Pyramidal Tools and Applications

  • Virginio Cantoni
  • Marco Ferretti
Part of the Advances in Computer Vision and Machine Intelligence book series (ACVM)


The pyramidal architecture supports several powerful paradigms for “machine algorithms,” including pyramid building, tree search, and horizontal and verti- cal propagation. Such paradigms are supported by a set of basic algorithms, for which many types of pyramid or pyramid-related approaches and data struc- tures have been proposed. This chapter reviews some of these fundamental techniques from a computational theoretical point of view and in the light of their effectiveness in application development.


Optical Flow Coarse Level Candidate Parent Laplacian Pyramid Multiple Resolution 
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. 1.
    S. L. Tanimoto and A. Klinger (eds.), Structured Computer Vision: Machine Perception through Hierarchical Computation Structures ,Academic Press, New York (1980).Google Scholar
  2. 2.
    A. Rosenfeld, (ed.) Multiresolution Image Processing and Analysis ,Springer-Verlag, Berlin (1984).MATHGoogle Scholar
  3. 3.
    V. Cantoni and S. Levialdi (eds.), Pyramidal Systems for Computer Vision ,Springer-Verlag, Berlin (1986).MATHGoogle Scholar
  4. 4.
    L. Uhr (ed.), Parallel Computer Vision ,Academic Press, Orlando, FL (1987).MATHGoogle Scholar
  5. 5.
    C. R. Dyer, Multiscale image understanding, in Parallel Computer Vision (L. Uhr, ed.), pp. 171–213, Academic Press, Orlando, FL (1987).Google Scholar
  6. 6.
    A. Rosenfeld, Image analysis and computer vision: 1991, CVGIP: Image Understanding 55(3), 349–380 (1992).MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    M. Ferretti, Overlapping in compact pyramids, in Pyramidal Systems for Computer Vision (V. Cantoni and S. Levialdi, eds.), pp. 247–259, Springer-Verlag, Berlin (1986).CrossRefGoogle Scholar
  8. 8.
    R. Miller and Q. F. Stout, Parallel Algorithms for Regular Architectures ,MIT Press, Cambridge, MA (1992).Google Scholar
  9. 9.
    Q. F. Stout, Pyramid algorithms optimal for the worst case, in Parallel Computer Vision (L. Uhr, ed.), pp. 147–168, Academic Press, New York (1987).Google Scholar
  10. 10.
    R. Miller and Q. F. Stout, Data movement techniques for the pyramid computer, SIAM Cornput. 16 (1), 38–60 (1987).MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    S. L. Tanimoto, Algorithms for median filtering of images on a pyramid machine, in Computing Structures for Image Processing (M. J. B. Duff, ed.), pp. 123–141, Academic Press, London (1983).Google Scholar
  12. 12.
    S. L. Tanimoto, Sorting, histogramming, and other statistical operations on a pyramid machine, in Multiresolution Image Processing and Analysis (A. Rosenfeld, ed.), pp. 136–145, Springer-Verlag, Berlin (1984).CrossRefGoogle Scholar
  13. 13.
    Q. F. Stout, Sorting, merging, selecting and filtering on tree and pyramid machines, Proc. 1983 Int. Conf Parallel Processing ,1983, pp. 214–221.Google Scholar
  14. 14.
    Q. F. Stout, Supporting divide-and-conquer algorithms for image processing, J. Parallel Distribut. Comput. 4, 147–168 (1987).CrossRefGoogle Scholar
  15. 15.
    S. L. Tanimoto, Programming techniques for hierarchical parallel image processors, in Multicomputers and Image Processing Algorithms and Programs (K. Preston and L. Uhr, eds.), pp. 421–429, Academic Press, New York (1982).Google Scholar
  16. 16.
    R. Miller and Q. F. Stout, Computing convexity properties of images on a pyramid computer, Algorithmica 6, 659–684 (1991).MathSciNetCrossRefGoogle Scholar
  17. 17.
    R. Miller and Q. F. Stout, Simulating essential pyramids, IEEE Trans. Comput. TC-37(12), 1642–1648 (1988).MathSciNetCrossRefGoogle Scholar
  18. 18.
    W. G. Kropatsch, Rezeptive felder in bildpyramiden, in Mustererkennung 1988 (H. Bunke, O. Küubler, and P. Stucki, eds.), pp. 333–339, Springer-Verlag, Berlin (1988).Google Scholar
  19. 19.
    W. G. Kropatsch, A pyramid that grows by powers of 2, Pattern Recognition Lett. 3(9), 315–322 (1985).CrossRefGoogle Scholar
  20. 20.
    P. Meer, Stochastic image pyramids, CVGIP 45, pp. 269–294 (1989).Google Scholar
  21. 21.
    P. Meer, C. A. Sher, and A. Rosenfeld, The chain pyramid: hierarchical contour processing, IEEE Trans. Pattern Anal. Machine Intell. PAMI-12(4) 363–376 (1990).CrossRefGoogle Scholar
  22. 22.
    P. Meer, S. Jiang, E. S. Baugher, and A. Rosenfeld, Robustness of image pyramids under structural perturbations, CVGIP 44, 307–331 (1988).Google Scholar
  23. 23.
    A. Montanvert, P. Meer, and A. Rosenfeld, Hierarchical image analysis using irregular tessellations, IEEE Trans. Pattern Anal. Machine Intell. PAMI-13(4) 307–316 (1991).CrossRefGoogle Scholar
  24. 24.
    J. M. Jolion and A. Montanvert, The adaptive pyramid: a framework for 2D image analysis, CVGIP: Image Understanding 55(3), 339–348 (1992).MATHCrossRefGoogle Scholar
  25. 25.
    S. Peleg, O. Federbush, and R. Hummel, Custom-made pyramids, in Parallel Computer Vision (L. Uhr, ed.), pp. 125–147, Academic Press, New York (1987).Google Scholar
  26. 26.
    Ph. Clermont, Méthodes de programmasion de machine paralléle pyramidale. applications en segmentation d’images, Thése de Doctorat, Université Paris VII (1990).Google Scholar
  27. 27.
    Ph. Clermont and A. Merigot, Efficient parallel pyramidal primitives for image analysis, in Progress in Image Analysis and Processing II (V. Cantoni, M. Ferretti, S. Levialdi, R. Negrini, and R. Stefanelli, eds.), pp. 544–550, World Scientific, Singapore (1992).Google Scholar
  28. 28.
    F. Glazer, Multilevel relaxation in low-level computer vision, in Multiresolution Image Processing and Analysis (A. Rosenfeld, ed.), pp. 312–330, Springer-Verlag, Berlin (1984).CrossRefGoogle Scholar
  29. 29.
    W. Hackbusch, Multigrid Methods and Applications ,Springer-Verlag, New York (1985).Google Scholar
  30. 30.
    A. Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comp. 31, 333–390 (1977).MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    D. Terzopoulos, Multilevel computational processes for visual surface reconstruction, CVGIP 24, 52–96 (1983).Google Scholar
  32. 32.
    D. Terzopoulos, Image analysis using multigrid relaxation methods, IEEE Trans. Pattern Anal. Machine Intell. PAMI-8(2), 129–139 (1986).CrossRefGoogle Scholar
  33. 33.
    D. Gannon, On the structure of parallelism in a highly concurrent PDE solver, Proc. 7th Symp. Computer Arithmetics ,1985, pp. 252–259.Google Scholar
  34. 34.
    P. Burt, T. H. Hong, and A. Rosenfeld, Segmentation and estimation of image region properties through cooperative hierarchical computation, IEEE Trans. Syst., Man, Cybernet. SMC-11, 802–804 (1981).Google Scholar
  35. 35.
    T. Hong, K. A. Narayanan, S. Peleg, A. Rosenfeld, and T. Silberberg, Image smoothing and segmentation by multiresolution pixel linking: further experiments and extensions, IEEE Trans. Syst., Man, Cybernet. SMC-12(5), 611–622 (1982).Google Scholar
  36. 36.
    J. M. Cibulskis and C. R. Dyer, An analysis of node linking in overlapped pyramids, IEEE Trans. Syst., Man, Cybernet. SMC-14(3), 424–436 (1984).CrossRefGoogle Scholar
  37. 37.
    T. Hong and A. Rosenfeld, Compact region extraction using weighted pixel linking in a pyramid, IEEE Trans. Pattern Anal. Machine Intell. PAMI-6(2), 222–229 (1984).CrossRefGoogle Scholar
  38. 38.
    M. Spann, Figure/ground separation using stochastic pyramid relinking, Pattern Recognition 24(10), 993–1002 (1991).CrossRefGoogle Scholar
  39. 39.
    A. P. Witkin, Scale-space filtering, Proc. 7th Int. Joint Conf. Artificial Intelligence, 1983, pp. 1019–1021.Google Scholar
  40. 40.
    A. L. Yuille and T. A. Poggio, Scaling theorems for zero crossings, IEEE Trans. Pattern Anal. Machine Intell. PAMI-8(2), 15–25 (1986).CrossRefGoogle Scholar
  41. 41.
    T. Hong, M. Shneier, and A. Rosenfeld, Border extraction using linked edge pyramids, IEEE Trans. Syst., Man, Cybernet. SMC-12(5), 660–668 (1982).Google Scholar
  42. 42.
    T. H. Hong and M. Shneier, Extracting compact objects using linked pyramids, IEEE Trans. Pattern Anal. Machine Intell. PAMI-6(2), 229–237 (1984).CrossRefGoogle Scholar
  43. 43.
    R. Hartley, A Gaussian-weighted multiresolution edge detector, CVGIP 30, 70–83 (1985).Google Scholar
  44. 44.
    P. Burt, Fast filter transforms for image processing, CVGIP 16, 20–51 (1981).Google Scholar
  45. 45.
    R. Park and P. Meer, Edge-preserving artifact-free smoothing with image pyramids, Pattern Recognition Lett. 12(9), 467–475 (1991).CrossRefGoogle Scholar
  46. 46.
    A. Rosenfeld and A. Sher, Detection and delineation of compact objects using intensity pyramids, Pattern Recognition 21, 147–151 (1988).CrossRefGoogle Scholar
  47. 47.
    C. A. Sher and A. Rosenfeld, Pyramid cluster detection and delineation by consensus, Pattern Recognition Lett. 12(9), 477–482 (1991).CrossRefGoogle Scholar
  48. 48.
    P. Meer, D. Mintz, A. Montanvert, and A. Rosenfeld, Consensus vision, Proc. AAAI-90 Workshop on Qualitative Vision, Boston, MA, 1990, pp. 111–115.Google Scholar
  49. 49.
    J. M. Jolion, P. Meer, and A. Rosenfeld, Border delineation in image pyramids by concurrent tree growing, Pattern Recognition Lett. 11(2), 107–115 (1990).MATHCrossRefGoogle Scholar
  50. 50.
    L. Van Gool, P. Dewaele, and A. Oosterlinck, Texture analysis anno 1983, CVGIP 29, 336–357 (1985).Google Scholar
  51. 51.
    M. Pietikäinen and A. Rosenfeld, Image segmentation by texture using pyramid node linking, IEEE Trans. Syst., Man, Cybernet. SMC-11(12), 822–825 (1981).Google Scholar
  52. 52.
    L. I. Larkin and P. Burt, Multi-resolution texture energy measures, Proc. IEEE Comput. Soc. Conf. CVPR ,Washington, DC, 1983, pp. 519–520.Google Scholar
  53. 53.
    B. P. Kjell and C. R. Dyer, Edge separation and orientation texture measures, Proc. IEEE Conf. CVPR, 1985, pp. 306–311.Google Scholar
  54. 54.
    B. P. Kjell and C. R. Dyer, Segmentation of textured images by pyramid linking, in Pyramidal Systems for Computer Vision (V. Cantoni and S. Levialdi, eds.), pp. 273–288, Springer-Verlag, Berlin (1986).CrossRefGoogle Scholar
  55. 55.
    S. Peleg, J. Naor, R. Hartley, and D. Avnir, Multiple resolution texture analysis and classification, IEEE Trans. Pattern Anal. Machine Intell. PAMI-6(4), 518–523 (1984).CrossRefGoogle Scholar
  56. 56.
    D. B. Mandelbrot, The Fractal Geometry of Nature ,Freeman, San Francisco, CA (1982).MATHGoogle Scholar
  57. 57.
    C. Bouman and B. Liu, Multiple resolution segmentation of textured images, IEEE Trans. Pattern Anal. Machine Intell. PAMM3(2), 99–113 (1991).CrossRefGoogle Scholar
  58. 58.
    M. Bister, J. Cornelis, and A. Rosenfeld, A critical view of pyramid segmentation algorithms, Pattern Recognition Lett. ,11(9), 605–617 (1990).MATHCrossRefGoogle Scholar
  59. 59.
    A. Rosenfeld and G. J. VanderBrug, Coarse-fine template matching, IEEE Trans. Syst., Man ,Cybernet. SMC-7(2), 104–107 (1977).Google Scholar
  60. 60.
    R. Y. Wong and E. L. Hall, Sequential hierarchical scene matching, IEEE Trans. Comput. C-27(4), 359–366 (1978).MathSciNetCrossRefGoogle Scholar
  61. 61.
    S. L. Tanimoto, Template matching in pyramids, CVGIP 16, 356–369 (1981).Google Scholar
  62. 62.
    F. Glazer, G. Reynolds, and A. Anandan, Scene matching by hierarchical correlation, Proc. IEEE CS Conf. CVPR, Washington, DC, 1983, pp. 432–441.Google Scholar
  63. 63.
    P. V. C. Hough, Method and means for recognizing complex patterns, U.S. Patent 3069654 (1962).Google Scholar
  64. 64.
    D. Ballard, Generalizing the hough transform to detect arbitrary shapes, Pattern Recognition 13(2), 111–122 (1981).MATHCrossRefGoogle Scholar
  65. 65.
    H. Li, M. A. Lavin, and R. J. Le Master, Fast hough transform: a hierarchical approach, CVGIP 36, 139–161 (1986).Google Scholar
  66. 66.
    S. L. Tanimoto, From pixels to predicates in pyramid machines, in From Pixels to Features (J. C. Simon, ed.), pp. 383–392, Elsevier, North-Holland (1989).Google Scholar
  67. 67.
    J. M. Jolion and A. Rosenfeld, A O(log n) pyramid Hough transform, TR-2066, Center for Automation Research, University of Maryland, College Park, MD (1988).Google Scholar
  68. 68.
    J. Princen, J. Illingworth, and J. Kittler, A hierarchical approach to line extraction based on the hough transform, CVGIP 52, 57–77 (1990).Google Scholar
  69. 69.
    G. Bongiovanni, C. Guerra, and S. Levialdi, Computing the Hough transform on a pyramid architecture, Machine Vision Appl. 3(2), 117–123 (1990).CrossRefGoogle Scholar
  70. 70.
    H. Samet, The Design and Analysis of Spatial Data Structures ,Addison-Wesley, Reading, MA (1990).Google Scholar
  71. 71.
    H. Samet, Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS ,Addison-Wesley, Reading, MA (1990).Google Scholar
  72. 72.
    W. G. Kropatsch, Curve representations in multiple resolution, Pattern Recognition Lett. 6(8), 179–184 (1987).CrossRefGoogle Scholar
  73. 73.
    W. G. Kropatsch, Elimination von ’kleinen’ kurvenstücken in der 2x2/2 kurvenpyramide: algorithmus und test, DIBAG-Report Nr. 25, Institut für Digitale Bildverarbeitung und Grafik, Graz (1987).Google Scholar
  74. 74.
    K. A. Narayanan and A. Rosenfeld, Approximation of waweform and contours by one-dimensional pyramid linking, Pattern Recognition 15(5), 389–396 (1982).CrossRefGoogle Scholar
  75. 75.
    H. Freeman, Computer processing of line-drawing images, Comput. Surveys 6, 57–97 (1974).MATHCrossRefGoogle Scholar
  76. 76.
    P. Meer, E. S. Baugher, and A. Rosenfeld, Extraction of trend lines and extrema from multiscale curves, Pattern Recognition 21(3), 217–226 (1988).CrossRefGoogle Scholar
  77. 77.
    S. Connelly and A. Rosenfeld, A pyramid algorithm for fast curve extraction, Center for Automation Research Tech. Report CAR-TR-270, University of Maryland (1987).Google Scholar
  78. 78.
    C. Arcelli, L. P. Cordelia, and G. Sanniti di Baja (eds.), Visual Form: Analysis and Recognition ,Plenum Press, New York (1992).Google Scholar
  79. 79.
    V. Cantoni and S. Levialdi, Contour labeling by pyramidal processing, in Intermediate-Level Image Processing (M. J. B. Duff, ed.), pp. 181–190, Academic Press, London (1986).Google Scholar
  80. 80.
    A. Bengtsson and J. Eklundh, Shape representation by multiscale contour approximation, IEEE Trans. Pattern Anal. Machine Intell. PAMI-13(1), 85–93 (1991).CrossRefGoogle Scholar
  81. 81.
    H. Zabrodsky, S. Peleg, and A. Avnir, Hierarchical symmetry, Proc. 11th Int. Conf. Pattern Recognition, Vol. C, 1992, pp. 9–12.Google Scholar
  82. 82.
    L. S. Davis, Hierarchical generalized Hough transform and line-segment based Hough transform, Technical Report, University of Texas (1979).Google Scholar
  83. 83.
    V. Cantoni, L. Carrioli, M. Diani, M. Ferretti, L. Lombardi, and M. Savini, Object recognition and location by a bottom-up approach in Image Analysis and Processing (V. Cantoni, V. Di Gesù, and S. Levialdi, eds.), pp. 329–336, Plenum Press, New York (1988).Google Scholar
  84. 84.
    M-K. Wu, Visual pattern recognition by moment invariants, IIRE Trans. Inform. Theory IT8, 179–187 (1962).Google Scholar
  85. 85.
    A. P. Reeves and A. Rostampour, Shape analysis of segmented objects using moments, Conf. Pattern Recognition and Image Processing, Dallas, 1981, pp. 171–174.Google Scholar
  86. 86.
    P. J. Burt, Smart sensing within a pyramid vision machine, Proc. IEEE 76(8), 1006–1015 (1988).CrossRefGoogle Scholar
  87. 87.
    K. R. Sloan and S. L. Tanimoto, Progressive refinement of raster images, IEEE Trans. Comput. C-28(11), 871–874 (1979).CrossRefGoogle Scholar
  88. 88.
    P. J. Burt and E. H. Adelson, The Laplacian pyramid as a compact image code, IEEE Trans. Commun. COM-31(4), 532–540 (1983).CrossRefGoogle Scholar
  89. 89.
    E. H. Adelson, E. Simoncelli, and R. Hingorani, Orthogonal pyramid transforms for image coding, SPIE, Vol. 845, Visual Communications and Image Processing II, 1987, pp. 50– 58.Google Scholar
  90. 90.
    M. G. Albanesi, I. De Lotto, and L. Carrioli, Image compression by the wavelet decomposition, European Trans. Telecommunications ,3(2), 45–54 (1992).Google Scholar
  91. 91.
    H. Mayer and W. G. Kropatsch, Progressive bildübertragung mit der 3x3/2 pyramide, in Informatik Fachberichte 219: Mustererkennung 1989 (H. Burkardt, K. H. Köhne, and B. Neumann, eds.), pp. 160–167, Springer-Verlag, Hamburg (1989).Google Scholar
  92. 92.
    H. Mayer and W. G. Kropatsch, Kompakte bildkodierung mit der 3 x 3/2 pyramide, in Wis senbasierte Mustererkennung (A. Pinz, ed.), pp. 195–210, Oldenbourg, Austria (1989).Google Scholar
  93. 93.
    A. Singh, Optic Flow Computation ,IEEE Computer Society Press, Los Alamitos, CA (1991).Google Scholar
  94. 94.
    A. Verri and T. Poggio, Against quantitative optical flow, Proc. First ICCV, London, 1987, pp. 171–180.Google Scholar
  95. 95.
    E. H. Adelson and J. R. Bergen, Spatio-temporal energy models for the perception of motion, J. Opt. Soc. Am. A 2(2), 284–299 (1985).CrossRefGoogle Scholar
  96. 96.
    P. Anandan, A unified perspective on computational techniques for the measurement of visual motion, Proc. 1st ICCV, 1987, pp. 219–230.Google Scholar
  97. 97.
    B. K. P. Horn and B. Schunck, Determining optical flow, Artif. Intell. 17, 185–203 (1981).CrossRefGoogle Scholar
  98. 98.
    H. H. Nagel, Displacement vectors derived from second order intensity variations in image sequences, CVGIP 21, 85–117 (1983).Google Scholar
  99. 99.
    W. Enkelmann, Investigation of multigrid algorithms for the estimation of optical flow fields in image sequences, CVGIP 43, 150–177 (1988).Google Scholar
  100. 100.
    R. Battiti, E. Amaldi, and C. Koch, Computing optical flow across multiple scales: an adaptive coarse-to-fine strategy, Int. J. Comput. Vision 6(2), 133–145 (1991).CrossRefGoogle Scholar
  101. 101.
    P. J. Burt, C. Yen, and X. Xu, Multi-resolution flow-through motion analysis, Proc. IEEE CS Conf. CVPR, Washington, DC, 1983, pp. 246–252.Google Scholar
  102. 102.
    P. J. Burt, Multiresolution pyramid architectures for real-time motion analysis, IAPR Workshop on Machine Vision Applications, Tokyo, 1990, pp. 317–321.Google Scholar
  103. 103.
    P. J. Burt, J. R. Berger, R. Hingorani, R. Kolczynski, W. A. Lee, A. Leung, J. Lubin, and H. Shvaytser, Object tracking with a moving camera, Proc. IEEE Workshop on Visual Motion, Princeton, NJ, 1991, pp. 2–12.Google Scholar
  104. 104.
    P. Anandan and R. Weiss, Introducing a smoothness constraint in a matching approach for the computation of displacement fields, Proc. SPIE Intelligent Robots and Computer Vision Conf., 521, 1984, pp. 184–194.Google Scholar
  105. 105.
    R. Bajcsy, R. Lieberson, and M. Reivic, A computerized system for the elastic matching of deformed radiographic images to idealized atlas images J. Comp. Assoc. Tomography 7(4), 618–625 (1983).CrossRefGoogle Scholar
  106. 106.
    J. Dengler, Local motion estimation with the dynamic pyramid, in Pyramidal Systems for Computer Vision (V. Cantoni and S. Levialdi, eds.), pp. 289–298, Springer-Verlag, Berlin (1986).CrossRefGoogle Scholar
  107. 107.
    V. Venkateswar and R. Chellappa, Hierarchical feature based matching for motion correspondence, Proc. IEEE Workshop on Visual Motion, Princeton, NJ, 1991, pp. 280–285.Google Scholar
  108. 108.
    W. I. Grosky and R. Jain, Region matching in pyramids for dynamic scene analysis, in Multiresolution Image Processing and Analysis (A. Rosenfeld, ed.), pp. 331–342, Springer-Verlag, Berlin (1984).CrossRefGoogle Scholar
  109. 109.
    K. J. Hanna, Direct multi-resolution estimation of ego-motion and structure from motion, Proc. IEEE Workshop on Visual Motion, Princeton, NJ, 1991, pp. 156–162.Google Scholar
  110. 110.
    D. Marr and T. Poggio, A computational theory of human stereo vision, Proc. R. Soc. London B 204, 1979, pp. 359–365.CrossRefGoogle Scholar
  111. 111.
    J. J. Clark and P. D. Lawrence, A theoretical basis for diffrequency stereo, CVGIP 35, 1–19 (1986).Google Scholar
  112. 112.
    V. Cantoni, A. Griffini, and L. Lombardi, Stereo vision in multi-resolution, in Progress in Image Analysis and Processing (V. Cantoni, L. P. Cordelia, S. Levialdi, and G. Sanniti di Baja, eds.), pp. 706–713, World Scientific, Singapore (1990).Google Scholar
  113. 113.
    T. Darell and K. Wohn, Depth from focus using a pyramid architecture, Pattern Recognition Lett. 11(12), 787–796 (1990).MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Virginio Cantoni
    • 1
  • Marco Ferretti
    • 1
  1. 1.University of PaviaPaviaItaly

Personalised recommendations