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Multiresolution Maximum Intensity Volume Rendering by Morphological Pyramids

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Part of the book series: Eurographics ((EUROGRAPH))

Abstract

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.

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References

  1. Burt, P. J., and Adelson, E. H. The Laplacian pyramid as a compact image code. IEEE Trans. Commun. 31 (1983), 532–540.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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. 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. 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. 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.

    Article  Google Scholar 

  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. 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. Malzbender, T. Fourier volume rendering. ACM Transactions on Graphics 12, 3 (1993), 233–250.

    Article  Google Scholar 

  11. Mroz, L., König, A., and Gröller, E. Maximum intensity projection at warp speed. Computers &Graphics 24 (2000), 343–352.

    Google Scholar 

  12. Muraki, S. Volume data and wavelet transforms. IEEE Computer Graphics and Applications 13, 4 (1993), 50–56.

    Article  Google Scholar 

  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.

    Chapter  Google Scholar 

  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.

    MathSciNet  Google Scholar 

  15. Serra, J. Image Analysis and Mathematical Morphology. Academic Press, New York, 1982.

    MATH  Google Scholar 

  16. Sternberg, S. R. Grayscale morphology. Comp. Vis. Graph. Im. Proc. 35 (1986), 333–355.

    Google Scholar 

  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.

    Article  Google Scholar 

  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. Westover, L. A. Footprint evaluation for volume rendering. Computer Graphics 24, 4 (1990), 367–376.

    Article  Google Scholar 

  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 

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© 2001 Springer-Verlag Wien

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Roerdink, J.B.T.M. (2001). Multiresolution Maximum Intensity Volume Rendering by Morphological Pyramids. In: Ebert, D.S., Favre, J.M., Peikert, R. (eds) Data Visualization 2001. Eurographics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6215-6_6

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  • DOI: https://doi.org/10.1007/978-3-7091-6215-6_6

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83674-3

  • Online ISBN: 978-3-7091-6215-6

  • eBook Packages: Springer Book Archive

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