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A Tutorial on Quadtree Research

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Multiresolution Image Processing and Analysis

Part of the book series: Springer Series in Information Sciences ((SSINF,volume 12))

Abstract

Region representation is an important issue in image processing, cartography, and computer graphics. A wide number of representations is currently in use. Recently, there has been much interest in a hierarchical data structure termed the quadtree. It is compact and depending on the nature of the region saves space as well as time and also facilitates operations such as search. In this section we give a brief overview of the quadtree data structure and related research results.

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References

  1. D. Rutovitz: “Data structures for operations on digital images”, in Pictorial Pattern Recognition, ed. by G. C. Cheng et al. (Thompson Book CO., Washington, DC, 1968), pp. 105–133

    Google Scholar 

  2. H. Freeman: Computer processing of line-drawing images. Computing Surveys 6, 57–97 (1974)

    Article  MATH  Google Scholar 

  3. D. H. Ballard: Strip trees: a hierarchical representation for curves, Comm. ACM 24 310–321 (1981)

    Article  Google Scholar 

  4. H. Blum: “A transformation for extracting new descriptors of shape”, in Models for the Perception of Speech and Visual Form, ed. by W. Wathen-Dunn (M.I.T. Press, Cambridge, MA, 1967), pp. 362–380

    Google Scholar 

  5. J. L. Pfaltz, A. Rosenfeld: Computer representation of planar regions by their skeletons, Comm. ACM 10, 119–122 (1967)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  7. H. Samet: Deletion in two-dimensional quad trees, Comm. ACM 23 703–710 (1980)

    Article  Google Scholar 

  8. D. T. Lee, C. K. Wong: Worst-case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees, Acta Informatica 9, 23–29 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  9. Jo L. Bentley: Multidimensional binary search trees used for associative searching, Commo ACM 18, 509–517 (1975)

    Article  Google Scholar 

  10. C. M. Eastman: Representations for space planning. Comm. ACM 13, 242–250 (1970)

    Article  Google Scholar 

  11. J. E. Warnock: “A Hidden Surface Algorithm for Computer Generated Half Tone Pictures”, Computer Science Department TR 4–15, University of Utah (1969)

    Google Scholar 

  12. I. E. Sutherland, R. F. Sproull, R. A. Schumaeker: A characterization of ten hidden-surface algorithms, Computing Surveys 6 1–55 (1974)

    Article  MATH  Google Scholar 

  13. W. M. Newman, R. F. Sproull: Principles of Interactive Computer Graphics, 2nd ed. (McGraw-Hill, New York, 1971)

    Google Scholar 

  14. A. Klinger: “Patterns and search statistics”, in Optimizing Methods in Statistics, ed. by J. S. Rustagi (Academic Press, New York, 1972) pp. 303–339

    Google Scholar 

  15. A. Klinger, C. R. Dyer: Experiments in picture representation using regular decomposition. Computer Graphics Image Processing 14, 68–105 (1975)

    Google Scholar 

  16. S. L. Tanimoto, T. Pavlidis: A hierarchical data structure for image processing, Computer Graphics Image Processing 4, 104–119 (1976)

    Article  Google Scholar 

  17. S. L. Tanimoto: Pictorial feature distortion in a pyramid. Computer Graphics Image Processing 5, 333–352 (1976)

    Article  Google Scholar 

  18. E. M. Riseman, M. A. Arbib: Computational techniques in the visual segmentation of static scenes, Computer Graphics Image Processing 6, 221–276 (1976)

    Article  Google Scholar 

  19. A. Klinger, M. L. Rhodes: Organization and access of image data by areas, IEEE Trans. Pattern Analysis Machine Intelligence PAMI-1, 50–60 (1979)

    Article  Google Scholar 

  20. N. Alexandridis, A. Klinger: Picture decomposition, tree data-structures, and identifying directional symmetries as node combinations. Computer Graphics Image Processing 8, 43–77 (1978)

    Article  Google Scholar 

  21. G. M. Hunter: “Efficient Computation and Data Structures for Graphics”, Ph.D. dissertation. Department of Electrical Engineering and Computer Science, Princeton University (1978)

    Google Scholar 

  22. G. M. Hunter, K. Steiglitz: Operations on images using quad trees, IEEE Trans. Pattern Analysis Machine Intelligence PAMI-1, 145–153 (1979)

    Article  Google Scholar 

  23. M. Shneier: Calculations of geometric properties using quadtrees, Computer Graphics Image Processing 16, 296–302 (1981)

    Article  Google Scholar 

  24. G. M. Hunter, K. Steiglitz: Linear transformation of pictures represented by quad trees, Computer Graphics Image Processing 10, 289–296 (1979)

    Article  Google Scholar 

  25. D. R. Reddy, S. Rubin: “Representation of Three-Dimensional Objects”, Department of Computer Science Technical Report 78–113, Carnegie-Mellon University (1978)

    Google Scholar 

  26. C. L. Jackins, S. L. Tanimoto: Oct-trees and their use in representing three-dimensional objects. Computer Graphics Image Processing 14, 249–270 (1980)

    Article  Google Scholar 

  27. D. J. R. Meagher: “Octree Encoding: a New Technique for the Representation, Manipulation, and Display of Arbitrary 3-D Objects by Computer”, TR 80–111, Rensselaer Polytechnic Institute (1980)

    Google Scholar 

  28. S. N. Srihari, M. Yau: “A Hierarchical Data Structure for Multidimensional Digital Images”, Department of Computer Science Technical Report 185, State University of New York at Buffalo (1981)

    Google Scholar 

  29. H. Samet: Region representation: quadtrees from binary arrays. Computer Graphics Image Processing 13, 88–93 (1980)

    Article  Google Scholar 

  30. H. Samet: An algorithm for converting rasters to quadtrees, IEEE Trans. Pattern Analysis Machine Intelligence PAMI-3, 93–95 (1981)

    Article  Google Scholar 

  31. H. Samet: “Algorithms for the Conversion of Quadtrees to Rasters”, Computer Graphics Image Processing, to appear

    Google Scholar 

  32. H. Samet: Region representation: quadtrees from boundary codes. Comm. ACM 23, 163–170 (1980)

    Article  MATH  Google Scholar 

  33. C. R. Dyer, A. Rosenfeld, H. Samet: Region representation: boundary codes from quadtrees, Comm. ACM 23, 171–179 (1980)

    Article  MATH  Google Scholar 

  34. H. Samet: Connected component labeling using quadtrees, J. ACM 28, 487–501 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  35. H. Samet: Computing perimeters of images represented by quadtrees, IEEE Trans. Pattern Analysis Machine Intelligence PAMI-3, 683–687 (1981)

    Article  Google Scholar 

  36. C. R. Dyer: Computing the Euler number of an image from its quadtree, Computer Graphics image Processing 13, 270–276 (1980)

    Article  Google Scholar 

  37. H. Samet: Distance transform for images represented by quadtrees, IEEE Trans. Pattern Analysis Machine Intelligence PAMI-4, 298–303 (1982)

    Article  Google Scholar 

  38. M. Shneier: Path-length distances for quadtrees, Information Sciénces 23, 49–67 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  39. S. Ranade, A. Rosenfeld, H. Samet: Shape approximation using quadtrees, Pattern Recognition 15, 31–40 (1982)

    Article  Google Scholar 

  40. S. Ranade: Use of quadtrees for edge enhancement, IEEE Trans. Systems, Man, Cybernetics SMC-11, 370–373 (1981)

    Google Scholar 

  41. S. Ranade, A. Rosenfeld, J. M. S. Prewitt: “Use of Quadtrees for Image Segmentation”, Computer Science TR-878, University of Maryland (1980)

    Google Scholar 

  42. A. Y. Wu, T. H. Hong, A. Rosenfeld: Threshold selection using quadtrees, IEEE Trans. Pattern Analysis Machine Intelligence PAMI-4, 90–94 (1982)

    Article  Google Scholar 

  43. S. Ranade M. Shneier: Using quadtrees to smooth images, IEEE Trans. Systems, Man, Cybernetics SMC-11, 373–376 (1981)

    Google Scholar 

  44. H. Samet: Neighbor finding techniques for images represented by quadtrees, Computer Graphics Image Processing 15, 37–57 (1982)

    Article  Google Scholar 

  45. A. Rosenfeld, A. C. Kak: Digital Picture Processing (Academic Press, New York, 1976)

    Google Scholar 

  46. H. Samet: A quadtree medial axis transform. Comm. ACM, to appear.

    Google Scholar 

  47. C. Jackins, S. L. Tanimoto: “Quad-trees, Oct-trees, and K-trees: a Generalized Approach to Recursive Decomposition of Euclidean Space”, IEEE Trans. Pattern Analysis Machine Intelligence, to appear.

    Google Scholar 

  48. C. R. Dyer: The space efficiency of quadtrees. Computer Graphics Image Processing 19, 335–348 (1982)

    Article  MATH  Google Scholar 

  49. W. I. Grosky, R. Jain: “Optimal Quadtrees for Image Segments”, IEEE Trans. Pattern Analysis Machine Intelligence PAMI-5, 1983, 77–83

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  51. L. Jones, S. S. Iyengar: “Representation of regions as a forest of quadtrees”, in Proc. Pattern Recognition and Image Processing Conf., Dallas, TX, 1981, pp. 57–59

    Google Scholar 

  52. I. Gargantini: An effective way to represent quadrees, Comm. ACM 25, 905–910 (1982)

    Article  Google Scholar 

  53. E. Kawaguchi, T. Endo, J. Matsunaga: “DF-Expression Viewed from Digital Picture Processing”, Department of Information Systems, Kyushu University (1982)

    Google Scholar 

  54. L. Gibson, D. Lucas: “Spatial data processing using generalized balanced ternary”, in Proc. Pattern Recognition and Image Processing Conf., Los Vegas, NV, 1982, pp. 566–571

    Google Scholar 

  55. N. Ahuja: “Approaches to recursive image decomposition”, in Proc. Pattern Recognition and Image Processing Conf., Dallas, TX, 1981, pp. 75–80

    Google Scholar 

  56. H. Samet, R. E. Webber: “On Encoding Boundaries with Quadtrees”, Computer Science TR-1162, University of Maryland (1982)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Maryland, 20742, College Park, MD, USA

    H. Samet

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  1. H. Samet
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Editor information

Editors and Affiliations

  1. Center for Automation Research, University of Maryland, 20742, College Park, MD, USA

    Azriel Rosenfeld

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© 1984 Springer-Verlag Berlin Heidelberg

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Samet, H. (1984). A Tutorial on Quadtree Research. In: Rosenfeld, A. (eds) Multiresolution Image Processing and Analysis. Springer Series in Information Sciences, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51590-3_15

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  • DOI: https://doi.org/10.1007/978-3-642-51590-3_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-51592-7

  • Online ISBN: 978-3-642-51590-3

  • eBook Packages: Springer Book Archive

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