A shearlet approach to edge analysis and detection

IEEE Transactions on Image Processing

Volumn 18, Issue 5, 2009, Pages 929-941

  Yi, Sheng ^a   Labate, Demetrio ^a   Easley, Glenn R ^b   Krim, Hamid ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b System Planning Corporation   (United States)

Author keywords

Curvelets; Edge detection; Feature extraction; Shearlets; Singularities; Wavelets

Indexed keywords

CURVELETS; DIRECTIONAL TRANSFORMS; EDGE ANALYSIS; EFFECTIVE ALGORITHMS; GEOMETRICAL FEATURES; MULTI-SCALE; MULTI-SCALE EDGES; NUMERICAL EXAMPLES; SHEARLETS; SINGULARITIES; STANDARD METHODS; WAVELETS;

FEATURE EXTRACTION; IMAGE ENHANCEMENT; NUMERICAL METHODS; WAVELET TRANSFORMS;

EDGE DETECTION;

EID: 67349117263     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2009.2013082     Document Type: Article

References (36)

1. S. Mallat and W. L. Hwang, "Singularity detection and processing with wavelets," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 617-643, Mar. 1992.
2. S. Mallat and S. Zhong, "Characterization of signals from multiscale edges," IEEE Trans. Pattern Anal. Mach. Intell., vol. 14, no. 7, pp. 710-732, Jul. 1992.
3. C. L. Tu, W. L. Hwang, and J. Ho, "Analysis of singularities from modulus complex wavelets," IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 1049-1062, Mar. 2005.
4. L. Zhang and P. Bao, "A wavelet-based edge detection method by scale multiplication," in Proc. Int. Conf. Pattern Recognition,, Aug. 2002, vol. 3, pp. 501-504.
5. J. Li, "A Wavelet Approach to Edge Detection," M.S. thesis, Sam Houston State Univ., Houston, TX, 2003.
6. M. N. Do and M. Vetterli, "The contourlet transform: An efficient directional multiresolution image representation," IEEE Trans. Image Process., vol. 14, no. 12, pp. 2091-2106, Dec. 2005.
7. D. D. Po and M. N. Do, "Directional multiscale modeling of images using the contourlet transform," IEEE Trans. Image Process., vol. 15, no. 6, pp. 1610-1620, Jun. 2006.
8. I. W. Selesnick, R. G. Baraniuk, and N. G. Kingsbury, "The dual-tree complex wavelet transform," IEEE Signal Process. Mag., vol. 22, no. 6, pp. 123-151, Nov. 2005.
9. E. J. Candès and D. L. Donoho, "Ridgelets: A key to higher-dimensional intermittency?," Phil. Trans. Roy. Soc. London A vol. 357, pp. 2495-2509, 1999.
10. 2 singularities," Commun. Pure Appl. Math., vol. 56, pp. 219-266, 2004.
11. F. J. Canny, "A computational approach to edge detection," IEEE Trans. Pattern Anal. Mach. Intell., vol. 8, no. 6, pp. 679-698, 1986.
12. T. Lindeberg, "Edge detection and ridge detection with automatic scale selection," in Proc. IEEE Int. Conf. Computer Vision and Pattern Recognition, San Francisco, CA, Jun. 1996, pp. 465-470.
13. T. Lindeberg, "Feature detection with automatic scale selection," Int. J. Comput. Vis., vol. 30, no. 2, pp. 79-116, 1998.
14. S. Mallat, A Wavelet Tour of Signal Processing. San Diego, CA: Academic, 1998.
15. D. Ziou and S. Tabbone, "Edge detection techniques an overview," Int. J. Pattern Recognit. Image Anal., vol. 8, no. 4, pp. 537-559, 1998.
16. P. Perona, "Steerable-scalable kernels for edge detection and junction analysis," Image Vis. Comput., vol. 10, pp. 663-672, 1992.
17. J. Weickert, "Foundations and applications of nonlinear anisotropic diffusion filtering," Zeitschr. Angewandte Math. Mechan., vol. 76, pp. 283-286, 1996.
18. J. Geusebroek, A. W. M. Smeulders, and J. van de Weijer, "Fast anisotropic gauss filtering," IEEE Trans. Image Process., vol. 8, pp. 938-943, 2003.
19. G. Easley, D. Labate, and W.-Q. Lim, "Sparse directional image representations using the discrete shearlet transform," Appl. Comput. Harmon. Anal., vol. 25, pp. 25-46, 2008.
20. D. Labate, W.-Q. Lim, G. Kutyniok, and G. Weiss, "Sparse multidimensional representation using shearlets," in Proc. SPIE Wavelets XI, San Diego, CA, 2005, vol. 5914, pp. 254-262.
21. K. Guo and D. Labate, "Optimally sparse multidimensional representation using shearlets," SIAM J. Math. Anal., vol. 9, pp. 298-318, 2007.
22. E. J. Candès and D. L. Donoho, "Continuous curvelet transform: I. Resolution of the wavefront set," Appl. Comput. Harmon. Anal., vol. 19, pp. 162-197, 2005.
23. S. Dekel and A. Sherman, Curvelets: A Low-Level System for Computer Vision, preprint 2008.
24. W. Freeman and E. Adelson, "The design and use of steerable filters," IEEE Trans. Pattern Anal. Mach. Intell., vol. 13, pp. 891-906, 1991.
25. E. Simoncelli and W. Freeman, "The steerable pyramid: A flexible architecture for multi-scale derivative computation," presented at the IEEE Int. Conf. Image Processing, Washington, DC, 1995.
26. M. Holschneider, Wavelets. Analysis Tool. Oxford, U.K.: Oxford Univ. Press, 1995.
27. G. Kutyniok and D. Labate, "Resolution of the wavefront set using continuous shearlets," Trans. Amer. Math. Soc., vol. 361, pp. 2719-2754, 2009, in press.
28. K. Guo, D. Labate, and W. Lim, "Edge analysis and identification using the continuous shearlet transform," Appl. Comput. Harmon. Anal..
29. J. P. Antoine, R. Murenzi, P. Vandergheynst, and S. T. Ali, Two-Dimensional Wavelets and their Relatives. Cambridge, U.K.: Cambridge Univ. Press, 2004.
30. P. Perona, "Orientation diffusion," IEEE Trans. Image Process., vol. 7, no. 3, pp. 457-467, Mar. 1998.
31. R. Mester, "Orientation estimation: Conventional techniques and a new non-differential approach," presented at the 10th Eur. Signal Processing Conf, 2000.
32. J. Bigun, G. H. Granlund, and J. Wiklund, "Multidimensional orientation estimation with applications to texture analysis and optical flow," IEEE Trans. Pattern Anal. Mach. Intell., vol. 13, no. 8, pp. 775-790, Aug. 1991.
33. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification. New York: Wiley-Interscience, 2000.
34. E. Davies, Machine Vision: Theory, Algorithms and Practicalities. New York: Academic, 1990.
35. W. K. Pratt, Digital Image Processing. New York: Wiley-Interscience, 1978.
36. T. Aydin, Y. Yemes, E. Anarim, and B. Sankur, "Multidirectional and multiscale edge detection via M-band wavelet transform," IEEE Trans. Image Process., vol. 5, pp. 1370-1377, 1996.