Max J. Egenhofer

Point-Set Topological Spatial Relations

Abstract Practical needs in geographic information systems (GIS) have led to the investigation of formal and sound methods of describing spatial relations. After an introduction to the basic ideas and notions of topology, a novel theory of topological spatial relations between sets is developed in which the relations are defined in terms of the intersections of the boundaries and interiors of two sets. By considering empty and non-empty as the values of the intersections, a total of sixteen topological spatial relations is described, each of which can be realized in R 2. This set is reduced to nine relations if the sets are restricted to spatial regions, a fairly broad class of subsets of a connected topological space with an application to GIS. It is shown that these relations correspond to some of the standard set theoretical and topological spatial relations between sets such as equality, disjointness and containment in the interior.

Reasoning about Binary Topological Relations

A new formalism is presented to reason about topological relations. It is applicable as a foundation for an algebra over topological relations. The formalism is based upon the nine intersections of boundaries, interiors, and complements between two objects. Properties of topological relations are determined by analyzing the nine intersections to detect, for instance, symmetric topological relations and pairs of converse topological relations. Based upon the standard rules for the transitivity of set inclusion, the intersections of the composition of two binary topological relations are determined. These intersections are then matched with the intersections of the eight fundamental topological relations, giving an interpretation to the composition of topological relations.

Using Ontologies for Integrated Geographic Information Systems

Today, there is a huge amount of data gathered about the Earth, not only from new spatial information systems, but also from new and more sophisticated data collection technologies. This scenario leads to a number of interesting research challenges, such as how to integrate geographic information of different kinds. The basic motivation of this paper is to introduce a GIS architecture that can enable geographic information integration in a seamless and flexible way based on its semantic value and regardless of its representation. The proposed solution is an ontology-driven geographic information system that acts as a system integrator. In this system, an ontology is a component, such as the database, cooperating to fulfill the system’s objectives. By browsing through ontologies the users can be provided with information about the embedded knowledge of the system. Special emphasis is given to the case of remote sensing systems and geographic information systems. The levels of ontologies can be used to guide processes for the extraction of more general or more detailed information. The use of multiple ontologies allows the extraction of information in different stages of classification. The semantic integration of aerial images and GIS is a crucial step towards better geospatial modeling.

Spatial SQL: a query and presentation language

Recently, attention has been focused on spatial databases, which combine conventional and spatially related data, such as geographic information systems, CAD/CAM, or VLSI. A language has been developed to query such spatial databases. It recognizes the significantly different requirements of spatial data handling and overcomes the inherent problems of the application of conventional database query languages. The spatial query language has been designed as a minimal extension to the interrogative part of SQL and distinguishes from previously designed SQL extensions by: the preservation of SQL concepts; the high-level treatment of spatial objects; and the incorporation of spatial operations and relationships. It consists of two components, a query language to describe what information to retrieve and a presentation language to specify how to display query results. Users can ask standard SQL queries to retrieve nonspatial data based on nonspatial constraints, use Spatial SQL commands to inquire about situations involving spatial data, and give instructions in the Graphical Presentation Language, GPL to manipulate or examine the graphical presentation. >

Toward the semantic geospatial web

With the growth of the World Wide Web has come the insight that currently available methods for finding and using information on the web are often insufficient. In order to move the Web from a data repository to an information resource, a totally new way of organizing information is needed. The advent of the Semantic Web promises better retrieval methods by incorporating the datas semantics and exploiting the semantics during the search process. Such a development needs special attention from the geospatial perspective so that the particularities of geospatial meaning are captured appropriately. The creation the Semantic Geospatial Web needs the development multiple spatial and terminological ontologies, each with a formal semantics; the representation of those semantics such that they are available both to machines for processing and to people for understanding; and the processing of geospatial queries against these ontologies and the evaluation of the retrieval results based on the match between the semantics of the expressed information need and the available semantics of the information resources and search systems. This will lead to a new framework for geospatial information retrieval based on the semantics of spatial and terminological ontologies. By explicitly representing the role of semantics in different components of the information retrieval process (people, interfaces, search systems, and information resources), the Semantic Geospatial Web will enable users to retrieve more precisely the data they need, based on the semantics associated with these data.

Reasoning about Gradual Changes of Topological Relationships

Geographic objects and phenomena may gradually change their location, orientation, shape, and size over time. A qualitative change occurs if the deformation of an object affects its topological relationship with respect to another object. The observation of such changes is particularly interesting, because qualitative changes frequently require different decisions or trigger new actions. Investigations of a closed set of mutually exclusive binary topological relationships led to a formal model to determine for each topological relationship the relationships closest to it. Applied to the entire set of binary topological relationships between spatial regions, this model describes a partial order over topological relationships and provides a measure to assess how far two relationships are apart from each other. The changes to the binary topological relationship caused by such deformations as translation, rotation, reduction, and expansion of an object are mapped onto this graph. The graphs show characteristic traverses for each kind of deformation. Using these characteristic traverses as knowledge about deformations, one can infer from multiple observations the kind of deformation that caused the change and predict the next topological relationship. Particularly, it provides answers to three kinds of qualitative space-time inferences: (1) Given a process and a state, what is the next most likely state? (2) Given an ordered pair of states, what process may have occurred? (3) Given an ordered pair of states and a process, in what states must the two objects have been in between?

Interoperating Geographic Information Systems

From the Publisher: Interoperating Geographic Information Systems is about efforts to improve the ability of GISs to interoperate, and has been assembled through a collaboration between academic researchers and the software vendor community under the auspices of the US National Center for Geographic Information and Analysis and the Open GIS Consortium Inc. It includes chapters on the basic principles and the various conceptual frameworks that the research community has developed to think about the problem. Other chapters review a wide range of applications and the experiences of the authors in trying to achieve interoperability at a practical level. Interoperability opens enormous potential for new ways of using GIS and new mechanisms for exchanging data, and these are covered in chapters on information marketplaces, with special reference to geographic information. Institutional arrangements are also likely to be profoundly affected by the trend towards interoperable systems, and nowhere is the impact of interoperability more likely to cause fundamental change than in education, as educators address the needs of a new generation of GIS users with access to a new generation of tools. The book is suitable as a secondary text for graduate level courses in computer science, geography, spatial databases, and interoperability and as a reference for researchers and practitioners in industry, commerce and government.

Query Processing in Spatial-Query-by-Sketch *

Abstract Spatial-Query-by-Sketch is the design of a query language for geographic information systems. It allows a user to formulate a spatial query by drawing the desired configuration with a pen on a touch-sensitive computer screen and translates this sketch into a symbolic representation that can be processed against a geographic database. Since the configurations queried usually do not match exactly the sketch, it is necessary to relax the spatial constraints drawn. This paper describes the representation of a sketch and outlines the design of the constraint relaxation methods used during query processing.

Ontology-driven geographic information systems

Information integration is the combination of different types of information in a framework so that it can be queried, retrieved, and manipulated. Integration of geographic data has gained in importance because of the new possibilities arising from the interconnected world and the increasing availability of geographic information. Many times the need for information is so pressing that it does not matter if some details are lost, as long as integration is achieved. To integrate information across computerized information systems it is necessary first to have explicit formalizations of the mental concepts that people have about the real world. Furthermore, these concepts need to be grouped by communities in order to capture the basic agreements that exist within different communities. The explicit formalization of the mental models within a community is an ontology. This thesis introduces a framework for the integration of geographic information. We use ontologies as the foundation of this framework. By integrating ontologies that are linked to sources of geographic information we allow for the integration of geographic information based primarily on its meaning. Since the integration may occurs across different levels, we also create the basic mechanisms for enabling integration across different levels of detail. The use of an ontology, translated into an active, information-system component, leads Ontology-Driven Geographic Information Systems. The results of this thesis show that a model that incorporates hierarchies and roles has the potential to integrate more information than models that do not incorporate these concepts. We developed a methodology to evaluate the influence of the use of roles and of hierarchical structures for representing ontologies on the potential for information integration. The use of a hierarchical structure increases the potential for information integration. The use of roles also improves the potential for information integration, although to a much lesser extent than did the use of hierarchies. The combined effect of roles and hierarchies had a more positive effect in the potential for information integration than the use of roles alone or hierarchies alone. These three combinations (hierarchies, roles, roles and hiearchies) gave better results than the results using neither roles nor hierarchies.

Topological relations in the world of minimum bounding rectangles: a study with R-trees

Recent developments in spatial relations have led to their use in numerous applications involving spatial databases. This paper is concerned with the retrieval of topological relations in Minimum Bounding Rectangle-based data structures. We study the topological information that Minimum Bounding Rectangles convey about the actual objects they enclose, using the concept of projections. Then we apply the results to R-trees and their variations, R+-trees and R*-trees in order to minimise disk accesses for queries involving topological relations. We also investigate queries that involve complex spatial conditions in the form of disjunctions and conjunctions and we discuss possible extensions.