Wavelet Based Texture Resampling

  • Silviu Borac
  • Eugene Fiume
Conference paper
Part of the Eurographics book series (EUROGRAPH)


The integral equation arising from space variant 2-D texture resampling is reformulated through wavelet analysis. We transform the standard convolution integral in texture space into an inner product over sparse representations for both the texture and the warped filter function. This yields an algorithm that operates in constant time in the area of the domain of convolution, and that is sensitive to the frequency content of both the filter and the texture. The reformulation admits further acceleration for space-invariant resampling.


Wavelet Coefficient Sparse Representation Wavelet Decomposition Wavelet Representation Refinement Level 
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  1. [1]
    C. K. Chui, An Introduction to Wavelets, Academic Press 1992.Google Scholar
  2. [2]
    A. Cohen, I. Daubechies, J.C. Feauveau, “Biorthogonal bases of compactly supported wavelets”, Comm. Pure Appl. Math., 45 (1992), pp. 485–500.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    I. Daubechies, Ten Lectures on Wavelets, SIAM 1992.Google Scholar
  4. [4]
    I.S. Duff, A. M. Erisman, J.K. Reid, Direct methods for sparse matrices, Oxford University Press, London, 1986.MATHGoogle Scholar
  5. [5]
    A. Fournier, E. Fiume, “Constant-Time Filtering with Space-Variant Kernels”, ACM SIGGRAPH ’88 Conference Proceedings, also published as ACM Computer Graphics 22, 4, (Aug. 1988), pp. 229–238.CrossRefGoogle Scholar
  6. [6]
    R. Lansdale, Texture-Mapping and Resampling for Computer Graphics, M.A.Sc. Thesis, Department of Electrical Engineering, University of Toronto, October 1989.Google Scholar
  7. [7]
    C. Gotsman, “Constant-time filtering by singular value decomposition”, Computer Graphics Forum 13, 2 (March 1994), pp. 153–163.CrossRefGoogle Scholar
  8. [8]
    N. Greene, and P.S. Heckbert, “Creating raster omnimax images from multiple perspective views using the elliptical weighted average filter”, IEEE Computer Graphics and Applications 6, 6 (June 1986), pp. 21–27.Google Scholar
  9. [9]
    P.S. Heckbert, Fundamentals of Texture Mapping and Image Warping, M.Sc. Thesis, Department of Computer Science and Electrical Engineering, University of California, Berkeley, 1989.Google Scholar
  10. [10]
    P.S. Heckbert, “Survey of texture mapping”, IEEE Computer Graphics and Applications 6, 11 (Nov. 1986), pp. 56–67.CrossRefGoogle Scholar
  11. [11]
    L. McMillan and G. Bishop, “Plenoptic Modeling: An Image-Based Rendering System”, SIGGRAPH 95 Conference Proceedings (Aug., 1995), pp. 39–46; Annual Conference Series, Addison Wesley.Google Scholar
  12. [12]
    N. Saito, G. Beylkin, “Multiresolution Representations using the Auto-Correlation Functions of Compactly Supported Wavelets”, IEEE Transactions on Signal Processing, special issue on Wavelets and Signal Processing, 1992.Google Scholar
  13. [13]
    W. Sweldens, “Wavelets, signal compression and image processing”, in Wavelets and Their Applications in Computer Graphics, SIGGRAPH ’95 Course Notes, 1995 (http://www.cs.ubc.ca/nest/imager/contributions/bobl/wvlt/download/notes.ps.Z.saveme).Google Scholar
  14. [14]
    M.V. Wickerhauser, Lectures on Wavelet Packet Algorithms, INRIA/Rocquencourt Minicourse Lecture Notes, 1991 (http://wuarchive.wustl.edu/doc/techreports/wustl.edu/math/papers/inria300.ps.Z)Google Scholar
  15. [15]
    L. Williams, “Pyramidal Parametrics”, Computer Graphics (SIGGRAPH ’83 Proceedings) 17, 3 (July 1983), pp. 1–11.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1996

Authors and Affiliations

  • Silviu Borac
    • 1
  • Eugene Fiume
    • 1
    • 2
  1. 1.Alias|WavefrontTorontoCanada
  2. 2.University of TorontoCanada

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