Nonlinear multiresolution signal decomposition schemes - Part II: morphological wavelets

IEEE Transactions on Image Processing

Volumn 9, Issue 11, 2000, Pages 1897-1913

  Heijmans, Henk J A M ^a,b   Goutsias, John ^a,c  

^a IEEE

^b CWI   (Netherlands)

^c Johns Hopkins University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE CODING; IMAGE ENHANCEMENT; IMAGE QUALITY; MATHEMATICAL MORPHOLOGY; MATHEMATICAL OPERATORS; WAVELET TRANSFORMS;

MULTIRESOLUTION SIGNAL DECOMPOSITION; NONLINEAR WAVELET TRANSFORMS; WAVELET DECOMPOSITION;

IMAGE RECONSTRUCTION;

EID: 0034316249     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.877211     Document Type: Article

References (46)

1. J. Goutsias and H. J. A. M. Heijmans, "Nonlinear multiresolution signal decomposition schemes - Part I: Morphological pyramids," IEEE Trans. Image Processing, vol. 9, pp. 1862-1876, Nov. 2000.
2. P. J. Burt and E. H. Adelson, "The Laplacian pyramid as a compact image code," IEEE Trans. Commun., vol. 31, pp. 532-540, 1983.
3. P. Maragos, "Morphological skeleton representation and coding of binary images," IEEE Trans. Acoust., Speech, Signal Processing, vol. 34, pp. 1228-1244, 1986.
4. O. Egger and W. Li, "Very low bit rate image coding using morphological operators and adaptive decompositions," in Proc. IEEE Int. Conf. Image Processing, Austin, TX, 1994, pp. 326-330.
5. D. A. F. Florêncio and R. W. Schafer, "A nonexpansive pyramidal morphological image coder," in Proc. IEEE Int. Conf. Image Processing, Austin, TX, 1994, pp. 331-335.
6. O. Egger, W. Li, and M. Kunt, "High compression image coding using an adaptive morphological subband decomposition," Proc. IEEE, vol. 83, pp. 272-287, 1995.
7. D. A. F. Florêncio, "A new sampling theory and a framework for nonlinear filter banks," Ph.D. dissertation, School Elect. Eng., Georgia Inst. Technol., Atlanta, 1996.
8. F. J. Hampson and J.-C. Pesquet, "A nonlinear subband decomposition with perfect reconstruction," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, Atlanta, GA, May 7-10, 1996, pp. 1523-1526.
9. H. Cha and L. F. Chaparro, "Adaptive morphological representation of signals: Polynomial and wavelet methods," Multidimen. Syst. Signal Process., vol. 8, pp. 249-271, 1997.
10. R. Claypoole, G. Davis, W. Sweldens, and R. Baraniuk, "Nonlinear wavelet transforms for image coding," Proc. 31st Asilomar Conf. Signals, Systems, Computers, vol. 1, pp. 662-667, 1997.
11. F. J. Hampson, "Méthodes non linéaires en codage d'images et estimation de mouvement," Ph.D. dissertation, Univ. Paris XI Orsay, Paris, France, 1997.
12. R. L. Claypoole, R. G. Baraniuk, and R. D. Nowak, "Adaptive wavelet transforms via lifting," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, Seattle, WA, May 12-15, 1998.
13. _, "Lifting construction of nonlinear wavelet transforms," in Proc. IEEE-SP Int. Symp. Time-Frequency Time-Scale Analysis, Pittsburgh, PA, Oct. 6-9, 1998, pp. 49-52.
14. P. L. Combettes and J.-C. Pesquet, "Convex multiresolution analysis," IEEE Trans. Pattern Anal. Machine Intell., vol. 20, pp. 1308-1318, 1998.
15. J. Goutsias and H. J. A. M. Heijmans, "An axiomatic approach to multiresolution signal decomposition," in Proc. IEEE Int. Conf. Image Processing, Chicago, IL, Oct. 4-7, 1998.
16. _, "Multiresolution signal decomposition schemes - Part 1: Linear and morphological pyramids," CWI, Amsterdam, The Netherlands, Tech. Rep. PNA-R9810, Oct. 1998.
17. F. J. Hampson and J.-C. Pesquet, "M-band nonlinear subband decompositions with perfect reconstruction," IEEE Trans. Image Processing, vol. 7, pp. 1547-1560, Nov. 1998.
18. H. J. A. M. Heijmans and J. Goutsias, "Some thoughts on morphological pyramids and wavelets," in Signal Processing IX: Theories and Applications, S. Theodoridis, I. Pitas, A. Stouraitis, and N. Kaloupsidis, Eds. Rhodes, Greece: EUSIPCO, Sept. 8-11, 1998, pp. 133-136.
19. _, "Morphology-based perfect reconstruction filter banks," in Proc. IEEE-SP Int. Symp. Time-Frequency Time-Scale Analysis, Pittsburgh, PA, Oct. 6-9, 1998, pp. 353-356.
20. B. Pouye, A. Benazza-Benyahia, I. Pollak, J.-C. Pesquet, and H. Krim, "Nonlinear frame-like decompositions," in Signal Processing IX: Theories and Applications, S. Theodoridis, I. Pitas, A. Stouraitis, and N. Kaloupsidis, Eds. Rhodes, Greece: EUSIPCO, Sept. 8-11, 1998, pp. 1393-1396.
21. R. L. de Queiroz, D. A. F. Florêncio, and R. W. Schafer, "Nonexpansive pyramid for image coding using a nonlinear interbank," IEEE Trans. Image Processing, vol. 7, pp. 246-252, Feb. 1998.
22. R. L. Claypoole, R. G. Baraniuk, and R. D. Nowak, "Adaptive wavelet transforms via lifting," Dept. Elect. Comput. Eng., Rice Univ., Houston, TX, Tech. Rep. 9304, Apr. 1999.
23. W. Sweldens, "The lifting scheme: A new philosophy in biorthogonal wavelet constructions," in Proc. SPIE Wavelet Applications Signal Image Processing III, vol. 2569, A. F. Lain and M. Unser, Eds., 1995, pp. 68-79.
24. _, "The lifting scheme: A custom-design construction of biorthogonal wavelets," Appl. Comput. Harmon. Anal., vol. 3, pp. 186-200, 1996.
25. _, "The lifting scheme: A construction of second generation wavelets," SIAM J. Math. Anal., vol. 29, pp. 511-546, 1998.
26. F. A. M. L. Bruekers and A. W. M. van den Enden, "New networks for perfect inversion and perfect reconstruction," IEEE J. Select. Areas Commun., vol. 10, pp. 130-137, 1992.
27. H. J. A. M. Heijmans and J. Goutsias, "Constructing morphological wavelets with the lifting scheme," in Pattern Recognition Information Processing, Proc. 5th Int. Conf. Pattern Recognition Information Processing (PRIP'99), Minsk, Belarus, May 18-20, 1999, pp. 65-72.
28. S.-C. Pei and F.-C. Chen, "Subband decomposition of monochrome and color images by mathematical morphology," Opt. Eng., vol. 30, pp. 921-933, 1991.
29. _, "Hierarchical image representation by mathematical morphology subband decomposition," Pattern Recognit. Lett., vol. 16, pp. 183-192, 1995.
30. S. Mallat, A Wavelet Tour of Signal Processing. San Diego, CA: Academic, 1998.
31. H. J. A. M. Heijmans and J. Goutsias, "Multiresolution signal decomposition schemes - Part 2: Morphological wavelets," CWI, Amsterdam, The Netherlands, Tech. Rep. PNA-R9905, July 1999.
32. M. Vetterli and J. Kovačević, Wavelets and Subband Coding. Englewood Cliffs, NJ: Prentice-Hall, 1995.
33. S. Rǎnganath and H. Blume, "Hierarchical image decomposition and filtering using the S-transform," Proc. SPIE Workshop Medical Imaging II, vol. 914, pp. 799-814, 1988.
34. A. Said and W. A. Pearlman, "An image multiresolution representation for lossless and lossy compression," IEEE Trans. Image Processing, vol. 5, pp. 1303-1310, 1996.
35. J. Serra, Image Analysis and Mathematical Morphology. London, U.K.: Academic Press, 1982.
36. H. J. A. M. Heijmans, Morphological Image Operators. Boston, MA: Academic, 1994.
37. A. R. Calderbank, I. Daubechies, W. Sweldens, and B.-L. Yeo, "Wavelet transforms that map integers to integers," Appl. Comput. Harmon. Anal., vol. 5, pp. 332-369, 1998.
38. I. Daubechies and W. Sweldens, "Factoring wavelet transforms into lifting steps," J. Fourier Anal. Applicat., vol. 4, pp. 245-267, 1998.
39. D. L. Donoho, "De-noising by shoft-thresholding," IEEE Trans. Inform. Theory, vol. 41, pp. 613-627, 1995.
40. M. D. Swanson and A. H. Tewfik, "A binary wavelet decomposition of binary images," IEEE Trans. Image Processing, vol. 5, pp. 1637-1650, Dec. 1996.
41. R. Chellappa, C. L. Wilson, and S. Sirohey, "Human and machine recognition of faces: A survey," Proc. IEEE, vol. 83, pp. 705-740, 1995.
42. L. Alvarez and J. M. Morel, "Formalization and computational aspects of image analysis," Acta Numer., pp. 1-59, 1994.
43. R. W. Brockett and P. Maragos, "Evolution equations for continuous-scale morphological filtering," IEEE Trans. Signal Processing, vol. 42, pp. 3377-3386, 1994.
44. P. T. Jackway and M. Deriche, "Scale-space properties of the multiscale morphological dilation-erosion," IEEE Trans. Pattern Anal. Machine Intell., vol. 18, pp. 38-51, Jan. 1996.
45. R. van den Boomgaard and A. Smeulders, "The morphological structure of images: The differential equations of morphological scale-space," IEEE Trans. Pattern Anal. Machine Intell., vol. 16, pp. 1101-1113, 1994.
46. J. Weickert, Anisotropic Diffusion in Image Processing. Stuttgart, Germany: Teubner-Verlag, 1998.