Shiftable Multiscale Transforms

IEEE Transactions on Information Theory

Volumn 38, Issue 2, 1992, Pages 587-607

  Simoncelli, Eero P ^a   Freeman, William T ^a   Adelson, Edward H ^a   Heeger, David J ^b,c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b NASA AMES RESEARCH CENTER   (United States)

^c STANFORD UNIVERSITY   (United States)

Author keywords

aliasing; image processing; image representation; interpolation; multiscale; orientation; pyramid; sampling; steerable filters; Wavelet

Indexed keywords

IMAGE PROCESSING - ENHANCEMENT; MATHEMATICAL TECHNIQUES - INTERPOLATION; SIGNAL FILTERING AND PREDICTION; SIGNAL PROCESSING - SAMPLING;

FRACTALS; IMAGE REPRESENTATION; ORIENTATION; ORTHOGONAL WAVELET TRANSFORMS; SHIFTABLE MULTISCALE TRANSFORMS; STEERABLE FILTERS;

MATHEMATICAL TRANSFORMATIONS;

EID: 0026735337     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.119725     Document Type: Article

References (50)

1. E. H. Adelson, C. H. Anderson, J. R. Bergen, P. J. Burt, and J. M. Ogden, “Pyramid methods in image processing,” RCA Engineer, vol. 29, no. 6, pp. 33–41, Nov./Dec. 1984.
2. E. H. Adelson and E. P. Simoncelli, “Truncated subband coding of images,” U.S. Patent #4,917,812, 1989.
3. E. H. Adelson, E. P. Simoncelli, and R. Hingorani, “Orthogonal pyramid transforms for image coding,” in Proc. SPIE, Cambridge, MA, Oct. 1987, vol. 845, pp. 50–58.
4. R. N. Bracewell, The Fourier Transform and Its Applications. New York: McGraw-Hill, 1978.
5. P. J. Burt and E. H. Adelson, “The Laplacian pyramid as a compact image code.” IEEE Trans. Commun. vol. COM-31, pp. 532–540, Apr. 1983.
6. C. R. Carlson, E. H. Adelson, and C. H. Anderson, “System for coring an image-representing signal,” U.S. Patent #4,523,230, 1985.
7. A. Croisier, D. Esteban, and C. Galand, “Perfect channel splitting by use of interpolation/decimation/tree decomposition techniques,” in Int. Conf. Inform. Sci. Syst., Patras, Greece, Aug. 1976, pp. 443–446.
8. I. Daubechies, “Frames of coherent states—Phase space localization and signal analysis,” unpublished manuscript.
9. I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Commun. Pure Appl. Math., vol. 41, pp. 909–996, 1988.
10. I. Daubechies, “The wavelet transform time-frequency localization and signal analysis,” IEEE Trans. Inform. Theory, vol. 36, pp. 961–1005, Sept. 1990.
11. J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. A, vol. 2, no. 7, pp. 1160–1169, July 1985.
12. J. G. Daugman, “Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression,” IEEE Trans. Acoust. Speech Signal Processing, vol. 36, pp. 1169–1179, 1988.
13. D. Esteban and C. Galand, “Application of quadrature mirror filters to split band voice coding schemes,” in Proc. ICASSP, 1977, pp. 191–195.
14. W. T. Freeman and E. H. Adelson, “Steerable filters,” in Topical Meeting on Image Understanding and Machine Vision, vol. 14. Optical Society of America, June 1989. Technical Digest Series.
15. W. T. Freeman and E. H. Adelson, “The design and use of steerable filters.” IEEE Pattern Anal. Machine Intell., vol. 13, pp. 891–906, 1991.
16. D. Gabor, “Theory of communication,” J. IEE, vol. 93, pp. 492–457, 1946.
17. H. Gharavi and A. Tabatabai, “Sub-band coding of digital images using two-dimensional quadrature mirror filtering,” Proc of SPIE, vol. 707, pp. 51–61, 1986.
18. R. A. Gopinath and C. S. Burrus, “Efficient computation of the wavelet transforms,” in ICASSP, 1990, pp. 1599–1601.
19. G. H. Granlund, “In search of a general picture processing operator,” Comput. Graphics Image Processing, vol. 8, pp. 155–173, 1978.
20. A. Grossmann and J. Morlet, “Decomposition of Hardy functions into square integrable wavelets of constant shape,” SIAM J. Math., vol. 15, pp. 723–736, 1984.
21. B. Julesz, “Experiments in the visual perception of texture.” Scientific Amer. vol. 232, no. 4, pp. 34–43, 1975.
22. H. Knutsson and G. H. Granlund, “Texture analysis using two-dimensional quadrature filters,” in IEEE Comput. Soc. Workshop Comput. Architecture Pattern Anal. Image Database Management 1983, pp. 206–213.
23. H. Knutsson, R. Wilson, and G. H. Granlund, “Anisotropic nonstationary image estimation and its applications: Part 1-Restoration of noisy images,” IEEE Trans. Commun., vol. 31, pp. 388–397, Mar. 1983.
24. J. J. Koenderink, “The structure of images.” Biol. Cybern., vol. 50, pp. 363–370, 1984.
25. R. M. Lerner, Lectures on Communication System Theory. New York: McGraw-Hill, 1961, ch. 10.
26. J. Lim, Two-Dimensional Signal and Image Processing. Englewood Cliffs, NJ: Prentice Hall, 1990.
27. B. D. Lucas and T. Kanade, “An iterative image registration technique with an application to stereo vision,” in Proc. Seventh IJCAI, Vancouver, BC, Canada, 1981, pp. 674–679.
28. S. G. Mallat, “Multifrequency channel decomposition of images and wavelet models,” IEEE Trans. Acoust. Speech Signal Processing, vol. 37, pp. 2091–2110, Dec. 1989.
29. S. G. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Pattern Anal. Machine Intell., vol. 11, pp. 674–693, July 1989.
30. S. G. Mallat, “Zero-crossing of a wavelet transform,” IEEE Trans. Inform. Theory, vol. 37, pp. 1019–1033, July, 1991.
31. D. Marr, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. San Franscisco, CA: W. H. Freeman and Company, 1982.
32. J. B. Martens, “The Hermite transform-theory,” IEEE Trans. Acoust. Speech Signal Processing, vol. 38, pp. 1595–1606, Sept. 1990.
33. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1975.
34. A. P. Pentland, “Fractal based description of natural scenes.” IEEE Pattern Anal. Machine Intell., vol. 6, pp. 661–674, June 1984.
35. P. Perona, “Deformable kernels for early vision,”in IEEE Comput. Soc. Conf. Comput. Vision and Pattern Recogn., Maui, 1991, pp. 222–227.
36. P. Perona and J. Malik, “Detecting and localizing edges composed of steps, peaks and roofs,” in Proc. 3rd Int. Conf. Comput. Vision, Osaka, Japan, 1990.
37. P. G. Powell and B. E. Bayer, “A method for the digital enhancement of unsharp, grainy photographic images.” in IEEE Int. Conf. Electron. Image Processing, no. 214, 1982, p. 179.
38. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C. New York: Cambridge Univ. Press, 1988.
39. E. P. Simoncelli, “Orthogonal sub-band image transforms,” Master’s thesis, Massachusetts Inst. of Technol., Dept. of Elect. Eng. and Comput. Sci., Cambridge, MA, May 1988.
40. E. P. Simoncelli and E. H. Adelson, “Non-separable extensions of quadrature mirror filters to multiple dimensions,” in Proc. IEEE. Special Issue on Multidimensional Signal Processing, April 1990.
41. E. P. Simoncelli and E. H. Adelson, “Subband transforms,” in Subband Image Coding, John W. Woods, Ed., Norwell, MA: Kluwer, 1990, ch. 4.
42. G. T. Strang, “Wavelets and dilation equations: A brief introduction.” SIAM Rev., vol. 31, no. 4, pp. 614–627, Dec. 1989.
43. A. Tran, K. Liu, K. Tzou, and E. Vogel, “An efficient pyramid image coding system,” Proc. ICASSP, vol. 2, 1987, p. 18.6.1-18.6.4.
44. P. P. Vaidyanathan, “On power-complementary FIR filters,” IEEE Trans. Circuits Syst., vol. CAS-32, pp. 1308–1310, Dec. 1985.
45. M. Vetterli, “Multidimensional subband coding: some theory and algorithms.” Signal Processing, vol. 6, no. 2, pp. 97–112, 1984.
46. M. Vetterli, “A theory of multirate filter banks,” IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-35, pp. 356–372, Mar. 1987.
47. A. B. Watson, “The cortex transform: rapid computation of simulated neural images,” Comput. Vision Graphics Image Processing, vol. 39, pp. 311–327, 1987.
48. A. P. Witkin, “Scale-space filtering,” in Proc. Int. Joint Conf. Artificial Intell., 1985, 1019–1021.
49. J. W. Woods, Ed., Subband Image Coding. Norwell, MA: Kluwer, 1990.
50. J. W. Woods and S. D. O’Neil, “Subband coding of images,” IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-34, pp. 1278–1288, Oct. 1986.