Some computational aspects of geoinformatics

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Some computational aspects of geoinformatics

• Mike Worboys
• NCGIA, University of Maine, USA

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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

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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
•  

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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, 1993.
• Smith, B. and Varzi, A., Fiat and bona fide
  boundaries, Philosophy and Phenom. Research,
  2000.
• 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  unpublished.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.

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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. 2001.
• Egenhofer, M. and Franzosa, R., Point-set
  topological relations, IJGIS, 1991.
• 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., 1991.
• 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, 1993.
• Guting, R.H., An introduction to spatial database
  systems, VLDB Journ., 1994.
• Randell, D., Cui, Z. and Cohn, A., A spatial
  logic based on regions and connection, 3rd Int.
  Conf. on KRR, 1992.
• Smith, B., Topological foundations of cognitive
  science, workshop notes.

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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, 1994.
• Goodchild, M. and Proctor, J., Scale in a digital
  geographic world, Geog. and Env. Modelling, 1997.
• Jarvinen, J., Rough sets defined by tolerances,
  Rough Sets and Current Trends in Computing, 2000.
• Pawlak, Z., Rough sets, IJ Comp Inf Sci, 1982.
• Varzi, A., Vagueness in geography, Philosophy and
  Geography, 2002.
• Zadeh, L. Fuzzy sets, Information and Control
  1965.

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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, 1983.
• Allen, J., Towards a general theory of action and
  time, AI, 1984.
• Griffiths, T. et al., Tripod A comprehensive
  system for the management of spatial and aspatial
  historical objects, ACM GIS Conf., 2001.
• Guting et al., A foundation for representing and
  querying moving objects, ACM TODS, 2000.
• Smith, B. SNAP/SPAN ontology. Unpublished notes.

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Process issues

• Classes
• Mike Worboys formal presentations of material
  related to the course
• Student presentation of key papers
• Assessment
• Students own presentation (including supporting
  material) (40)
• Students notes of the presentation of others
  (30)
• Class test (30)

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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)

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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
• ...

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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

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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

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Richer structure

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

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Change

• Spatial and aspatial change
• Motion