Steerable wavelet frames based on the Riesz transform

IEEE Transactions on Image Processing

Volumn 19, Issue 3, 2010, Pages 653-667

  Held, Stefan ^a   Storath, Martin ^a   Massopust, Peter ^b   Forster, Brigitte ^a,b  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b INSTITUTE OF EPIDEMIOLOGY   (Germany)

Author keywords

Analytical signal; Clifford algebra; Contrast enhancement; Descreening; Hilbert transform; Monogenic signal; Phase; Phase direction; Riesz transform; Steerable filters; Wavelet

Indexed keywords

ANALYTICAL SIGNALS; CLIFFORD ALGEBRA; CONTRAST ENHANCEMENT; HILBERT TRANSFORM; MONOGENIC SIGNAL; RIESZ TRANSFORM; STEERABLE FILTERS;

ALGEBRA; IMAGE ANALYSIS; MATHEMATICAL TRANSFORMATIONS; WAVELET ANALYSIS;

WAVELET DECOMPOSITION;

EID: 77249104069     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2009.2036713     Document Type: Article

References (29)

1. E. M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton, NJ: Princeton Univ. Press, 1970.
2. S. Mallat, A Wavelet Tour of Signal Processing. New York: Academic, 1998.
3. I. W. Selesnick, R. G. Baraniuk, and N. G. Kingsbury, "The dual-tree complex wavelet transform," IEEE Signal Process. Mag., Nov. 2005.
4. T. Bülow, "Hypercomplex Spectral Signal Representations for Image Processing and Analysis," Ph.D. dissertation, University of Kiel, Kiel, Germany, 1999.
5. W. L. Chan, H. Choi, and R. G. Baraniuk, "Coherent multiscale image processing using dual-tree quaternion wavelets," IEEE Trans. Image Process., vol.17, no.7, pp. 1069-1082, Jul. 2008.
6. W. L. Chan, H. Choi, and R. Baraniuk, "Directional hypercomplex wavelets for multidimensional signal analysis and processing," presented at the IEEE Int. Conf. Acoustics, Speech, and Signal Processing, 2004.
7. A. Calderón and A. Zygmund, "On the existence of certain singular integrals," Acta Math., 1952.
8. M. Nabighian, "Toward a three-dimensional automatic interpretation of potential field data via generalized hilbert transforms: Fundamental relations," Geophysics, vol. 49, no. 6, pp. 780-786, 1984.
9. K. Larkin, D. Bone, and M. Oldfield, "Natural demodulation of twodimensional fringe patterns: I," J. Opt. Soc. Amer. A, vol. 18, no. 8, pp. 1862-1870, 2001.
10. B. Forster, T. Blu, D. Van De Ville, and M. Unser, "Shift-invariant spaces from rotation-covariant functions," Appl. Comput. Harmon. Anal., vol.25, no.2, pp. 240-265, 2008.
11. D. Van De Ville and M. Unser, "Complex wavelet bases, steerability, and the marr-like pyramid," IEEE Trans. Image Process., vol.17, no.11, Nov. 2008.
12. M. Felsberg, "Low-Level Image Processing With the Structure Multivector," Ph.D. dissertation, Christian-Albrechts-Univ. Kiel, Kiel, Germany, 2002.
13. S. Olhede and G. Metikas, "Multiple multidimensional morse wavelets," IEEE Trans. Image Process., vol.55, no.3, Mar. 2007.
14. M. Unser, K. Balać, and D. Van De Ville, "The monogenic Riesz- Laplacewavelet transform," presented at the 16th European Signal Processing Conf., Lausanne, VD, Switzerland, Aug. 25-29, 2008.
15. M. Unser, D. Sage, and D. Van de Ville, "Multiresolution monogenic signal analysis using the Riesz-Laplace wavelet transform," IEEE Trans. Image Proces., to be published.
16. d), submitted preprint.
17. W. T. Freeman and E. H. Adelson, "The design and use of steerable filters," IEEE Trans. Pattern Anal. Mach. Intell., vol.13, no.9, Sep. 1991.
18. E. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, "Shiftable multiscale transforms," IEEE Trans. Inf. Theory, vol.38, no.2, Mar. 1992.
19. E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces. Princteon, NJ: Princeton Univ. Press, 1971.
20. F. Brackx, R. Delanghe, and F. Sommen, Clifford Analysis. London, U.K.: Pitman Books, Ltd., 1982.
21. K. Gürlebeck, W. Sprössig, and K. Habetha, Holomorphic Functions in the Plane and n-Dimensional Space. Berlin, Germany: Birkhäuser, 2007.
22. O. Christensen, An Introduction to Frames and Riesz Bases, ser. ANHA. Berlin, Germany: Birkhäuser, 2003.
23. A. Aldroubi, C. Cabrelli, and U. Molter, Wavelets on Irregular Grids With Arbitrary Dilation Matrices, and Frame Atoms for - [Online]. Available: http://arxiv.org/abs/math/0703438
24. W. Rasband, ImageJ [Online]. Available: http://rsbweb.nih.gov/ij/
25. M. Storath and S. Held, Monogenic Wavelet Toolbox [Online]. Available: http://www.mamebia.de/Software/monogenicwavelets.html
26. A. K. Jain, Fundamentals of Digital Image Processing. Upper Saddle River, NJ: Prentice-Hall, 1989.
27. A. V. Oppenheim and J. S. Lim, "The importance of phase in signals," Proc. IEEE, vol.69, no.5, May 1981.
28. M. Felsberg, "Optical flow estimation from monogenic phase," Complex Motion, vol.3417/2007, 2007.
29. E. Adelson, Checkershadow Illusion Massachusetts Inst. Technol., Cambridge,MA[Online]. Available: http://web.mit.edu/persci/people/ adelson/checkershadow-illusion.html