Some computational aspects of geoinformatics Mike Worboys NCGIA, University of Maine, USA

Overview Much of the early technology for spatial data handling (e.g. spatial indices, object-oriented spatial data models) is now well understood. A personal view of interesting current topics in computational geographic information science will be the subject of these lectures. Topics will include spatial reasoning uncertainty multi-contextuality: levels of detail, integration, mode adding time

1. Introduction and formal preliminaries pre-requisites (sets, functions, relations) kinds of relations tolerance relation equivalence relation order relation structures poset lattice Boolean algebra semilattice closure system topology

2. Spatial ontologies, cognition, integration Representations of crisp and vague geographic entities. Cognitive issues. Spatial information integration. Resources Mark, D., Toward a theoretical framework for geographic entity types, COSIT, Smith, B. and Varzi, A., Fiat and bona fide boundaries, Philosophy and Phenom. Research, Worboys, M. and Duckham, Commonsense notions of proximity and direction in environmental space, unpublished. Worboys, M. and Duckham, M. Integrating spatio-thematic information. Second International Conference GIScience 2002, M. Egenhofer and D. Mark (eds.), Lecture Notes in Computer Science 2478, Berlin: SpringerVerlag.

3. Formal models of space and spatial reasoning Spatial reasoning and computational representation, Egenhofer's intersection method and the RCC calculus. Issues in discretization. Key issues in spatial databases. Resources Cohn, A. and Hazarika, S., Qualitative spatial representation and reasoning: An overview, Fund. Inf Egenhofer, M. and Franzosa, R., Point-set topological relations, IJGIS, Egenhofer, M. and Herring, J., Categorizing binary topological relations between regions, lines and points in geographic databases, Tech. Rep. Department of Surveying Engineering, University of Maine, Orono, ME., Guting, R. and Schneider, M., Realms: A foundation for spatial data types in database systems, 3rd Int. Symp. on Large Spatial Databases, 14-35, Singapore, Guting, R.H., An introduction to spatial database systems, VLDB Journ., Randell, D., Cui, Z. and Cohn, A., A spatial logic based on regions and connection, 3 rd Int. Conf. on KRR, Smith, B., Topological foundations of cognitive science, workshop notes.

4. Imperfection and uncertainty in spatial representation and reasoning Typology of uncertainty, scale, granularity and roughness, vagueness, fuzzy sets, rough sets defined by tolerances and equivalences. Resources Cohn, A. and Gotts, N., A theory of spatial regions with indeterminate boundaries, Goodchild, M. and Proctor, J., Scale in a digital geographic world, Geog. and Env. Modelling, Jarvinen, J., Rough sets defined by tolerances, Rough Sets and Current Trends in Computing, Pawlak, Z., Rough sets, IJ Comp Inf Sci, Varzi, A., Vagueness in geography, Philosophy and Geography, Zadeh, L. Fuzzy sets, Information and Control 1965.

5. Models of the dynamic world Ontology of movement and change, ST architectures (e.g. TRIPOD), ST-ontology, event and process models as front ends to STIS, representation and reasoning issues. Resources Allen, J., Maintaining knowledge about temporal intervals, Comm. ACM, Allen, J., Towards a general theory of action and time, AI, Griffiths, T. et al., Tripod: A comprehensive system for the management of spatial and aspatial historical objects, ACM GIS Conf., Guting et al., A foundation for representing and querying moving objects, ACM TODS, Smith, B. SNAP/SPAN ontology. Unpublished notes.

Process issues Classes: Mike Worboys formal presentations of material related to the course Student presentation of key papers Assessment Student’s own presentation (including supporting material) (40%) Student’s notes of the presentation of others (30%) Class test (30%)

Qualitative spatial reasoning (QSR) Qualitative vs. quantitative (discrete vs. continuous). Relevant discretizations. Predictions, diagnoses and explanations of the behavior of spatial entities and systems. “The challenge of QSR is to provide calculi which allow a machine to represent and reason with spatial entities without resort to the traditional quantitative techniques prevalent in e.g. computer graphics or computer vision” (Cohn and Hazarika)

Applications GIS Robotic and human navigation Computer vision (e.g. object recognition through shape matching, scene description) Spatial semantics of natural language Common-sense reasoning about physical systems Visual language syntax and semantics...

Ontology Point-based and region-based ontologies. Single and mixed dimensions The nature of the embedding space (continuous vs. discrete) Primitive entities, relationships and operations

Mereology and topology Mereology and topology are key foundations of QSR. Traditional mathematical topology may not be the appropriate formalization for topological relationships in QSR. Alternative formalizations Clarke, RCC Egenhofer 4-intersection, 9-intersection Boolean connection algebras Key notions: part connection boundary

Richer structure Orientation Distance Size Shape (e.g. convexity) Vagueness, uncertainty and granularity Configuration

Change Spatial and aspatial change Motion