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Filter Banks, Wavelets, and Frames with Applications in Computer Vision and Image Processing (A Review)

  • Ivar Austvoll
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2749)

Abstract

The purpose of this article is to present some of the fundamental principles of filter banks, wavelets and frames and their connections, with special emphasis on applications in computer vision and image processing. This is a vast field and we can only give a glimpse of it. We start with a short historical review and a rather broad discussion of filter banks, wavelets and frames. It is discussed how filter banks and wavelets are connected via multiresolution. Some of the most important structures and properties are presented but hardly no mathematical details are given. We focus especially on directional filter banks and wavelets, on analysis and extraction of directional features in images and image sequences. A system for motion estimation (estimation of optical flow) is presented.

Keywords

Computer Vision Discrete Wavelet Transform Motion Estimation Sparse Representation Filter Bank 
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.

References

  1. [1]
    Watson, A. B., Ahumada, A. J. Jr.: Model of human visual-motion sensing, Journal of Optical Society of America 2 No. 2 (1985) 322–342CrossRefGoogle Scholar
  2. [2]
    Adelson, E. H. and Bergen, J. R.: Spatiotemporal energy models for the perception of motion, Journal of the Optical Society of America 2 No. 2 (1985) 284–299Google Scholar
  3. [3]
    Jain, A. K.: Fundamentals of Digital Image Processing. Prentice-Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  4. [4]
    Gonzales R. C., Woods R. E.: Digital Image Processing. Addison-Wesley Publishing Company (1993)Google Scholar
  5. [5]
    Witkin, A.: Scale-space filtering. 8th International Joint Conference Artificial Intelligense, (1983) 1019–1022Google Scholar
  6. [6]
    Burt, P. J.: The Pyramid as a Structure for Efficient Computation. Multi Resolution Image Processing and Analysis. (1984) Springer Verlag 6–35Google Scholar
  7. [7]
    Burt, P. J.: Multiresolution techniques for image representation, analysis, and’ smart’ transmission. Visual Communications and Image Processing IV, SPIE 1199, (1989) 2–15Google Scholar
  8. [8]
    Pauwels, E. J., Van Gool, L. J., Fiddelaers, P., Moons, T.: An Extended Class of Scale-Invariant and Recursive Scale Space Filters. IEEE Trans. Pattern Anal. and Machine Intell. 17 No. 7 (1995) 691–701CrossRefGoogle Scholar
  9. [9]
    Granlund, G. H.: In search of a general picture processing operator. Computer Graphics and Image Processing 8 No. 2 (1978) 155–178CrossRefGoogle Scholar
  10. [10]
    Woods J. W., O’Neill S. D.: Subband Coding of Images. IEEE Trans. Acoust., Speech, Signal Processing ASSP-34 No. 5 (1986) 1278–1288CrossRefGoogle Scholar
  11. [11]
    Esteban D., Galand C.: Application of quadarature mirror filters to split band voice coding schemes. Proc. Int. Conf. Acoust. Speech, Signal Proc. (1977) 191–195Google Scholar
  12. [12]
    Morlet J.: Sampling theory and wave propagaation. NATO ASI Series 1, Issues in Acoustic signal/Image processing and recognition, Chen C. H., ed., Springer Verlag, Berlin, 233–261Google Scholar
  13. [13]
    Mallat, S.G.: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. and Machine Intell. 11 No. 7 (1989) 674–693zbMATHCrossRefGoogle Scholar
  14. [14]
    Vetterli, M., Herley, C.: Wavelets and Filter Banks: Theory and Design. IEEE Trans. Signal Processing 40 No. 9 (1992) 2207–2232zbMATHCrossRefGoogle Scholar
  15. [15]
    Duffin R.J., Shaeffer A.C.: A class of nonharmonic Fourier series. Trans.Amer.Math.Soc. 72 (1952) 341–366zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    Daubechies, I.: Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania (1992)zbMATHGoogle Scholar
  17. [17]
    Ramstad, T.A., Aase, S.A., Husøy, J.H.: Subband Compression of Images — Principles and Examples, Advances in Image Communication 6. ELSEVIER Science Publishers BV, North Holland (1995)Google Scholar
  18. [18]
    Rioul, O.: A discrete-time multiresolution theory. IEEE Trans. Signal Processing 41 No. 8 (1993) 2591–2606zbMATHCrossRefGoogle Scholar
  19. [19]
    Rabbani, M, Joshi, R.: An overview of the JPEG still image compression standard. Signal Processing: Image Communication 17 (2002) 3–48CrossRefGoogle Scholar
  20. [20]
    Winger L.L., Venetsanopoulos A.N.: Biorthogonal nearly coiflet wavelets for image compression. Signal Processing: Image Communication 16 (2001) 859–869CrossRefGoogle Scholar
  21. [21]
    Randen, T., Husøy, J.H.: Optimal Texture Filtering. IEEE Int. Conf. on Image Proc. Proceedings, (1995), Washington, D.C., 374–377Google Scholar
  22. [22]
    Randen, T., Husøy, J.H.: Filtering for Texture Classification: A Comparative Study. IEEE Trans. Pattern Anal. and Machine Intell. 21 No. 4 (1999) 291–310CrossRefGoogle Scholar
  23. [23]
    Vaidyanathan, P.P.: Multirate Systems and Filter Banks. Prentice Hall, Englewood Cliffs (1993)zbMATHGoogle Scholar
  24. [24]
    Austvoll, I.: Motion Estimation using Directional Filters. PhD thesis (1999) Stavanger University College (HIS)/The Norwegian University of Science and Technology (NTNU), PoBox 8002 Ullandhaug, N-4068 Stavanger, Norway.Google Scholar
  25. [25]
    Austvoll, I.: Directional filters and a new structure for estimation of optical flow. IEEE Int. Conf. on Image Proc. Proceedings, (2000), Vancouver, Canada.Google Scholar
  26. [26]
    Shensa, M.J.: The Discrete Wavelet Transform: Wedding the Á Trous and Mallat Algorithms. IEEE Trans. Signal Processing, 40 No. 10 (1992) 2464–2482zbMATHCrossRefGoogle Scholar
  27. [27]
    Daubechies, I.: Orthonormal Bases of Compactly Supported Wavelets. Communications on Pure and Applied Mathematics, XLI (1988) 909–996CrossRefMathSciNetGoogle Scholar
  28. [28]
    Antoine, J.-P., Carrette, P., Murenzi, R., Piette, B.: Image analysis with two-dimensional continuous wavelet transform. Signal Processing, Elsevier, 31 (1993) 241–272zbMATHCrossRefGoogle Scholar
  29. [29]
    Antoine, J.-P., Murenzi R.: Two-dimensional directional wavelets and scale-angle representation. Signal Processing, Elsevier, 52 (1996) 259–281zbMATHCrossRefGoogle Scholar
  30. [30]
    Unser M., Blu T.: Wavelet Theory Demystified. IEEE Trans. Signal Processing, 51 No. 2 (2003) 470–483CrossRefMathSciNetGoogle Scholar
  31. [31]
    Unser M.: Splines: A Perfect Fit for Signal and Image Processing. IEEE Signal Processing Magazine, 16 No. 6 (1999) 22–38CrossRefGoogle Scholar
  32. [32]
    Pei, S-C., Yeh, M-H.: An introduction to discrete finite frames. IEEE Signal Processing Magazine, 14 No. 6 (1997) 84–96CrossRefGoogle Scholar
  33. [33]
    Aase, S.A., Husøy, J.H., Skretting, K., Engan, K.: Optimized Signal Expansions for Sparse Representation. IEEE Trans. Signal Processing, 49 No. 5 (2001) 1087–1096CrossRefGoogle Scholar
  34. [34]
    Engan, K.: Frame Based Signal Representation and Compression. PhD thesis. (2000) Stavanger University College (HIS)/The Norwegian University of Science and Technology (NTNU), PoBox 8002 Ullandhaug, N-4068 Stavanger, Norway.Google Scholar
  35. [35]
    Skretting, K.: Sparse Signal Representation using Overlapping Frames. PhD thesis. (2002) Stavanger University College (HIS)/The Norwegian University of Science and Technology (NTNU), PoBox 8002 Ullandhaug, N-4068 Stavanger, Norway.Google Scholar
  36. [36]
    Skretting, K., Engan, K., Husøy, J.H., Aase, S.A.: Sparse representation of images using overlapping frames. Proc. 12th Scandianavian Conference on Image Analysis, SCIA 2001, Bergen, Norway (2001) 613–620Google Scholar
  37. [37]
    Knutsson, H.: Filtering and Reconstruction in Image Processing. Diss. No. 88 (1982) Linköping University, S-581 83 Linköping, SwedenGoogle Scholar
  38. [38]
    Knutsson, H., Granlund, G.H.: Texture Analysis Using Two-Dimensional Quadrature Filters. CAPAIDM Workshop, Pasadena, California Oct. (1983)Google Scholar
  39. [39]
    Granlund, G.H., Knutsson, H.: Signal Processing for Computer Vision, Kluwer Academic Publishers (1995)Google Scholar
  40. [40]
    Leduc, J.-P.: Spatio-temporal wavelet transforms for digital signal analysis. Signal Processing, 60, Elsevier (1997) 23–41zbMATHCrossRefGoogle Scholar
  41. [41]
    Bovik, A. C., Clark, M., Geisler, W. S.: Multichannel Texture Analysis Using Localized Spatial Filters. IEEE Trans. Pattern Anal. and Machine Intell. 12 No. 1 (1990) 55–72CrossRefGoogle Scholar
  42. [42]
    Candés, E. J.: Ridgelets: Theory and applications. Ph.D. dissertation, (1998), Dept. Statistics, Stanford Univ., Stanford, CA, USA.Google Scholar
  43. [43]
    Candés, E. J., Donoho, D. L.: Curvelets-a suprisingly effective nonadaptive representation for objects with edges. In Curve and Surface Fitting. Eds.: Cohen, A., Rabut, C., Schumaker, L. L., Saint-Malo, (1999) Vanderbilt University PressGoogle Scholar
  44. [44]
    Do, M. N., Vetterli, M.: Pyramidal Directional Filter Banks and Curvelets. Proc. IEEE Int. Conf. on Image Proc. Proceedings, (2001), Thessaloniki, Greece.Google Scholar
  45. [45]
    Do, M. N., Vetterli, M.: Contourlets: A Directional Multiresolution Image Representation. Proc. IEEE Int. Conf. on Image Proc. Proceedings, (2002), Rochester, New YorkGoogle Scholar
  46. [46]
    Do, M. N., Vetterli, M.: The Finite Ridgelet Transform for Image Representation. IEEE Trans. Image Processing, 12 No. 1 (2003) 16–28CrossRefMathSciNetGoogle Scholar
  47. [47]
    Starck, J.-L., Candés, E. J., Donoho, D. L.: The Curvelet Transform for Image Denoising. IEEE Trans. Image Processing, 11 No. 6 (2002) 670–684CrossRefGoogle Scholar
  48. [48]
    Ulfarsson, M. O., Sveinsson, J. R., Benediktsson, J. A.: Speckle Reduction of SAR Images in The Curvelet Domain. Proc. IEEE Int. Conf. on Image Proc. Proceedings, (2002), Rochester, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ivar Austvoll
    • 1
  1. 1.Department of Electrical Engineering and Computer ScienceStavanger University CollegeStavangerNorway

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