Multiresolution Maximum Intensity Volume Rendering by Morphological Pyramids

  • Jos B. T. M. Roerdink
Part of the Eurographics book series (EUROGRAPH)


We propose a multiresolution representation for maximum intensity projection (MIP) volume rendering, based on morphological pyramids which allow progressive refinement and have the property of perfect reconstruction. The pyramidal analysis and synthesis operators are composed of morphological erosion and dilation, combined with dyadic downsampling for analysis and dyadic upsampling for synthesis. The structure of the multiresolution MIP representation is very similar to wavelet splatting, the main differences being that (i) linear summation of voxel values is replaced by maximum computation, and (ii) linear wavelet filters are replaced by (nonlinear) morphological filters.


Maximum Intensity Projection Volume Rendering Morphological Operator Perfect Reconstruction Detail Signal 
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.
    Burt, P. J., and Adelson, E. H. The Laplacian pyramid as a compact image code. IEEE Trans. Commun. 31 (1983), 532–540.CrossRefGoogle Scholar
  2. 2.
    Cai, W., and Sakas, G. Maximum intensity projection using splatting in sheared object space. Computer Graphics Forum (Proc. Proc. Eurographics’98) 17, 3 (1998), C113–124.CrossRefGoogle Scholar
  3. 3.
    Goutsias, J., and Heijmans, H. J. A. M. Multiresolution signal decomposition schemes. Part 1: Linear and morphological pyramids. Tech. Rep. PNA-R9810, Centre for Mathematics and Computer Science, Amsterdam, Oct. 1998.Google Scholar
  4. 4.
    Grosso, R., and Ertl, T. Biorthogonal wavelet filters for frequency domain volume rendering. In Proceedings of Visualization in Scientific Computing’ 95 (1995), J. van Wijk, R. Scateni, and P. Zanarini, Eds.Google Scholar
  5. 5.
    Heijmans, H.J.A.M. Morphological Image Operators, vol. 25 of Advances in Electronics and Electron Physics, Supplement. Academic Press, New York, 1994.Google Scholar
  6. 6.
    Heijmans, H. J. A. M., and Goutsias, J. Multiresolution signal decomposition schemes. Part 2: morphological wavelets. Tech. Rep. PNA-R9905, Centre for Mathematics and Computer Science, Amsterdam, June 1999.Google Scholar
  7. 7.
    Lippert, L., and Gross, M. H. Fast wavelet based volume rendering by accumulation of transparent texture maps. Computer Graphics Forum 14, 3 (1995), 431–443.CrossRefGoogle Scholar
  8. 8.
    Lippert, L., Gross, M. H., and Kurmann, C. Compression domain volume rendering for distributed environments. In Proc. Eurographics’97 (1997), pp. 95–107.Google Scholar
  9. 9.
    Liirig, C, and Ertl, T. Hierarchical volume analysis and visualization based on morphological operators. In Proc. IEEE Visualization’ 98 (1998), IEEE Computer Society Press, pp. 335–341.Google Scholar
  10. 10.
    Malzbender, T. Fourier volume rendering. ACM Transactions on Graphics 12, 3 (1993), 233–250.CrossRefGoogle Scholar
  11. 11.
    Mroz, L., König, A., and Gröller, E. Maximum intensity projection at warp speed. Computers &Graphics 24 (2000), 343–352.Google Scholar
  12. 12.
    Muraki, S. Volume data and wavelet transforms. IEEE Computer Graphics and Applications 13, 4 (1993), 50–56.CrossRefGoogle Scholar
  13. 13.
    Roerdink, J. B. T M., and Blaauwgeers, G. S. M. Visualization of Minkowski operations by computer graphics techniques. In Mathematical Morphology and its Applications to Image Processing, J. Serra and P. Soille, Eds. Kluwer Acad. Publ., Dordrecht, 1994, pp. 289–296.CrossRefGoogle Scholar
  14. 14.
    Roerdink, J. B. T. M., and Westenberg, M. A. Wavelet-based volume visualization. Nieuw Archief voor Wiskunde 17 (Fourth Series), 2 (July 1999), 149–158.MathSciNetGoogle Scholar
  15. 15.
    Serra, J. Image Analysis and Mathematical Morphology. Academic Press, New York, 1982.MATHGoogle Scholar
  16. 16.
    Sternberg, S. R. Grayscale morphology. Comp. Vis. Graph. Im. Proc. 35 (1986), 333–355.Google Scholar
  17. 17.
    Westenberg, M. A., and Roerdink, J. B. T. M. Frequency domain volume rendering by the wavelet X-ray transform. IEEE Trans. Image Processing 9,7 (2000), 1249–1261.CrossRefGoogle Scholar
  18. 18.
    Westermann, R., and Ertl, T. Amultiscale approach to integrated volume segmentation and rendering. In Proc. Eurographics’ 97, Vienna, D. Fellner and L. Szirmay-Kalos, Eds., vol. 16. 1997, pp.C-117-C-127.Google Scholar
  19. 19.
    Westover, L. A. Footprint evaluation for volume rendering. Computer Graphics 24, 4 (1990), 367–376.CrossRefGoogle Scholar
  20. 20.
    Zuiderveld, K. J., Koning, A. H. J., and Viergever, M. A. Techniques for speeding up highquality perspective Maximum Intensity Projection. Pattern Recognition Letters 15 (1994), 507–517.Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Jos B. T. M. Roerdink
    • 1
  1. 1.Institute for Mathematics and Computing ScienceUniversity of GroningenAV GroningenThe Netherlands

Personalised recommendations