Abstract
Internal Cardinal Direction (ICD) relations can be considered as the refinement to the contains/within topological relation. It is widely used to describe the position of an object in a region. In this paper, three ICD models with varying degrees of details are presented – ICD-5, ICD-9 and ICD-13. In each of these, the notion of a “middle part” is defined using Minimum Bounding Rectangles (MBR). Then focusing on ICD-9, three representation methods are discussed. They are major portion, point set of intersections and proportions of intersections respectively. The ICD-9 model is validated by a cognitive experiment, which helped to determine the size of the middle part in ICD-9 and validate the MBR-based partition method. Based on a psychological theory about vague predicates, conceptual neighborhood and intersection of ICD relations are also discussed briefly.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bennett, B.: Logical Representations for Automated Reasoning about Spatial Relations. PhD thesis, School of Computer Studies, University of Leeds (1997)
Bonini, N., Osherson, D., Viale, R., Williamson, T.: On the Psychology of Vague Predicates. Mind and Language 14, 373–393 (1999)
Car, A., Frank, A.: Modeling of the Hierarchy of Space Applied to Large Road Networks. In: Nievergelt, J., Widmayer, P., Roos, T., Schek, H.-J. (eds.) IGIS 1994. LNCS, vol. 884, pp. 15–24. Springer, Heidelberg (1994)
Clementini, E., Felice, P., Hernández, D.: Qualitative Representation of Positional Information. Artifical Intelligence 95, 317–356 (1997)
Cohn, A.G., Hazarika, S.M.: Qualitative Spatial Representation and Reasoning: An Overview. Fundamenta Informaticae 46, 1–29 (2001)
Cui, Z., Cohn, A.G., Randell, D.A.: Qualitative and Topological Relationships in Spatial Databases. In: Abel, D.J., Ooi, B.-C. (eds.) SSD 1993. LNCS, vol. 692, pp. 296–315. Springer, Heidelberg (1993)
Duckham, M., Worboys, M.: Computational Structure in Three-valued Nearness Relations. In: Montello, D.R. (ed.) Spatial Information Theory: Foundations of Geograpic Information Science. LNCS, vol. 2005, pp. 76–91. Springer, Berlin (2001)
Egenhofer, M.J.: Reasoning about Binary Topological Relationships. In: Switzerland, Z., Gunther, O., Schek, H.J. (eds.) SSD 1991. LNCS, vol. 525, pp. 143–160. Springer, Heidelberg (1991)
Faltings, B.: Qualitative Spatial Reasoning Using Algebraic Topology. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 17–30. Springer, Heidelberg (1995)
Frank, A.U.: Qualitative Spatial Reasoning about Distances and Directions in Geographic Space. Journal of Visual Languages and Computing 3, 343–371 (1992)
Gahegan, M.: Proximity Operators for Qualitative Spatial Reasoning. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 31–44. Springer, Heidelberg (1995)
Goyal, R., Egenhofer, M.J.: The Direction-Relation Matrix: A Representation for Directions Relations between Extended Spatial Objects. In: The annual assembly and the summer retreat of University Consortium for Geographic Information Science (June 1997)
Goyal, R., Egenhofer, M.J.: Cardinal Directions between Extended Spatial Objects. In: IEEE Transactions on Data and Knowledge Engineering (2000) (in press) Available at http://www.spatial.maine.edu/~max/RJ36.html
Goyal, R., Egenhofer, M.J.: Similarity of Cardinal Directions. In: Jensen, C.S., Schneider, M., Seeger, B., Tsotras, V.J. (eds.) SSTD 2001. LNCS, vol. 2121, pp. 36–55. Springer, Heidelberg (2001)
Hernández, D., Clementini, E., Felice, P.D.: Qualitative Distance. In: Frank, A.U., Kuhn, W. (eds.) COSIT 1995. LNCS, vol. 988, pp. 45–57. Springer, Heidelberg (1995)
Hernández, D.: Qualitative vs. Fuzzy Representation of Spatial Distance. In: Freksa, C., Jantzen, M., Valk, R. (eds.) Foundations of Computer Science. LNCS, vol. 1337, pp. 389–398. Springer, Heidelberg (1997)
Hernández, D.: Qualitative Representation of Spatial Knowledge. LNCS, vol. 804. Springer, Heidelberg (1994)
Hirtle, S.C., Jonides, J.: Evidence of hierarchies in Cognitive Maps. Memory & Cognition 13, 208–217 (1985)
Leung, Y., Keung, K.S., He, J.Z.: A Generic Concept-based Object-oriented Geographical Information System. International Journal of Geographical Information Science 13, 475–498 (1999)
Ligozat, G.: Reasoning About Cardinal Directions. Journal of Visual Languages and Computing 9, 23–44 (1998)
Longley, P.A., Goodchild, M.F., Maguire, D., Rhind, D.W.: Geographic Information Systems and Science, pp. 79–96. John Wiley & Sons, Ltd., Chichester (2001)
Mark, D., Comos, D., Egenhofer, M., Freundschuh, S., Gould, M., Nunes, J.: Evaluating and Refining Computational Models of Spatial Relations through Cross-linguistic Human-subjects Testing. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 553–568. Springer, Heidelberg (1995)
Mark, D.M.: Spatial Representation: A Cognitive View. In: Maguire, D.J., Goodchild, M.F., Rhind, D.W., Longley, P. (eds.) Geographical Information Systems: Principles and Applications, 2nd edn., vol. 1, pp. 81–89. John Wiley & Sons, New York (1999)
Mennis, L.M., Peuquet, D.J., Qian, L.: A Conceptual Framework for Incorporating Cognitive Principles into Geographical Database Representation. International Journal of Geographical Information Science 14, 501–520 (2000)
Montello, D.: Scale and Multiple Psychologies of Space. In: Campari, I., Frank, A.U. (eds.) COSIT 1993. LNCS, vol. 716, pp. 312–321. Springer, Heidelberg (1993)
Papadias, D., Theodoridis, Y., Sellis, T., Egenhofer, M.: Topological Relations in the World of Minimum Bounding Rectangles: A Study with R-trees. In: Carey, M., Schneider, D. (eds.) Proceedings of ACM SIGMOD, San Jose, CA, pp. 92–103 (1995)
Papadias, D., Egenhofer, M.: Algorithms for Hierarchical Spatial Reasoning. Geoinformatica 1, 251–273 (1997)
Randell, D., Cui, Z., Cohn, A.: A Spatial Logic Based on Regions and Connection. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Third International Conference (KR 1992), pp. 165–176. Morgan Kaufmann, San Francisco (1992)
Renz, J., Nebel, B.: On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus. Artificial Intelligence 12, 95–149 (1999)
Renz, J., Mitra, D.: Qualitative Direction Calculi with Arbitrary Granularity. In: Zhang, C., Guesgen, H.W., Yeap, W.-K. (eds.) PRICAI 2004. LNCS (LNAI), vol. 3157, pp. 65–74. Springer, Heidelberg (2004)
Schamber, L., Eisenberg, M.B., Nilan, M.S.: A re-examination of relevance: toward a dynamic, situational definition. Information Processing & Management 26, 755–776 (1990)
Sistla, A.P., Yu, C., Haddad, R.: Reasoning About Spatial Relationships in Picture Retrieval Systems. In: Jorge, B., Jarke, M., Zaniolo, C. (eds.) Proceedings of VLDB, pp. 570–581. Morgan Kaufmann, San Francisco (1994)
Skiadopoulos, S., Koubarakis, M.: Composing Cardinal Direction Relations. In: Jensen, C.S., et al. (eds.) SSTD 2001. LNCS, vol. 2121, pp. 299–317. Springer, Heidelberg (2001)
Smith, B., Varzi, A.C.: Fiat and Bona Fide Boundaries. Philosophy and Phenomenological Research 60, 401–420 (2000)
Stevens, A., Coupe, P.: Distortions in Judged Spatial Relations. Cognitive Psychology 10, 422–437 (1978)
Timpf, S., Volta, G.S., Pollock, D.W., Egenhofer, M.J.: A Conceptual Model of Wayfinding Using Multiple Levels of Abstraction. In: Frank, A.U., Formentini, U., Campari, I. (eds.) GIS 1992. LNCS, vol. 639, pp. 348–367. Springer, Heidelberg (1992)
Timpf, S., Frank, A.U.: Using Hierarchical Spatial Data Structures for Hierarchical Spatial Reasoning. In: Frank, A.U. (ed.) COSIT 1997. LNCS, vol. 1329, pp. 69–83. Springer, Heidelberg (1997)
Worboys, M.F.: Nearness Relations in Environmental Space. International Journal of Geographical Information Science 15, 633–651 (2001)
Yashino, R.: A Note on Cognitive Map: An Optimal Spatial Knowledge Representation. Journal of Mathematical Psychology 35, 371–393 (1991)
Zimmermann, K.: Enhancing Qualitative Spatial Reasoning- Combining Orientation and Distance. In: Campari, I., Frank, A.U. (eds.) COSIT 1993. LNCS, vol. 716, pp. 69–76. Springer, Heidelberg (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, Y., Wang, X., Jin, X., Wu, L. (2005). On Internal Cardinal Direction Relations. In: Cohn, A.G., Mark, D.M. (eds) Spatial Information Theory. COSIT 2005. Lecture Notes in Computer Science, vol 3693. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556114_18
Download citation
DOI: https://doi.org/10.1007/11556114_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28964-7
Online ISBN: 978-3-540-32020-3
eBook Packages: Computer ScienceComputer Science (R0)