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    ACRS 1997

    GIS
    Talking GIS : A Theoretical Basis

    5. Scope of the Study
    The GIS literature frequently cites three types of spatial relations as the most fundamental ones (Pullar and Egenhofer 1988; Wornboys 1992):

    Topological relations are those spatial relations that are invariant under continuous transformations with continuous inverses.
    • Metric relations refer to distance relations which may be quantative if the distance has been measured or computed or qualitative if distance descriptors such as near or far are used.
    • Direction relations refer to azimuth (or bearing) which are quantitative, or to direction descriptors such as forward, right, or east, which are qualitative.
    This research builds on strong evidence that among those spatial relations, topological properties are most fundamental (Lynch 1960; Kuipers 1978; Riesbeck 1980; Mark and Egenhofer 1994a), and that metric or direction properties are appropriate refinements of certain topological configuration: Topology matters, metric refines (Egenhofer and Mark 1995b). This research focuses on metric refinements of topological relations.

    In order to allow for qualitative queries, the semantics of natural-language spatial elations must be defined and represented within a GIS. A variety of properties may contribute to the choice of a particular spatial term (Mark et al. 1995), such as the natural language (English vs. Spanish), the culture, the semantics of the spatial objects involved, the tasks users envision, the context in which the objects are presented, the pictorial presentation ( a sketch vs. a topographic map), and the objects' geometrics. We will concentrate here on the geometrical aspects. The approach taken here is a refinement of the 9-intersection model (Egenhofer and Herring 1991) to accommodate more semantics of natural-language spatial relations. The 9-intersection model itself has proved to be highly successful in the human subject testing conducted in the first round (Mark and Egenhofer 1992; mark and Egenhofer 1994a; Mark and Egenhofer 1994b; Mark and Egenhofer 1995). The refined model in this research will thus provide a framework for further testing in the second iteration of he human subject testing procedures.

    Combinations of topological relations involve points, lines, and regions. The research on topological relations and spatial predicates in this research will be confined to line-region relationships only. For the purpose of carrying out the calibration of symbols, we focused on the road and park relationship (Mark and Egenhofer 1995).

    6. Topics Excluded from the Present Investigation
    Related issues that have been excluded from this investigations are:
    • Line-line and region-region relationships of the 9-intersection model have been excluded primarily to limit the scope of this work to line-region relations. The reasons are two fold: exploring the line-region relations aims to determine the basis principles of formalization and, secondly, the existence of human-subject data for the line-region relations aids the testing of the resulting formalism. The basic principles resulting form this investigation of line-region relations are expected to be extendible for line-line and line-region relationships, which will form a logical sequence for future work.
    • Orientations of the objects represented in a spatial configuration may have an influence on the choice of terms employed to describe the spatial relationships between these objects. Such orientations could play a role in refining further the semantics that are derived from mere metric information about the scene From a formal perspective, there is a need to formalize the role of orientations (Abdelmoty 1994). This will require separate treatment and is not addressed in this research.
    • The normal definition of spatial entities is not included in this work as such formal semantics (Rugg 1995) are provided for in current standards such as the Spatial Data Transfer Standard. Future work in this area is being carried out by the sub-committees of the Federal Geographic Data Committee.
    • Context of the configuration and tasks envisioned by users are factors that may influence the choice of spatial relationships. For example, Bangor airport is near the University of Maine if one had to board a plane. However, if one needed to buy groceries, then the shops in Bangor are far from Orono. However, we do not consider this issue in this research, because the scope of this research is focused primarily on the computational formal framework of spatial relationships.
    • The pictorial representations of configurations may have an effect on the determination of the best spatial description to be used. There is evidence that people use different entries to judge pictures and sentences instantiating the same sense (Herskiovits to appear). As this issue deals with the representation of the spatial entities themselves and not of spatial relationships, it is excluded form the investigation in this research.
    • This work is not concerned with cultural and linguistic aspects per se of spatial prepositions. We propose a formal framework for capturing the semantics of spatial relationships and validate our model by testing it with data obtained from experimental involving human subjects.
    7. Major Results and Conclusions
    The major finding of this research is that it is possible to create a formal model for representing natural-language spatial relations. The model identifies metric parameters that are a refinement of topology. The results revealed that these proposed parameters provide the discriminatory function in the grouping of the natural-language terms. For terms with the same topology, it was proven that metric influences the choice of natural-language spatial terms.

    It was also found that when a parameter is significant for a spatial term in the prototypical test then for the agreement task (Mark 1996) there is a corresponding significant increase in agreement for that particular spatial term in describing a configuration in which this parameter is present. This observation was found to be true for the English data sets that were tested. As these findings are based on the analysis of two separate and distinct data sets, they thus prove that the results from the prototypical tests are not data dependent.

    The formal model has the flexibility of having its parameters calibrated for particular spatial terms as well as domain of users. Based on the data available, the minimum and maximum extent of the parameter values for each group as well as for each natural-language spatial term used in this investigation was calibrated. These results were complied to create a Metric Table of Spatial Terms. This table is significant as it allows for the discrimination between spatial terms based on the topologic and metric parameters.

    Bibliography
    • A. Abdelmoty (1995) Modelling and Reasoning in Spatial Databases: a Deductive Object-Oriented Approach Ph. D. thesis, Department of Computer Science, Heriot-Watt University, Edinburgh, Scotland.
    • I. Campari (1994) GIS Commands As Small Scale Space Terms: Cross-Cultural Conflict on their Spatial Content. In: T. Waugh and R. Healey (eds.), Sixth International Symposium on Spatial Data Handling, Edinburgh, Scotland, pp. 554-571.
    • M. Egenhofer and J. Herring (1991) Categorizing Binary Topological Relationships Between Regions, Lines, and Points in Geographic Databases. Department of Surveying Engineering, University of Maine. Orono, ME.
    • M. Egenhofer and D. Mark (1995b) Naïve Geography. In: A. Frank and W. Kuhn (eds)., Spatial Information Theory-A Theoretical Basis for GIS, International Conference COSIT'95. Semmering , Austria. Lecture Notes in Computer Science 988, pp. 1-15, Berlin: Springer-Verlag.
    • A. Frank (1992) Qualitative Reasoning about Distance and Directions in Geographic Space. Journal of Visual Languages and Computing 3(4): 343-371.
    • D. Hernandez, E. Clementini, and P. Di Felice (1995) Qualitative Distances. In A. Frank and W. Kuhn (eds.), Spatial Information Theory-A Theoretical Basis for GIS. International Conference COSIT '95 Semmering, Austria, Lecture Notes in Computer Science 988, pp. 45-58, Berlin: Springer-Verlag.
    • A. Herskovits (to appear) Language, Spatial Cognition, and Vision. In: O. Stock (ed.) Temporal and Spatial Reasoning, Dordrecht, The Netherlands : Kluwer.
    • A. Herskovits (1986) Language and Spatial Cognition: An Interdisciplinary Study of the Prepositions in English, Cambridge, MA: Cambridge University Press.
    • J. Hong (1994) Qualitative Distance and Direction Reasoning in Geographic Space. Ph. D. Thesis, Department of Spatial Information Science and Engineering, University of Maine, ME.
    • J. Hong, M. Egenhofer, and A. Frank (1995) On the Robustness of Qualitative Distance and Directions Reasoning in: D. Peuquet (ed.), Autocarto 12, Charlotte, NC, pp. 301-310.
    • B. Kuipers (1978) Modeling Spatial Knowledge Cognitive Science 2: 129-153.
    • K. Lynch (1960) The Image of a City, Cambridge, MA: MIT Press.
    • D. Mark (1996) Data collected by Mark (personal communication).
    • D. Mark, D. Comas, M. Egenhofer, S. Freundschuh, M. Gould, and J. Nunes (1995) Evaluating and Refining Computational Models of Spatial Relations Through Cross-Linguistic Human-Subject Testing in: A. Frank and W. Kuhn (edsd.), Spatial Information Theory-A Theoretical Basis for GIS, International Conference COSIT '95. Semmering, Austria. Lecture Notes in Computer Science 988, pp. 553-568, Berlin: Springer-Verlag.
    • D. Mark and M. Egenhofer (1992) An Evaluation of the 9-intersection for Region-Line Relations. In :GIS/LIS '92, San Jose, CA , pp. 513-521.
    • D. Mark and M. Egenhofer (1994a) Calibrating the Meaning of Spatial Predicates from Natural Language: Line-Region Relations. In: T. Waugh and R. Healey (eds.), Sixth International Symposium on Spatial Data Handling, Edinburgh, Scotland, pp. 538-553.
    • D. Mark and M. Egenhofer (1995) Topology of Prototypical Spatial Relations Between Lines and Regions in English and Spanish. In: D. Pseuquet (ed.), Autocarto 12, Charlotte, NC, pp. 245-254.
    • D. Peuquet and Z. Ci-Xiang (1987) An algorithm to determine the directional relationship between arbitrarily shaped polygons in the plane. Pattern Recognition 20(1): 65-74.
    • Pullar and M. Egenhofer (1988) Towards Formal Definitions of Topological Relations Among Spatial Objects in: D. Marble (ed.), Third International Symposium on Spatial Data Handling, Sydney, Australia, pp. 225-242.
    • T. Regier (1995) A model of the human capacity for categorizing spatial relations, Cognitive Linguistics 6(1): 63-88.
    • C. Riesbeck (1980) "You Can't miss It" Judging the Clarity of Directions. Cognitive Science 4: 285-303.
    • R. Rugg (1995) Extending the SDTS Model of Features and Attributes, Association of American Geographers: 91st. Annual meeting, Chicago, IL, p. 266.
    • L. Talmy (1983) How Language Structures Space. In: H. Pick and L. Acredolo (eds), Spatial Orientation, New York: Plenium Press, pp. 225-282.
    • M. worboys (1992) A geometric Model for Planar Geographical Objects. International Journal of Geographical Information Systems 6(5): 353-372.
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