This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A New Way to Represent the Relative Position between Areal Objects
July 1999 (vol. 21 no. 7)
pp. 634-643
ASCII Text
x 
 
Pascal Matsakis, Laurent Wendling, "A New Way to Represent the Relative Position between Areal Objects," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 7, pp. 634-643, July, 1999.
 
 
BibTex
x
 
@article{ 10.1109/34.777374,
author = {Pascal Matsakis and Laurent Wendling},
title = {A New Way to Represent the Relative Position between Areal Objects},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {21},
number = {7},
issn = {0162-8828},
year = {1999},
pages = {634-643},
doi = {http://doi.ieeecomputersociety.org/10.1109/34.777374},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - A New Way to Represent the Relative Position between Areal Objects
IS - 7
SN - 0162-8828
SP634
EP643
EPD - 634-643
A1 - Pascal Matsakis,
A1 - Laurent Wendling,
PY - 1999
KW - Pattern recognition
KW - parameter extraction
KW - spatial relationships
KW - fuzzy subsets.
VL - 21
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 

Abstract—The fuzzy qualitative evaluation of directional spatial relationships (such as “to the right of,”“to the south of$\ldots$,”) between areal objects often relies on the computation of a histogram of angles, which is considered to provide a good representation of the relative position of an object with regard to another. In this paper, the notion of the histogram of forces is introduced. It generalizes and may supersede the histogram of angles. The objects (2D entities) are handled as longitudinal sections (1D entities), not as points (0D entities). It is thus possible to fully benefit from the power of integral calculus and, so, ensure rapid processing of raster data, as well as of vector data, explicitly considering both angular and metric information.

[1] I. Block, “Fuzzy Relative Position Between Objects in Images: A Morphological Approach,” Proc. Int'l Conf. Image Processing Proc., 96, vol. II, pp. 987-990, Lausanne, Switzerland, 1996.
[2] D. Dubois and M.C. Jaulent, ”A General Approach to Parameter Evaluation in Fuzzy Digital Pictures,” Pattern Recognition Letters, vol. 6, pp. 251-259, 1987.
[3] D. Dubois and H. Prade, “Fuzzy Sets and Systems: Theory and Applications,” Mathematics in Science and Eng., vol. 144, p. 40, 1980.
[4] S. Dutta, “Approximate Spatial Reasoning: Integrating Qualitative and Quantitative Constraints,” Int'l J. Approximate Reasoning, vol. 5, pp. 307-331, 1991.
[5] J. Freeman, “The Modelling of Spatial Relations,” Computer Graphics and Image Processing, vol. 4, pp. 156-171, 1975.
[6] K.P. Gapp, “Basic Meanings of Spatial Relations: Computation and Evaluation in 3D Space,” Proc. 12th Nat'l Conf. Artificial Intelligence (AAAI-94), pp. 1,393-1,398, 1994.
[7] D. Eager and J. Zahorjan, "Enhanced run-time support for shared memory parallel computing," ACM Trans. Computer Systems, vol. 11, pp. 1-32, Feb. 1993.
[8] J.M. Keller and X. Wang, “Comparison of Spatial Relation Definitions in Computer Vision,” ISUMA-NAFIPS'95: Special Session on Fuzzy Sets and Systems in Signal Processing Applications, pp. 679-684, Univ. of Maryland, College Park, 1995.
[9] J.M. Keller and X. Wang, “Learning Spatial Relationships in Computer Vision,” Proc. IEEE Fifth Int'l Conf. Fuzzy Systems, 1996.
[10] L.T. Kòczy, “On the Description of Relative Position of Fuzzy Patterns,” Pattern Recognition Letters, vol. 8, pp. 21-28, 1988.
[11] R. Krishnapuram, J.M. Keller, and Y. Ma, “Quantitative Analysis of Properties and Spatial Relations of Fuzzy Image Regions,” IEEE Trans. Fuzzy Systems, vol. 1, no. 3, pp. 222-233, 1993.
[12] S.Y. Lee and F. Hsu, “Spatial Reasoning and Similarity Retrieval of Images using 2D C-Strings Knowledge Representation,” Pattern Recognition, vol. 25, no. 3, pp. 305-318, 1992.
[13] T.S. Levitt and D.T. Lawton, “Qualitative Navigation for Mobile Robots,” Artificial Intelligence, vol. 44, no. 3, pp. 305-360, 1990.
[14] P. Matsakis, “Relations Spatiales Structurelles et Interprétation d'Images” PhD thesis, Institut de Recherche en Informatique de Toulouse, France, 1998.
[15] P. Matsakis, L. Wendling, and J. Desachy, “Représentation de la Position Relative d'Objets 2D au Moyen d'un Histogramme de Forces,” Traitement du Signal, vol. 15, no. 1, pp. 25-38, 1998.
[16] K. Miyajima and A. Ralescu, “Spatial Organization in 2D Segmented Images: Representation and Recognition of Primitive Spatial Relations” Fuzzy Sets and Systems, vol. 65, pp. 225-236, 1994.
[17] D.J. Peuquet and Z. Ci-Xiang, “An Algorithm to Determine the Directional Relationship between Arbitrarily-Shaped Polygons in the Plane,” Pattern Recognition, vol. 20, no. 1, pp. 65-74, 1987.
[18] G. Retz-Schmidt, “Various Views on Spatial Prepositions,” AI Magazine, vol. 9, no. 2, pp. 95-105, 1988.
[19] D.F. Rogers, Procedural Elements for Computer Graphics, pp. 34-42. New York: McGraw-Hill, 1985.
[20] R. Röhrig, “Representation and Processing of Qualitative Orientation Knowledge,” Proc. KI-97 (Künstliche Intelligenz '97) Learning from Large Datasets; Knowledge Discovery in Databases, pp. 219-230. 1997.
[21] A. Rosenfeld and A.C. Kak,Digital Picture Processing. Academic Press, 2nd ed., 1982
[22] C. Schlieder, “Representing Visible Locations for Qualitative Navigation,” Qualitative Reasoning and Decision Technologies, N. Piera Carretéand M. G. Singh, eds. pp. 523-532, 1993.
[23] J. Sharma and D.M. Flewelling, “Inferences from Combined Knowledge about Topology and Directions,” Advances in Spatial Databases, pp. 279-291, 1995.
[24] L. Wendling and J. Desachy, “Isomorphism between Strong Fuzzy Relational Graphs Based on k-Formula,” Graph Based Representations in Pattern Recognition, Computing, pp. 63-71. New York: Springer-Verlag, 1998.
[25] P.H. Winston, The Psychology of Computer Vision. New York: McGraw-Hill, 1975.
[26] M.F. Worboys, GIS–A Computing Perspective, pp. 120-127. Taylor and Francis, 1995.

Index Terms:
Pattern recognition, parameter extraction, spatial relationships, fuzzy subsets.
Citation:
Pascal Matsakis, Laurent Wendling, "A New Way to Represent the Relative Position between Areal Objects," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 7, pp. 634-643, July 1999, doi:10.1109/34.777374
Usage of this product signifies your acceptance of the Terms of Use.