Similarity of Cardinal Directions

  • Roop K. Goyal
  • Max J. Egenhofer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2121)


Like people who casually assess similarity between spatial scenes in their routine activities, users of pictorial databases are often interested in retrieving scenes that are similar to a given scene, and ranking them according to degrees of their match. For example, a town architect would like to query a database for the towns that have a landscape similar to the landscape of the site of a planned town. In this paper, we develop a computational model to determine the directional similarity between extended spatial objects, which forms a foundation for meaningful spatial similarity operators. The model is based on the direction-relation matrix. We derive how the similarity assessment of two direction-relation matrices corresponds to determining the least cost for transforming one direction-relation matrix into another. Using the transportation algorithm, the cost can be determined efficiently for pairs of arbitrary direction-relation matrices. The similarity values are evaluated empirically with several types of movements that create increasingly less similar direction relations. The tests confirm the cognitive plausibility of the similarity model.


Target Object Reference Object Cardinal Direction Similarity Assessment Basic Feasible Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. W. Al-Khatib, Y. Day, A. Ghafoor, and P. Berra (1999) Semantic Modeling and Knowledge Representation in Multimedia Databases. IEEE Transactions on Knowledge and Data Engineering 11(1): 64–80.CrossRefGoogle Scholar
  2. Y. Aslandogan and C. Yu (1999) Techniques and Systems for Image and Video Retrieval. IEEE Transactions on Knowledge and Data Engineering 11(1): 56–63.CrossRefGoogle Scholar
  3. T. Bruns and M. Egenhofer (1996) Similarity of Spatial Scenes. in: M.-J. Kraak and M. Molenaar (eds.), Seventh International Symposium on Spatial Data Handling, Delft, The Netherlands, pp. 173–184.Google Scholar
  4. W. Chu, C. Hsu, A. Cardenas, and R. Taira (1998) Knowledge-based Image Retrieval with Spatial and Temporal Constructs. IEEE Transactions on Knowledge and Data Engineering 10(6): 872–888.CrossRefGoogle Scholar
  5. W. Chu, I. Leong, and R. Taira (1994) A Semantic Modeling Approach for Image Retrieval by Content. VLDB Journal 3(4): 445–477.CrossRefGoogle Scholar
  6. G. Dantzig (1963) Linear Programming And Extensions. Princeton University Press, Princeton, NJ.zbMATHGoogle Scholar
  7. G. Dantzig and M. Thapa (1997) Linear Programming. Springer-Verlag, New York.zbMATHGoogle Scholar
  8. A. DelBimbo and P. Pala (1997) Visual Image Retrieval by Elastic Matching of User Sketches. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(2): 121–132.CrossRefGoogle Scholar
  9. A. DelBimbo, E. Vicario, and D. Zingoni (1995) Symbolic Description and Visual Querying of Image Sequences Using Spatio-Temporal Logic. IEEE Transactions on Knowledge and Data Engineering 7(4): 609–622.CrossRefGoogle Scholar
  10. M. Egenhofer (1997) Query Processing in Spatial-Query-by-Sketch. Journal of Visual Languages and Computing 8(4): 403–424.CrossRefGoogle Scholar
  11. M. Egenhofer and K. Al-Taha (1992) Reasoning About Gradual Changes of Topological Relationships. in: A. Frank, I. Campari, and U. Formentini (eds.), Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, Pisa, Italy, Lecture Notes in Computer Science, 639: 196–219.Google Scholar
  12. M. Flickner, H. Sawhney, W. Niblack, Q. Huang, B. Dom, M. Gorkani, J. Hafner, D. Lee, D. Petkovic, D. Steele, and P. Yanker (1995) Query by Image and Video Content: The QBIC System. IEEE Computer 28(9): 23–32.Google Scholar
  13. C. Freksa (1992) Temporal Reasoning Based on Semi-Intervals. Artificial Intelligence 54: 199–227.CrossRefMathSciNetGoogle Scholar
  14. R. Goyal (2000) Similarity Assessment for Cardinal Directions Between Extended Spatial Objects. Ph.D. Thesis, Department of Spatial Information Science and Engineering, University of Maine, Orono, ME, Google Scholar
  15. R. Goyal and M. Egenhofer (in press) Cardinal Directions between Extended Spatial Objects. IEEE Transactions in Knowledge and Data Engineering (in press).Google Scholar
  16. R. Goyal and M. Egenhofer (2000) Consistent Queries over Cardinal Directions across Different Levels of Detail. in: A.M. Tjoa, R. Wagner, and A. Al-Zobaidie (eds.), 11th International Workshop on Database and Expert Systems Applications, Greenwich, U.K. pp. 876–880.Google Scholar
  17. R. Gonzalez and R. Woods (1992) Digital Image Processing. Addison-Wesley Publishing Company, Reading, MA.Google Scholar
  18. V. Gudivada and V. Raghavan (1995) Design and Evaluation of Algorithms for Image Retrieval by Spatial Similarity. ACM Transactions on Information Systems 13(2): 115–144.CrossRefGoogle Scholar
  19. H. Jiang and A. Elmagarmid (1998) Spatial and Temporal Content-based Access to Hypervideo Databases. VLDB Journal 7: 226–238.CrossRefGoogle Scholar
  20. K. Murty (1976) Linear and Combinatorial Programming. John Wiley & Sons, Inc., New York.zbMATHGoogle Scholar
  21. M. Nabil, J. Shepherd, and A. Ngu (1995) 2D Projection Interval Relationships: A Symbolic Representation of Spatial Relationships. in: M. Egenhofer and J. Herring (eds.), Advances in Spatial Databases—4th International Symposium, SSD’ 95, Portland, ME, Lecture Notes in Computer Science, 951: 292–309 Springer-Verlag, Berlin.Google Scholar
  22. D. Papadias and V. Delis (1997) Relation-Based Similarity. Fifth ACM Workshop on Advances in Geographic Information Systems, Las Vegas, NV, pp. 1–4.Google Scholar
  23. N. Pissinou, I. Radev, K. Makki, and W. Campbell (1998) A Topological-Directional Model for the Spatio-Temporal Composition of the Video Objects. in: A. Silberschatz, A. Zhang and S. Mehrotra (eds.), Eighth International Workshop on Research Issues on Data Engineering, Continuous-Media Databases and Applications, Orlando, FL, pp. 17–24.Google Scholar
  24. A. P. Sistla, C. Yu, C. Liu, and K. Liu (1995) Similarity based Retrieval of Pictures Using Indices on Spatial Relationships, in: U. Dayal, P. Gray, and S. Nishio (eds.), 21st International Conference on Very Large Data Bases, Zurich,. Switzerland, pp. 619–629.Google Scholar
  25. J. Strayer (1989) Linear Programming and Its Applications. Springer-Verlag, New York.zbMATHGoogle Scholar
  26. A. Tversky (1977) Features of Similarity. Psychological Review 84(4): 327–352.CrossRefGoogle Scholar
  27. A. Yoshitaka and T. Ichikawa (1999) A Survey on Content-based Retrieval for Multimedia Databases. IEEE Transactions on Knowledge and Data Engineering 11(1): 81–93.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Roop K. Goyal
    • 1
  • Max J. Egenhofer
    • 2
  1. 1.ESRIRedlandsUSA
  2. 2.National Center for Geographic Information and Analysis Department of Spatial Information Science and Engineering Department of Computer Science Boardman HallUniversity of MaineOronoUSA

Personalised recommendations