Introducing the Φ-Descriptor - A Most Versatile Relative Position Descriptor

Pascal Matsakis, Mohammad Naeem, Farhad Rahbarnia


Spatial prepositions, like above, inside, near, denote spatial relationships. A relative position descriptor is a basis from which quantitative models of spatial relationships can be derived. It is an image descriptor, like colour, texture, and shape descriptors. Various relative position descriptors can be found in the literature. In this paper, we introduce a new relative position descriptorthe -descriptorthat has about all the strengths of each and every one of its competitors, and none of the weaknesses. Our approach is based on the concept of the F-histogram and on an original categorization of pairs of consecutive boundary points on a line.


  1. J. F. Allen, 1983. “Maintaining Knowledge About Temporal Intervals,” Communications of the ACM, 26(11): 832-43.
  2. A. Buck, J. M. Keller, M. Skubic, 2013. “A Memetic Algorithm for Matching Spatial Configurations with the Histograms of Forces,” IEEE Trans. on Evolutionary Computation, 17(4):588-604.
  3. J. C.-W. Chan, H. Sahli, Y. Wang, 2005. “Semantic Risk Estimation of Suspected Minefields Based on Spatial Relationships Analysis of Minefield Indicators from Multi-Level Remote Sensing Imagery,” Detection and Remediation Technologies for Mines and Minelike Targets X, Proceedings of SPIE, 5794(1):1071-9.
  4. A. G. Cohn, B. Bennett, J. Gooday, N. M. Gotts, 1997. “Qualitative Spatial Representation and Reasoning with the Region Connection Calculus,” GeoInformatica, 1(3):275-316.
  5. D. Dubois, M.-C. Jaulent, 1987. “A General Approach to Parameter Evaluation in Fuzzy Digital Pictures,” Pattern Recognition Letters, 6:251-59.
  6. M. J. Egenhofer, 2007. “Temporal Relations of Intervals with a Gap,” 14th Int. Symposium on Temporal Representation and Reasoning, Proceedings, 169-74.
  7. R. Krishnapuram, J. M. Keller, Y. Ma, 1993. “Quantitative Analysis of Properties and Spatial Relations of Fuzzy Image Regions,” IEEE Trans. on Fuzzy Systems, 1(3): 222-33.
  8. H. Kwasnicka, M. Paradowski, 2005. “Spread Histogram ? A Method for Calculating Spatial Relations Between Objects,” 4th Int. Conf. on Computer Recognition Systems (CORES), Proceedings, 30:249-56.
  9. P. Ladkin, 1986. The Logic of Time Representation, PhD Thesis, University of California at Berkeley.
  10. J. Malki, E.-H. Zahzah, L. Mascarilla, 2002. “Indexation et recherche d'image fondées sur les relations spatiales entre objets,” Traitement du Signal, 18(4):235-51.
  11. P. Matsakis, D. Nikitenko, 2005. “Combined Extraction of Directional and Topological Relationship Information from 2D Concave Objects,” in M. Cobb, F. Petry, V. Robinson (Eds.), Fuzzy Modeling with Spatial Information for Geographic Problems, Springer-Verlag, 15-40.
  12. P. Matsakis, L. Wawrzyniak, J. Ni, 2010. “Relative Positions in Words: A System that Builds Descriptions Around Allen Relations,” Int. J. of Geographical Information Science, 24(1):1-23.
  13. P. Matsakis, L. Wendling, 1999. “A New Way to Represent the Relative Position of Areal Objects,” IEEE Trans. on Pattern Analysis and Machine Intelligence, 21(7):634- 43.
  14. P. Matsakis, L. Wendling, J. Ni, 2010. “A General Approach to the Fuzzy Modeling of Spatial Relationships,” in R. Jeansoulin, O. Papini, H. Prade, S. Schockaert (Eds.), Methods for Handling Imperfect Spatial Information, Springer-Verlag, 49-74.
  15. M. Naeem, P. Matsakis, 2015, “Relative Position Descriptors: A Review,” 4th Int. Conf. on Pattern Recognition Applications and Methods, Proceedings, in press.
  16. C. Pappis, N. Karacapilidis, 1993. “A Comparative Assessment of Measures of Similarity of Fuzzy Values,” Fuzzy Sets and Systems, 56:171-4.
  17. N. Salamat, E.-H. Zahzah, 2012a. “Spatio-Temporal Reasoning by Combined Topological and Directional Relations Information,” Int. J. of Artificial Intelligence and Soft Computing, 3(2):185-201.
  18. N. Salamat, E.-H. Zahzah, 2012b. “On the Improvement of Combined Fuzzy Topological and Directional Relations Information,” Pattern Recognition, 45(4):1559-1568.
  19. N. Salamat, E.-H. Zahzah, 2012c. “Two-Dimensional Fuzzy Spatial Relations: A New Way of Computing and Representation,” Advances in Fuzzy Systems, 2012: 1-15.
  20. K.C. Santosh, L. Wendling, B. Lamiroy, 2010. “Unified Pairwise Spatial Relations: An Application to Graphical Symbol Retrieval,” in J.-M. Ogier, W. Liu, J. Llados (Eds.), Graphics Recognition. Achievements, Challenges, and Evolution, SpringerVerlag, 163-74.
  21. C.-R. Shyu, M. Klaric, G. J. Scott, A. S. Barb, C. H. Davis, K. Palaniappan, 2007. “GeoIRIS: Geospatial Information Retrieval and Indexing System ? Content Mining, Semantics Modeling, and Complex Queries,” IEEE Trans. on Geoscience and Remote Sensing, 45(4):839-52.
  22. O. Sjahputera, J. M. Keller, 2007. “Scene Matching Using F-Histogram-Based Features with Possibilistic C-Means Optimization,” Fuzzy Sets and Systems, 158(3):253-69.
  23. M. Skubic, P. Matsakis, G. Chronis, J. M. Keller, 2003. “Generating Multi-Level Linguistic Spatial Descriptions from Range Sensor Readings Using the Histogram of Forces,” Autonomous Robots, 14(1):51-69.
  24. M. Skubic, D. Perzanowski, S. Blisard, A. Schultz, W. Adams, M. Bugajska, D. Brock, 2004. “Spatial Language for Human-Robot Dialogs,” IEEE Trans. on Systems, Man, and Cybernetics (Part C), 34(2):154-67.
  25. C. Vaduva, D. Faur, I. Gavat, 2010. “Data Mining and Spatial Reasoning for Satellite Image Characterization,” 8th Int. Conf. on Communications (COMM), Proceedings, 173-176.
  26. Y. Wang, F. Makedon, A. Chakrabarti, 2004. “R*- Histograms: Efficient Representation of Spatial Relations between Objects of Arbitrary Topology,” 12th Annual ACM Int. Conf. on Multimedia (MM), Proceedings, 356-59.
  27. Y. Wang, F. Makedon, J. Ford, L. Shen, D. Goldin, 2004. “Generating Fuzzy Semantic Metadata Describing Spatial Relations from Images Using the R-Histogram,” 4th ACM/IEEE Joint Conf. on Digital Libraries, Proceedings, 202-11.
  28. W. Wang, B. Xiong, H. Sun, H. Cai, Y. Jiang, G. Kuang, 2012. “An Affine Invariant Relative Attitude Relationship Descriptor for Shape Matching Based on Ratio Histograms,” EURASIP J. on Advances in Signal Processing, 2012(1):1-10.

Paper Citation

in Harvard Style

Matsakis P., Naeem M. and Rahbarnia F. (2015). Introducing the Φ-Descriptor - A Most Versatile Relative Position Descriptor . In Proceedings of the International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM, ISBN 978-989-758-076-5, pages 87-98. DOI: 10.5220/0005210200870098

in Bibtex Style

author={Pascal Matsakis and Mohammad Naeem and Farhad Rahbarnia},
title={Introducing the Φ-Descriptor - A Most Versatile Relative Position Descriptor},
booktitle={Proceedings of the International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},

in EndNote Style

JO - Proceedings of the International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,
TI - Introducing the Φ-Descriptor - A Most Versatile Relative Position Descriptor
SN - 978-989-758-076-5
AU - Matsakis P.
AU - Naeem M.
AU - Rahbarnia F.
PY - 2015
SP - 87
EP - 98
DO - 10.5220/0005210200870098