Characterization and analysis of edges using the continuous shearlet transform

SIAM Journal on Imaging Sciences

Volumn 2, Issue 3, 2009, Pages 959-986

  Guo, Kanghui ^a   Labate, Demetrio ^b  

^a MISSOURI STATE UNIVERSITY   (United States)

^b University of Houston   (United States)

Author keywords

Analysis of singularities; Continuous wavelets; Curvelets; Directional wavelets; Edge detection; Shearlets; Wavelets

Indexed keywords

EDGE DETECTION; MATHEMATICAL TRANSFORMATIONS;

ANALYSIS OF SINGULARITIES; CONTINUOUS WAVELET; CURVELETS; DIRECTIONAL WAVELETS; SHEARLETS; WAVELETS;

CURVE FITTING;

EID: 77956985318     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/080741537     Document Type: Article

References (30)

1. F. Arandiga, A. Cohen, R. Donat, N. Dyn, and B. Matei, Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques, Appl. Comput. Harmon. Anal., 24 (2008), pp. 225-250.
2. E. Candès, L. Demanet, and L. Ying, Fast computation of Fourier integral operators, SIAM J. Sci. Comput., 29 (2007), pp. 2464-2493.
3. 2singularities, Comm. Pure Appl. Math., 56 (2004), pp. 219-266.
4. E. J. Candès and D. L. Donoho, Continuous curvelet transform. I. Resolution of the wavefront set, Appl. Comput. Harmon. Anal., 19 (2005), pp. 162-197.
5. F. J. Canny, A computational approach to edge detection, IEEE Trans. Pattern Anal. Mach. Intell., 8 (1986), pp. 679-698.
6. T. F. Chan and J. Shen, Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods, SIAM, Philadelphia, 2005.
7. M. N. Do and M. Vetterli, The contourlet transform: An efficient directional multiresolution image representation, IEEE Trans. Image Process., 14 (2005), pp. 2091-2106.
8. M. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, NJ, 1976.
9. D. L. Donoho, Wedgelets: Nearly minimax estimation of edges, Ann. Statist., 27 (1999), pp. 859-897.
10. P. L. Dragotti and M. Vetterli, Wavelet footprints: Theory, algorithms and applications, IEEE Trans. Signal Process., 51 (2003), pp. 1306-1323.
11. G. Easley, D. Labate, and W.-Q. Lim, Sparse directional image representations using the discrete shearlet transform, Appl. Comput. Harmon. Anal., 25 (2008), pp. 25-46.
12. K. Guo, G. Kutyniok, and D. Labate, Sparse multidimensional representations using anisotropic dilation and shear operators, in Wavelets and Splines, G. Chen and M. Lai, eds., Nashboro Press, Nashville, TN, 2006, pp. 189-201.
13. K. Guo and D. Labate, Optimally sparse multidimensional representation using shearlets, SIAM J. Math. Anal., 39 (2007), pp. 298-318.
14. K. Guo, W. Lim, and D. Labate, Edge analysis using the continuous shearlet transform, Appl. Comput. Harmon. Anal., 27 (2009), pp. 24-26.
15. C. S. Herz, Fourier transforms related to convex sets, Ann. of Math. (2), 75 (1962), pp. 81-92.
16. M. Holschneider, Wavelets. Analysis Tool, Oxford University Press, Oxford, UK, 1995.
17. A. P. Korostelev and A. B. Tsybakov, Minimax Theory of Image Reconstruction, Lecture Notes in Statist. 82, Springer-Verlag, New York, 1993.
18. G. Kutyniok and D. Labate, Resolution of the wavefront set using continuous shearlets, Trans Amer. Math. Soc., 361 (2009), pp. 2719-2754.
19. E. Le Pennec and S. Mallat, Sparse geometric image representations with bandelets, IEEE Trans. Image Process., 14 (2005), pp. 423-438.
20. T. Lindeberg, Edge detection and ridge detection with automatic scale selection, Int. J. Comput. Vision, 30 (1998), pp. 117-154.
21. D. G. Lowe, Distinctive image features from scale-invariant keypoints, Int. J. Comput. Vision, 60 (2004), pp. 91-110.
22. S. Mallat and W. L. Hwang, Singularity detection and processing with wavelets, IEEE Trans. Inform. Theory, 38 (1992), pp. 617-643.
23. S. Mallat and S. Zhong, Characterization of signals from multiscale edges, IEEE Trans. Pattern Anal. Mach. Intell., 14 (1992), pp. 710-732.
24. Y. Meyer, Wavelets and Operators, Cambridge Stud. Adv. Math. 37, Cambridge University Press, Cambridge, UK, 1992.
25. P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell., 12 (1990), pp. 629-639.
26. E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993.
27. M. B. Wakin, J. K. Romberg, H. Choi, and R. G. Baraniuk, Wavelet-domain approximation and compression of piecewise smooth images, IEEE Trans. Image Process., 15 (2006), pp. 1071-1087.
28. S. Yi, D. Labate, G. R. Easley, and H. Krim, A shearlet approach to edge analysis and detection, IEEE Trans. Image Process., 18 (2009), pp. 929-941.
29. D. Ziou and S. Tabbone, Edge detection techniques-an overview, Int. J. Pattern Recognition Image Anal., 8 (1998), pp. 537-559.
30. B. Zitova and J. Flusser, Image registration methods: A survey, Image Vision Comput., 21 (2003), pp. 977-1000.