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Using Quadtrees to Represent Spatial Data

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Part of the book series: NATO ASI Series ((NATO ASI F,volume 18))

Abstract

Use of the quadtree data structure in representing spatial data is reviewed. The focus is on its properties that make it appropriate for applications in image processing. A number of operations in which the quadtree finds use are discussed.

The support of the Engineering Topographic Laboratories (under Contract DAAK-70-31-C0059) is gratefully acknowledged, as is the help of Janet Salzman in preparing this paper.

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References

  1. A. Rosenfeld, H. Samet, C. Shaffer, and R. E. Webber, Application of hierarchical data structures to geographical information systems, Computer Science TR-1197, University of Maryland, College Park, MD, June 1982.

    Google Scholar 

  2. A. Klinger, Patterns and search statistics, in Optimizing Methods in Statistics, J. S. Rustagi, Ed., Academic Press, New York, 1971.

    Google Scholar 

  3. A. Klinger and C. R. Dyer, Experiments in picture representations using regular decomposition, Computer Graphics and Image Processing 5, 1976, 68–105.

    Article  Google Scholar 

  4. G. M. Hunter, Efficient computation and data structures for graphics, Ph.D. dissertation, Department of Electrical Engineering and Computer Science, Princeton University, Princeton, NJ, 1978.

    Google Scholar 

  5. R. A. Finkel and J. L. Bentley, Quad trees: a data structure for retrieval on composite keys, Acta Informatica 4, 1974, 1–9.

    Article  MATH  Google Scholar 

  6. D. E. Knuth, The Art of Computer Programming, vol. 1, Fundamental Algorithms, Second Edition, Addison-Wesley, Reading, MA, 1975.

    Google Scholar 

  7. J. L. Bentley, Multidimensional binary search trees used for associative searching, Communications of the ACM 18, September 1975, 509–517.

    Article  MATH  Google Scholar 

  8. J. L. Bentley and J. H. Friedman, Data structures for range searching, ACM Computing Surveys 11, December 1979, 397–409.

    Article  Google Scholar 

  9. J. L. Warnock, A hidden surface algorithm for computer generated half tone pictures, Computer Science Department TR 4–15, University of Utah, Salt Lake City, June 1969.

    Google Scholar 

  10. N. J. Nilsson, A mobile automaton: an application of artificial intelligence techniques, Proceedings of the First International Joint Conference on Artificial Intelligence, Washington, DC, 1969, 509–520.

    Google Scholar 

  11. C. M. Eastman, Representations for space planning, Communications of the ACM 13, April 1970, 242–250.

    Article  Google Scholar 

  12. M. D. Kelly, Edge detection in pictures by computer using planning, Machine Intelligence 6, 1971, 397–409.

    Google Scholar 

  13. L. Uhr, Layered “recognition cone” networks that preprocess, classify, and describe, IEEE Transactions on Computers 21, 1972, 758–768.

    Article  MATH  Google Scholar 

  14. E. M. Riseman and M. A. Arbib, Computational techniques in the visual segmentation of static scenes, Computer Graphics and Image Processing 6, 1977, 221–276.

    Article  Google Scholar 

  15. S. Tanimoto and T. Pavlidis, A hierarchical data structure for picture processing, Computer Graphics and Image Processing 4, 1975, 104–119.

    Article  Google Scholar 

  16. D. Rutovitz, Data structures for operations on digital images, in Pictorial Pattern Recognition, G. C. Cheng et al.,Eds., Thompson Book Co., Washington, DC, 1968, 105–133.

    Google Scholar 

  17. H. Blum, A transformation for extracting new descriptors of shape, in Models for the Perception of Speech and Visual Form, W. Wathen-Dunn, Ed., M.I.T. Press, Cambridge, MA, 1967, 362–380.

    Google Scholar 

  18. A. Rosenfeld and J. L. Pfaltz, Sequential operations in digital image processing, Journal of the ACM 13, October 1966, 471–494.

    Article  MATH  Google Scholar 

  19. N. Ahuja, On approaches to polygonal decomposition for hierarchical image representation, to appear in Computer Vision,Graphics and Image Processing, 1983 (see also Proceedings of the IEEE Conference on Pattern Recognition and Image Processing, Dallas, 1981, 75–80 ).

    Google Scholar 

  20. L. Gibson and D. Lucas, Vectorization of raster images using hierarchical methods, Computer Graphics and Image Processing 20, 1982, 82–89.

    Article  Google Scholar 

  21. A. Klinger and M. L. Rhodes, Organization and access of image data by areas, IEEE Transactions on Pattern Analysis and Machine Intelligence 1, 1979, 50–60.

    Article  Google Scholar 

  22. G. M. Hunter and K. Steiglitz, Operations on images using quad-trees, IEEE Transactions on Pattern Analysis and Machine Intelligence 1, 1979, 145–153.

    Article  Google Scholar 

  23. G. M. Hunter and K. Steiglitz, Linear transformation of pictures represented by quadtrees, Computer Graphics and Image Processing 10, 1979, 289–296.

    Article  Google Scholar 

  24. H. Samet, Neighbor finding techniques for images represented by quadtrees, Computer Graphics and Image Processing 18, 1982, 37–57.

    Article  MATH  Google Scholar 

  25. H. Samet, Region representation: quadtrees from binary arrays, Computer Graphics and Image Processing 18, 1980, 88–93.

    Article  Google Scholar 

  26. H. Samet, An algorithm for converting rasters to quadtrees, IEEE Transactions on Pattern Analysis and Machine Intelligence 3, 1981, 487–501.

    Article  MathSciNet  Google Scholar 

  27. H. Samet, Algorithms for the conversion of quadtrees to rasters, to appear in Computer Vision, Graphics, and Image Processing, 1933 (also University of Maryland Computer Science TR-979).

    Google Scholar 

  28. H. Freeman, Computer processing of line-drawing images, ACM Computing Surveys 6, March 1974, 57–97.

    Article  MATH  Google Scholar 

  29. C. R. Dyer, A. Rosenfeld, and H. Samet, Region representation: boundary codes from quadtrees, Communications of the ACM 23, March 1980, 171–179.

    Article  MATH  Google Scholar 

  30. H. Samet, Region representation: quadtrees from boundary codes, Communications of the ACM 23, March 1980, 163–170.

    Article  MATH  Google Scholar 

  31. M. Shneier, Calculations of geometric properties using quadtrees, Computer Graphics and Image Processing 16, 1981, 296–302.

    Article  Google Scholar 

  32. H. Samet and R. E. Webber, Using quadtrees to represent polygonal maps, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Washington, DC, 1983, 127–132.

    Google Scholar 

  33. S. Ranade, A. Rosenfeld, and J. M. S. Prewitt, Use of quadtrees for image segmentation, Computer Science TR-878, University of Maryland, College Park, MD, February 1980.

    Google Scholar 

  34. S. Ranade, Use of quadtrees for edge enhancement, IEEE Transactions on Systems, Man, and Cybernetics 11, 1981, 370–373.

    Article  Google Scholar 

  35. S. Ranade and M. Shneier, Using quadtrees to smooth images, IEEE Transactions on Systems, Man, and Cybernetics 11, 1981, 373–376.

    Article  Google Scholar 

  36. A. Y. Wu, T. H. Hong, and A. Rosenfeld, Threshold selection using quadtrees, IEEE Transactions on Pattern Analysis and Machine Intelligence 4, 1982, 90–94.

    Article  MATH  Google Scholar 

  37. H. Samet, Connected component labeling using quadtrees, Journal of the ACM 28, July 1981, 487–501.

    Article  MATH  MathSciNet  Google Scholar 

  38. R. E. Tarjan, On the efficiency of a good but not linear set union algorithm, Technical Report 72–148, Computer Science Department, Cornell University, Ithaca, New York, November 1972.

    Google Scholar 

  39. C. R. Dyer, A. Rosenfeld, and H. Samet, Region representation: boundary codes from quadtrees, Communications of the ACM 23, March 1980, 171–179.

    Article  MATH  Google Scholar 

  40. M. Minsky and S. Papert, Perceptrons: An Introduction to Computional Geometry, MIT Press, Cambridge, MA, 1969.

    Google Scholar 

  41. H. Samet, Computing perimeters of images represented by quadtrees, IEEE Transactions on Pattern Analysis and Machine Intelligence 3, 1981, 683–687.

    Article  Google Scholar 

  42. C. Jackins and S. L. Tanimoto, Quad–trees, oct–trees, and k–trees – a generalized approach to recursive decomposition of Euclidean space, Department of Computer Science Technical Report 82–02–02, University of Washington, Seattle, 1982.

    Google Scholar 

  43. C.R. Dyer, The space efficiency of quadtrees, Computer Graphics and Image Processing 19, 1982, 335–348.

    Article  MATH  Google Scholar 

  44. W. I. Grosky and R. Jain, Optimal quadtrees for image segments, IEEE Transactions on Pattern Analysis and Machine Intelligence 5, 1983, 77–83.

    Article  MATH  Google Scholar 

  45. M. Li, W. I. Grosky, and R. Jain, Normalized quadtrees with respect to translations, Computer Graphics and Image Processing 20, 1982, 72–81.

    Article  MATH  Google Scholar 

  46. H. Samet, A quadtree medial axis transform, Communications of the ACM, 26, November 1983, 680–693.

    Article  Google Scholar 

  47. E. Kawaguchi and T. Endo, On a method of binary picture representation and its application to data compression, IEEE Transactions on Pattern Analysis and Machine Intelligence 2, 1980, 27–35.

    Article  MATH  Google Scholar 

  48. I. Gargantini, An effective way to represent quadtrees, Communications of the ACM 25, December 1982, 905–910.

    Article  MATH  Google Scholar 

  49. D. J. Abel and J. L. Smith, A data structure and algorithm based on a linear key for a rectangle retrieval problem, to appear in Computer Vision, Graphics and Image Processing, 1983.

    Google Scholar 

  50. G. M. Morton, A computer oriented geodetic data base and a new technique in file sequencing, IBM Canada, 1966.

    Google Scholar 

  51. B. G. Cook, The structural and algorithmic basis of a geographic data base, in Proceedings of the First International Advanced Study Symposium on Topological Data Structures for Geographic Information Systems, G. Dutton, Ed., Harvard Papers on Geographic Information Systems, 1978.

    Google Scholar 

  52. W. Weber, Three types of map data structures, their ANDs and NOTs, and a possible OR, in Proceedings of the First International Advanced Study Symposium on Topological Data Structures for Geographic Information Systems, G. Dutton, Ed., Harvard Papers on Geographic Information Systems, 1978.

    Google Scholar 

  53. J. R. Woodwark, The explicit quadtree as a structure for computer graphics, Computer Journal 25, 1982, 235–238.

    Article  Google Scholar 

  54. M. A. Oliver and N. E. Wiseman, Operations on quadtree-encoded images, Computer Journal 26, 1983, 83–91.

    Article  Google Scholar 

  55. G. Nagy and S. Wagle, Geographic data processing, ACM Computing Surveys 11, June 1979, 139–181.

    Article  Google Scholar 

  56. D. H. Ballard, Strip trees: A hierarchical representation for curves, Communications of the ACM 24, May 1981, 310–321 (see also corrigendum, Communications of the ACM 25, March 1982, 213 ).

    Article  Google Scholar 

  57. W. Burton, Representation of many-sided polygons and polygonal lines for rapid processing, Communications of the ACM 20, March 1977, 166–171.

    Article  MATH  Google Scholar 

  58. T. Peucker, A theory of the cartographic line, International Yearbook of Cartography, 1976.

    Google Scholar 

  59. M. Shneier, Two hierarchical linear feature representations: edge pyramids and edge quadtrees, Computer Graphics and Image Processing 17, 1981, 211–224.

    Article  Google Scholar 

  60. J. J. Martin, Organization of geographical data with quad trees and least square approximation, Proceedings of the IEEE Conference on Pattern Recognition and Image Processing, Las Vegas, 1982, 458–463.

    Google Scholar 

  61. H. Samet and R. E. Webber, Line quadtrees: a hierarchical data structure for encoding boundaries, Proceedings of the IEEE Conference on Pattern Recognition and Image Processing, Las Vegas, 1982, 90–92 (also University of Maryland Computer Science TR-1162).

    Google Scholar 

  62. M. Tamminen, Encoding pixel trees, Laboratory of Information Processing Science, Helsinki University of Technology, Espoo, Finland, 1983.

    Google Scholar 

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© 1985 Springer-Verlag Berlin Heidelberg

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Samet, H. (1985). Using Quadtrees to Represent Spatial Data. In: Freeman, H., Pieroni, G.G. (eds) Computer Architectures for Spatially Distributed Data. NATO ASI Series, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82150-9_13

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  • DOI: https://doi.org/10.1007/978-3-642-82150-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82152-3

  • Online ISBN: 978-3-642-82150-9

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