Skip to main content
SpringerLink
Log in

Directional Wavelet Analysis with Fourier-Type Bases for Image Processing

  • Conference paper
Wavelet Analysis and Applications

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

Motivated by the fact that in natural images, there is usually a presence of local strongly oriented features such as directional textures and linear discontinuities, a representation which is both well-localised in frequency and orientation is desirable to efficiently describe those oriented features. Here we introduce a family of multiscale trigonometric bases for image processing using Fourier-type constructions, namely, the multiscale directional cosine transform and the multiscale Fourier transform. We also show that by seeking an adaptive basis locally, the proposed bases are able to capture both oriented harmonics as well as discontinuities, although the complexity of such adaptiveness varies significantly. We conducted denoising experiments with the proposed bases and the results show great promise of the proposed directional wavelet bases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Coifman and Y. Meyer, Remarques sur l’analyse de Fourier à fenêtre C.R. Acad. Sci. Paris Sér. I Math. (1991), Vol 1, No. 312, 259–261.

    MathSciNet  Google Scholar 

  2. H.S. Malvar, Lapped transforms for efficient transform/subband coding, IEEE Trans. Acoust. Speech Signal Processing, (1990), vol 38, 969–978

    Article  Google Scholar 

  3. F. Meyer and A. Averbuch and R. Coifman, Multilayered image representation: Application to image compression, IEEE Transactions on Image Processing, (2002), vol 11, 1072–1080

    Article  MathSciNet  Google Scholar 

  4. D.L. Donoho and M. Duncan, Digital curvelet transform: Strategy, implementation, and expe riments, Proceedings of Aerosense, Wavelet Applications VII, SPIE, (2000), pp4056

    Google Scholar 

  5. S. Mallat, A Theory for Multiresolution Signal Decomposition: The Wavelet Representation, IEEE Trans. on Patter n Analysis and Machine Intelligence, July, 1989, vol 11, 674–693

    Article  MATH  Google Scholar 

  6. A.P. Dempster and N.M. Laird and D.B. Rubin, Maximum-Likelihood from incomplete data via the EM algorithm, Journal of Royal Statistic Society Ser. B, (1977), vol 39

    Google Scholar 

  7. L. Ying and L. Demanet and E.J. Candés, 3D Discrete Curvelet Transforms, Proceedings SPIE Wavelet XI, Jul–Aug,2005, vol 5914

    Google Scholar 

  8. E. Candés and L. Demanet and D. Donoho and L. Ying, Fast Discrete Curvelet Transforms, California Institute of Technology, July 2005

    Google Scholar 

  9. M. Choi and R.Y. Kim and M.G. Kim, The Curvelet Transform for Image Fusion, Proceedings ISPRS Congress, Istanbul, July 2004, 59–64

    Google Scholar 

  10. R. Eslami and H. Radha, On Low Bit-Rate Coding using the Contourlet TransforOn Low Bit-Rate Coding using the Contourlet Transform, Proceedings Asilomar Conference on Signals Systems and Computers, Pacific Grove, CA, Nov 2003, 1524–1528

    Google Scholar 

  11. J.M Feng and T. Hsu and J.L. Kuo, Texture analysis based on affine transform coding, Proceedings IEEE ICIP, 1999, vol 1, 153–157

    Google Scholar 

  12. A.D. Calway, Image Representation Based on the Affine Symmetry Group, Proceedings IEEE ICIP, 1996, 189–192xs

    Google Scholar 

  13. A. Bhalerao and R. Wilson, Affine Invariant Image Segmentation, Proceedings British Machine Vision Conference, 2004

    Google Scholar 

  14. I.K. Levy and R. Wilson, Three-Dimensional Wavelet Transform Video Coding Using Symmetric Codebook Vector Quantization, IEEE Transactions on Image Processing, March 2001, vol 10, no 3, 470–475

    Article  MATH  MathSciNet  Google Scholar 

  15. N. Rajpoot and Z. Yao and R. Wilson, Adaptive Wavelet Restoration of Noisy Video Sequences, Proceedings IEEE ICIP 2004, Singapore, 2004, to appear

    Google Scholar 

  16. Z. Yao and N. Rajpoot, Radon/Ridgelet signature for image authentication, Proceedings IEEE ICIP 2004, Singapore, 2004, to appear

    Google Scholar 

  17. T.I. Hsu and R.G. Wilson, A Two-Component Model Of Texture For Analysis And Synthesis, IEEE Transactions on Image Processing, 1998, vol 7, 1466–1476

    Article  Google Scholar 

  18. N. Rajpoot and R. Wilson and Z Yao, Planelets: A New Analysis Tool for Planar Feature Extraction, Proceedings 5th International Workshop on Image Analysis for Multimedia Interactive Services (WIAMIS’2004), Lisbon,n Portugal,n April 2004

    Google Scholar 

  19. D.H. Hubel and T.N. Wiesel, Receptive fields,n binocular interaction and functional architecture in the cat’s visual cortex, Journal of Physiology, 1962, vol 160, 106–154

    Google Scholar 

  20. I. Daubechies, Ten lectures on wavelets, SIAM, 1992, Philadelphia

    Google Scholar 

  21. A. E. Jacquin, Fractal Image Coding: A Review, Proceedings of the IEEE, Oct 1993, vol 81, no 10,n 1451–1465

    Article  Google Scholar 

  22. F. Lefebvre and J. Czyz and B. Macq, A Robust Soft Hash Algorithm for Digital Image Signature, Proc. of ICIP, Barcelona, Sep 2003,n vol II, 495–498

    Google Scholar 

  23. C.Y. Lin and S.F. Chang, A Robust Image Authentication Method Distinguishing JPEG Compression from Malicious Manipulation, IEEE Trans. on Curcuits and Systems for Video Technology, Feb 2001, vol 11,n no 2, 153–168

    Article  MathSciNet  Google Scholar 

  24. C.S. Lu and H.Y.M. Liao,n Structural Digital Signature for Image Authentication: An Incidental Distortion Resistant Scheme, IEEE Trans. on Multimedia, 2003, vol 5, no 2, 161–173

    Article  MathSciNet  Google Scholar 

  25. C. E. Shannon, Communication theory of secrecy systems, Bell Syst. Tech. J., Oct 1949, vol 28,n 656–715

    MathSciNet  Google Scholar 

  26. M. Schneider and S.F. Chang,n A Robust Content Based Digital Signature for Image Authentication, Proc. of ICIP, 1996, vol 3, 227–230

    Google Scholar 

  27. G.L. Friedman, The Trustworthy Digital Camera: Restoring Credibility to the P hotographic Image, IEEE Trans. on Consumer Electronics, Nov 1993, vol 39, no 4, 905–910

    Article  Google Scholar 

  28. N. Holliman and N. Memon, Counterfeiting Attacks on Oblivious Block-wise Independent Invisible Watermarking Schemes, IEEE Trans. on Image Processing, Mar 2000, vol 9, no 3, 432–441

    Article  Google Scholar 

  29. J. Fridrich and M. Goljan and R. Du, Lossless data embedding-new paradigm in digital watermarking, EURASIP Journ. Appl. Sig. Proc., Feb 2002, vol 2002, no 2, 185–196

    Article  MATH  Google Scholar 

  30. E.T. Lin and E.J. Delp, A Review of Fragile Image Watermarks, Proc. of ACM Multimeida & Security Workshop, Orlando, 1999, 25–29

    Google Scholar 

  31. A. Averbuch and R. Coifman and D. Donoho and M. Israeli and J. Walden, The pseudopolar FFT and its applications, University of Yale, YaleU/DCS/RR-1178, 1999

    Google Scholar 

  32. A.G. Flesia and H. Hel-Or and A. Averbuch and E.J. Candés and R.R. Coifman and D.L. Donoho, Digital Implementation of Ridgelet Packets, Beyond Wavelets, Academic Press, Sep 2003, 31–60

    Google Scholar 

  33. A. Bhalerao and R. Wilson, A Fourier Approach to 3D Local Feature Estimation from Volume Data, Proc. British Machine Vision Conference (BMVC), Sep 2001, vol 2, 461–470

    Google Scholar 

  34. A. Papoulis, Signal Analysis, McGraw-Hill, 1984

    Google Scholar 

  35. P.J. Burt and E.H. Adelson, The Laplacian pyramid as a compact image code, IEEE Transactions on Communications, 1983, vol 31, 532–540

    Article  Google Scholar 

  36. N.G. Kingsbury, Image processing with complex wavelets, Phil. Trans. Royal Society. A, 1999

    Google Scholar 

  37. A. Pizurica and V. Zlokolika and W. Philips, Combined wavelet domain and temporal video denoising, Proceedings of IEEE International Conference on Advanced Video and Signal Based Surveillance (AVSS), Jul 2003

    Google Scholar 

  38. P.R. Meulemans, Hierarchical Image Sequence Analysis and Segmentation, University of Warwick, United Kingdom, May 2001

    Google Scholar 

  39. P.R. Meulemans and R.G. Wilson, Image motion analysis using a generalised wavelet transform, Proceedings IEEE International Conference on image Processing (ICIP), Santa Barbara, US, 1997

    Google Scholar 

  40. I.W. Selesnick and K.Y. Li, Video denoising using 2D and 3D dual-tree complex wavelet transforms, Proceedings of SPIE Wavelets X, Aug 2003

    Google Scholar 

  41. D. Gabor, Theory of communication, Journal of IEE, 1946, vol 93 429–457

    Google Scholar 

  42. A. Calway, The Multiresolution Fourier Transform: A General Purpose Tool for Image Analysis, University of Warwick, 1989

    Google Scholar 

  43. A.R. Davies, Image feature analysis using the Multiresolution Fourier Transform, University of Warwick, 1993

    Google Scholar 

  44. R. Wilson and A.D. Calway and E.R.S. Pearson, A generalized wavelet transform for Fourier analysis: the multiresolution Fourier transform and its application to image and audio signal analysis, IEEE Trans. on Information Theory, 1992, vol 38, 674–690

    Article  MathSciNet  Google Scholar 

  45. R.R. Coifman and M.V. Wickerhauser, Entropy-based algorithms for best basis selection, IEEE Trans. on Information Theory, 1992, vol 38, no 2, 713–718

    Article  MATH  Google Scholar 

  46. P. Auscher and G. Weiss and M.V. Wickerhauser, Local sine and Cosine bases of Coifman and Meyer and the Construction of Smooth Wavelets, Wavelets: A Tutorial in Theory and Applications, Academic Press, San Diego, 1992, 237–256

    Google Scholar 

  47. R.R. Coifman and Y. Meyer, Orthonormal Wave Packet Bases, Dept. of Mathematics, Yale University, New Haven, 1990

    Google Scholar 

  48. G. Aharoni and A. Averbuch, R. Coifman and M. Israeli, Local cosine transform-A method for the reduction of the blocking effect in JPEG, J. Math. Imag. Vision, 1993, vol 3, 7–38

    Article  MATH  MathSciNet  Google Scholar 

  49. K. Ramchandran and M. Vetterli, Best Wavelet packet bases in a rate distortion sense, IEEE Trans. on Image Processing, Apr 1993, vol 2, no 2, 160–175

    Article  Google Scholar 

  50. F.G. Meyer and A.Z. Averbuch and J-O. Strömberg, Fast adaptive wavelet packet image compression, IEEE Trans. on Image Processing, 2000, 792–800

    Google Scholar 

  51. N.M. Rajpoot and R.G. Wilson and F.G. Meyer and R.R. Coifman, Adaptive Wavelet Packet Basis Selection for Zerotree Image Coding, IEEE Trans. on Image Processing, Dec 2003, vol 12, no 12, 1460–1472

    Article  MathSciNet  Google Scholar 

  52. F.G. Meyer, Image Compression With Adaptive Local Cosines: A Comparative Study, IEEE Trans. Image Processing, Jun 2002, vol 11, no 6, 616–629

    Article  Google Scholar 

  53. Minh N. Do and Martin Vetterli, The Finite Ridgelet Transform for Image Representation, IEEE Trans. Image Processing, Jan 2003, vol 12, no 1, 16–28

    Article  MathSciNet  Google Scholar 

  54. E.J. Candés, Ridgelets: Theory and applications, Dept. of Stats, Stanford Univ., Stanford, CA, 1998

    Google Scholar 

  55. A. Averbuch and R. Coifman and D.L. Donoho and M. Israeli, Fast Slant Stack: A notion of Radon transform for data in a Cartesian grid which is rapidly computible, algebraically exact, geometrically faithful and invertible, to appear in SIAM Scientific Computing

    Google Scholar 

  56. S.R. Deans, The Radon Transform and Some of Its Applications, Wiley, New York, 1983

    MATH  Google Scholar 

  57. R.A. Zuidwijk, Directional and Time-Scale Wavelet Analysis, SIAM Journal of Mathematical Analysis, 2000, vol 31, no 2, 416–430

    Article  MATH  MathSciNet  Google Scholar 

  58. R.A. Zuidwijk, The wavelet X-ray transform, Centre Math. Computer Sci., 1997, PNA-R9703, ISSN 1386-3711

    Google Scholar 

  59. B. Sahiner and A.E. Yagle, Iterative inversion of the Radon transform using image adaptive wavelet constraints, Proceedings of ICIP 98, 1998, vol 2, 709–713

    Google Scholar 

  60. T. Olson and J. DeStefano, Wavelet localization of the Radon transform, IEEE Transactions on Signal Processing, 1994, vol 42, no 8, 2055–2067

    Article  Google Scholar 

  61. S. Zhao and G. Welland and G. Wang, Wavelet sampling and localization schemes for the Radon transform in two dimensions, SIAM Journal of Applied MAthematics, 1997, vol 57, no 6, 1749–1762

    Article  MATH  MathSciNet  Google Scholar 

  62. D.L. Donoho, Ridge Functions and Orthonormal Ridgelets, Journal of Approximation Theory, Aug 2001, vol 111, no 2, 143–179

    Article  MATH  MathSciNet  Google Scholar 

  63. D.L. Donoho, Orthonormal Ridgelets and Linear singularities, SIAM Journal on Mathematical Analysis, 2000, vol 31, no 5, 1062–1099

    Article  MATH  MathSciNet  Google Scholar 

  64. E.J. Candés and D.L. Donoho, Curvelets-a suprisingly effective nonadaptive representation for objects with edges, Curves and Surfaces, Vanderbilt University Press, Nashville, TN, 2000, 105–120

    Google Scholar 

  65. E.J. Candés and D.L. Donoho, New tight frames of curvelets and optimal representations of objects with C 2 smooth singularities, Department of Statistics, Stanford University, 2002, submitted

    Google Scholar 

  66. M.N. Do and M. Vetterli, Contourlet, Beyond Wavelets, Academic Press, 2003

    Google Scholar 

  67. M.N. Do and M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, Submitted to IEEE Transactions Image Processing, 2003

    Google Scholar 

  68. S.R. Deans, The Radon Transform and Some of Its Applications, Krieger Publishing Company, Revised edition, 1993

    Google Scholar 

  69. G.T. Herman, Image reconstruction from projections: The Fundamental of Computerized Tomography, Academic Press, New York, 1980

    Google Scholar 

  70. G. Beylkin, Discrete Radon transform, IEEE Transactions on Acoustics and Speech Signal Processing, 1987, vol 35, 162–172

    Article  MathSciNet  Google Scholar 

  71. M.L. Brady, A fast discrete approximation algorithm for the Radon transform, SIAM Journal of Computing, 1998, vol 27, no 1, 107–119

    Article  MATH  MathSciNet  Google Scholar 

  72. A. Brandt and J. Mann and M. Brodski and M. Galun, A fast and accurate Multilevel inversion of the Radon transform, SIAM journal of Applied Mathematics, 2000, vol 60, no 2, 437–462

    Article  MATH  MathSciNet  Google Scholar 

  73. W.A. Götze and H.J. Druckmüller, A fast digital Radon transform-an efficient means for evaluating the Hough transform, Pattern Recognition, 1995, vol 28, no 12, 1985–1992

    Article  MathSciNet  Google Scholar 

  74. F. Matúš and J. Flusser, Image representation via a finite Radon transform, IEEE Transactions on Pattern Analysis and Machine Intelligence, Oct 1993, vol 15, no 10, 996–1006

    Article  Google Scholar 

  75. D.L. Donoho, De-noising by soft-thresholding, IEEE Transactions on Information Theory, May 1995, vol 41, 613–627

    Article  MATH  MathSciNet  Google Scholar 

  76. D.L. Donoho and I.M. Johnstone, Ideal Spatial Adaptation via Wavelet Shrinkage, Biometrika, 1994, vol 81, 425–455

    Article  MATH  MathSciNet  Google Scholar 

  77. M. Jansen, Noise Reduction by Wavelet Thresholding, Springer-Verlag, 2001

    Google Scholar 

  78. C.M. Stein, Estimation of the mean of a multivariate normal distribution, Ann. Statist., 1981, vol 9, no 6, 1135–1151

    MATH  MathSciNet  Google Scholar 

  79. D.L. Donoho and I.M. Johnstone, Adapting to unknown smoothness via wavelet shrinkage, Journal of the American Statistical Association, Dec 1995, vol 90, no 432, 1200–1224

    Article  MATH  MathSciNet  Google Scholar 

  80. S.G. Chang and B. Yu and M. Vetterli, Adaptive wavelet thresholding for image denoising and compression, IEEE Transaction on Image Processing, Sep 2000, vol 9, no 9, 1532–1546

    Article  MATH  MathSciNet  Google Scholar 

  81. R.R. Coifman and D.L. Donoho, Translation invariant denoising, Wavelets in Statistics, Springer, New York, 1995, 125–150

    Google Scholar 

  82. A.G. Bruce and H-Y. Gao and W. Stuetzle, Subset-selection and ensemble methods for wavelet de-noising, Statistica Sinica, 1999, vol 9, 167–182

    MATH  MathSciNet  Google Scholar 

  83. D.B. Percival and A.T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, Cambridge, 2000

    MATH  Google Scholar 

  84. T.P.Y. Yu and A. Stoschek and D.L. Donoho, Translation-and direction-invariant denoising of 2D and 3D images: experience and algorithms, Proceedings of the SPIE, Wavelet Applications in Signal and Image Processing IV, 1996, vol 2825, 608–619

    Google Scholar 

  85. A. Chambolle and B.J. Lucier, Interpreting translation-invariant wavelet shrinkage as a new image smoothing scale space, IEEE Transactions on Image Processing, Jul 2001, vol 10, no 7, 993–1000

    Article  MATH  MathSciNet  Google Scholar 

  86. R. Eslami and H. Radha, The contourlet transform for image de-noising using cycle spinning, Proceedings of the 37th Asilomar Conference on Signals, Systems and Computers, Nov 2003, vol 2, 1982–1986

    Google Scholar 

  87. L.R. Varshney, Despeckling Synthetic Aperture Radar Imagery using the Contourlet Transform, Applications of Signal Processing (Spring 2004), Apr 2004

    Google Scholar 

  88. J. Starck and E.J. Candés and D.L. Donoho, The curvelet transform for image denoising, IEEE Transactions on Image Processing, Jun 2002, vol 11, no 6, 670–684

    Article  MathSciNet  Google Scholar 

  89. J. Starck and D.L. Donoho and E.J., Very high quality image restoration by combining wavelets and curvelets, Proceedings of SPIE Wavelets: Applications in Signal and Image Processing IX, 2001, vol 4478, 9–19

    Google Scholar 

  90. J. Starck and M.K. Nguyen and F. Murtagh, Wavelets and curvelets for image deconvolution: a combined approach, Signal Processing, 2003, vol 83, 2279–2283

    Article  Google Scholar 

  91. P. Carre and D. Helbert and E. Andres, 3-D Fast Ridgelet Transform, Proceedings IEEE International Conference on Image Processing (ICIP), Sep 2003, vol I, 1021–1024

    Google Scholar 

  92. S. Mallat and Z. Zhang, Atomic decomposition by basis pursuit, IEEE Transactions on Signal Processing, 1993, vol 41, no 12, 3397–3415

    Article  MATH  Google Scholar 

  93. N.M. Rajpoot, Local Discriminant Wavelet Packet Basis for Texture Classification, Proceedings SPIE Wavelets X, San Diego, California, Aug 2003

    Google Scholar 

  94. Z. Yao and R. Wilson, Hybrid 3D Fractal Coding with Neighbourhood Vector Quantisation, EURASIP Journal on Applied Signal Processing, Special Issue on Nonlinear Signal and Image Processing, Part II, Nov 2004, vol 2004, no 16, 2571–2579

    MATH  Google Scholar 

  95. Z. Yao and N. Rajpoot, Image Denoising Using Multiscale Directional Cosine Bases, Proceedings IEEE ICIP 2005, Genova, Italy, Sep 2005

    Google Scholar 

  96. S. Carlsson, Sketch based coding of gray level images, IEEE Transactions on Image Processing, Jan 1988, vol 15, no 1, 57–83

    Google Scholar 

  97. J. Elder, Are edges imcomplete?, International Journal Computer Vision, 1999, vol 34, no 2/3, 97–122

    Article  Google Scholar 

  98. X. Xue and X. Wu, Image compression based on multi-scale edge compensation, Proceedings IEEE ICIP, 1999, vol 3, 560–564

    Google Scholar 

  99. S. Mallat and S.S. Zhong, Wavelet transform maxima and multiscale e dges, Wavelets and their applications, Jones and Bartlett, 1992

    Google Scholar 

  100. A. Cohen and B. Matei, Nonlinear subdivisions schemes: Applications to image processing, Tutorial on Multiresolution in Geometric Modelling, Springer, New York, 2002

    Google Scholar 

  101. E. Le Pennec and S. Mallat, Image compression with geometrical wavelets, presented at IEEE ICIP, Vancouver, BC, Canada, Sep 2000

    Google Scholar 

  102. M. Dragotti and M. Vetterli, Wavelet footprints: Theory, algorithm and applications, IEEE Transactions on Signal Processing, May 2003, vol 51, no 5, 1306–1323

    Article  MathSciNet  Google Scholar 

  103. D. Donoho, Wedgelets: Nearly-minimax estimation of edges, Ann. Stat., 1999, vol 27, 353–382

    Article  MathSciNet  Google Scholar 

  104. R. Shukla and P.L. Dragotti and M.N. Do and M. Vetterli, Rate-distortion optimized tree structured compression algorithms, IEEE Transactions on Image Processing, to be published

    Google Scholar 

  105. M. Wakin and J. Romberg and H. Choi and R. Baraniuk, Rate-distortion optimized image compression using wedgelets, Proceedings IEEE ICIP, 2002, vol 3, 237–240

    Google Scholar 

  106. E. Le Pennec and S. Mallat, Sparse Geometric Image Representations with Bandelets, IEEE Transactions on Image Processing, Apr 2005, vol 14, no 4, 423–438

    Article  MathSciNet  Google Scholar 

  107. D. Wang and L. Zhang and A. Vincent and F. Speranza, Curved Wavelet Transform for Image Coding, Technical Report, Moving Picture Experts Group, Nov 2004

    Google Scholar 

  108. P. Campisi and D. Kundur and A. Neri, Robust Digital Watermarking in the ridgelet domain, IEEE Signal Processing Letters, Oct 2004, vol 11, no 10, 826–830

    Article  Google Scholar 

  109. H. Le Borgne and N. O’Connor, Ridgelet-based signatures for natural image classification, Proceedings 2nd Conference on Information Retrieval and Its Applications, Grenoble, France, 2005

    Google Scholar 

  110. A.L. Cunha and J. Zhou and M.N. Do, The Nonsubsampled Contourlet Transform: Theory, Design and Applications, IEEE Transactions on Image Processing, 2005, submitted

    Google Scholar 

  111. Y. Lu and M.N. Do, CRISP-contourlet: a critically sampled directional multiresolution image representation, Proceedings SPIE conference on Wavelet Applications in Signal and Image Processing, San Diego, Aug 2003

    Google Scholar 

  112. R. Eslami and H. Radha, Wavelet-based Contourlet Packet Image Coding, Proceedings Conference on Information Science and Systems, The Johns Hopkins University, Mar 2005

    Google Scholar 

  113. R. Eslami and H. Radha, Wavelet-based Contourlet Transform and Its Application to Image Coding, Proceedings IEEE ICIP, Singapore, Oct 2004

    Google Scholar 

  114. D.D. Po and M.N. Do, Directional Multiscale Modeling of Images using the Contourlet Transform, IEEE Transactions on Image Processing, 2003

    Google Scholar 

  115. F.G. Meyer and R.R. Coifman, Brushlets: Steerable Wavelet Packets, Beyond Wavelets, Academic Press Inc., 2001, 1–25

    Google Scholar 

  116. F.G. Meyer and R.R. Coifman, Brushlets: a tool for directional image analysis and image compression, Applied and Computational Harmonic Analysis, 1997, 147–187

    Google Scholar 

  117. Y. Meyer, Wavelets and operators, Cambridge University Press, 1993

    Google Scholar 

  118. H. F. Smith, A Parametrix Construction for Wave Equantions with C 1,1 Coefficients, Ann. Inst. Fourier, Grenoble, 1998, vol 48, no 3, 797–835

    MATH  MathSciNet  Google Scholar 

  119. T. Binford, Inferring surfaces from images, Artificial Intelligence, 1981, vol 17, 205–244

    Article  Google Scholar 

  120. B. Horn, The Binford-Horn linefinder, MIT AI Lab, Memo 284, 1971

    Google Scholar 

  121. G.H. Granlund, In search of a general picture processing operator, Computer Graphics and Image Processing, 1978, vol 8, 155–173

    Google Scholar 

  122. G. Peyré and S. Mallat, Discrete Bandelets with Geometric Orthogonal Filters, Proceedings IEEE ICIP, Genova, Italy, 2005, submitted

    Google Scholar 

  123. A.D. Calway and R. Wilson, Curve extraction in Images Using a multiresolution framework, CVGIP: Image Understanding, May 1994, vol 59, no 3, 349–366

    Article  Google Scholar 

  124. C.T. Li, Multiresolution Image Segmentation Integrating Gibbs Sampler and Region Merging Algorithm, Signal Processing, 2003, vol 83, no 1, 609–620

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Warwick, CV4 7AL, UK

    Zhen Yao, Nasir Rajpoot & Roland Wilson

Authors
  1. Zhen Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nasir Rajpoot
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roland Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Science and Technology, University of Macau, P.O. Box 3001, Macau

    Tao Qian  & Mang I Vai  & 

  2. Department of Mathematics, Syracuse University, 215 Carnegie Hall, Syracuse, NY, 13244-1150, USA

    Yuesheng Xu

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Yao, Z., Rajpoot, N., Wilson, R. (2006). Directional Wavelet Analysis with Fourier-Type Bases for Image Processing. In: Qian, T., Vai, M.I., Xu, Y. (eds) Wavelet Analysis and Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7778-6_13

Download citation

Publish with us

Policies and ethics

Search

Navigation