integrating these networks. In order to work in a hierarchical model, classical graph algorithms are generalised. This finding also has implications on the possible integration of separate navigation services and systems; • a novel set of core data structures and algorithms have been devised for modelling indoor environments. They cater to the unique characteristics of these environments and can be specifically used to provide enhanced navigation in buildings. Tested on models of several real buildings from our university, some preliminary but promising results were gained from a prototypical implementation and its application on the models

A Qualitative Representation of Spatial Scenes in R2 with Regions and Lines

Regions and lines are common geographic abstractions for geographic objects. Collections of regions, lines, and other representations of spatial objects form a spatial scene, along with their relations. For instance, the states of Maine and New Hampshire can be represented by a pair of regions and related based on their topological properties. These two states are adjacent (i.e., they meet along their shared boundary), whereas Maine and Florida are not adjacent (i.e., they are disjoint). A detailed model for qualitatively describing spatial scenes should capture the essential properties of a configuration such that a description of the represented objects and their relations can be generated. Such a description should then be able to reproduce a scene in a way that preserves all topological relationships, but without regards to metric details. Coarse approaches to qualitative spatial reasoning may underspecify certain relations. For example, if two objects meet, it is unclear if they meet along an edge, at a single point, or multiple times along their boundaries. Where the boundaries of spatial objects converge, this is called a spatial intersection. This thesis develops a model for spatial scene descriptions primarily through sequences of detailed spatial intersections and object containment, capturing how complex spatial objects relate. With a theory of complex spatial scenes developed, a tool that will automatically generate a formal description of a spatial scene is prototyped, enabling the described objects to be analyzed. The strengths and weaknesses of the provided model will be discussed relative to other models of spatial scene description, along with further refinements