A review of wavelet-based edge detection methods

International Journal of Pattern Recognition and Artificial Intelligence

Volumn 26, Issue 7, 2012, Pages

  Wang, P S P ^a,b   Yang, Jianwei ^c  

^a NORTHEASTERN UNIVERSITY   (United States)

^b ENCU   (China)

^c NANJING UNIVERSITY OF INFORMATION SCIENCE AND TECHNOLOGY   (China)

Author keywords

Edge detection; multiscale; shearlet; wavelet; wavelet transform

Indexed keywords

EDGE DETECTION METHODS; KEY ISSUES; LOCAL REGULARITY; MULTI-STRUCTURE; MULTISCALES; PROMINENT FEATURES; SHEARLET; WAVELET;

IMAGE PROCESSING; WAVELET TRANSFORMS;

EDGE DETECTION;

EID: 84873938115     PISSN: 02180014     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218001412550117     Document Type: Article

References (90)

1. M. Anderson, C. Bras̄eld, P. Gremaud, D. Labate, K. Maschmeyer, K. McGo and J. Siloti, Edge detection by multi-dimensional wavelets (2007), Available at http:// www4.ncsu.edu/egremaud/REU/̄nal paper.pdf
2. J.-P. Antoine, D. Barache, R. Cesar and L. da Fontoura Costa, Shape characterization with the wavelet transform, Signal Process. 62 (1997) 265-290 (Pubitemid 127401153)
3. J.P. Antoine, R. Murenzi and P. Vandergheynst, Directional wavelets revisited: Cauchy wavelets and symmetry detection in patterns, Appl. Comput. Harmon. Anal. 6 (1999) 314-345 (Pubitemid 129562931)
4. J.P. Antoinea and R. Murenzib, Two-dimensional directional wavelets and the scaleangle representation, Signal Process. 52 (1996) 259-281
5. F. Attneave, Some informational aspects of visual perception, Psychol. Rev. 61(3) (1954) 183-193
6. T. Aydin, Y. Yemes, E. Anarim and B. Sankur, Multidirectional and multiscale edge detection via m-band wavelet transform, IEEE Trans. Image Process. 5 (1996) 1370-1377 (Pubitemid 126782395)
7. H.L. Beus and S. S.H. Tiu, An improved corner detection algorithm based on chaincoded plane curves, Pattern Recogn. 20 (1987) 291-296 (Pubitemid 17617067)
8. E.J. Candes and D.L. Donoho, Ridgelets: B key to higher dimensional intermittency? Philos. Trans.R. Soc. Lond. A 357 (1999) 2495-2509
9. E.J. Candes and D.L. Donoho, Continuous curvelet transform: I. resolution of the wavefront set, Appl. Comput. Harmon. Anal. 19 (2005) 162-197 (Pubitemid 41214741)
10. J. Canny, A computational approach to edge detection, IEEE Trans. Pattern Anal. Mach. Intell. 8(6) (1986) 679-698
11. H.S. Chang and H. Yan, Analysis of stroke structures of hand written Chinese characters, IEEE Trans. Syst. Man Cybern. B, Cybern. 29 (1999) 47-61
12. G. C.-H. Chuang and C.-C.J. Kuo, Wavelet descriptor of planar curves: Theory and applications, IEEE Trans. Image Process. 5 (1996) 56-70 (Pubitemid 126776723)
13. C.K. Chui, Wavelet: B tutorial in theory and applications (Academic Press, New York, 1992
14. L.M. Cui, Yuan Y. Tang, P. S.P. Wang and F.C. Liao, Wavelet-based computational method in image transformation by singular integral equations with logarithmic kernel, in Pattern Recognition and Machine Vision, King-Sun Fu Memorial Book (River Pub, Denmark, 2010), pp. 37-53
15. S. Dahlke, G. Kutyniok, P. Maass, C. Sagiv, H.-G. Stark and G. Teschke, The uncertainty principle associated with the continuous shearlet transform, Int.J. Wavelets Multiresolut. Inf. Process. 6 (2008) 157-181 (Pubitemid 351728665)
16. I. Daubechies, Orthonormal bases of compactly supported wavelets, Commun. Pure Appl. Math. 41 (1988) 909-996
17. I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inf. Theory 36(5) (1990) 961-1005 (Pubitemid 20738359)
18. I. Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphia, 1992
19. J.H. Van Deemter and J.M. Du Buf, Psimultaneous detection of lines and edges using compound gabor ̄lters, Int.J. Pattern Recogn. Artif. Intell. 14(6) (2000) 757-777
20. N. Delprat, B. Escudie, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian and B. Torresani, Asymptotic wavelet and gabor analysis: Extraction of instantaneous frequencies, IEEE Trans. Inf. Theory 38(2) (1992) 644-664
21. M.N. Do and M. Vetterli, The contourlet transform: Bn e±cient directional multiresolution image representation, IEEE Trans. Image Process. 14(12) (2005) 2091-2106 (Pubitemid 41781516)
22. D.L. Donoho, For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution, Commun. Pure Appl. Math. 59 (2006) 797-829 (Pubitemid 43667226)
23. D.L. Donoho, A. Maleki, M. Shahram, V. Stodden and I. Ur-Rahman, Fifteen years of reproducible research in computational harmonic analysis, Tech. report, Statistics Department of Stanford University (2008
24. P.L. Dragotti and M. Vetterli, Wavelet footprints: Theory, algorithms, and applications, IEEE Trans. Signal Process. 51(5) (2003) 1306-1323
25. G. Easley, K. Guo and D. Labate, Analysis of singularities and edge detection using the shearlet transform, in Proc. SAMPTA 09, Marseille (2009
26. G. Easley, D. Labate and W.-Q. Lim, Sparse directional image representations using the discrete shearlet transform, Appl. Comput. Harmon. Anal. 25 (2008) 25-46 (Pubitemid 351713737)
27. L. Feng, C.Y. Suen, Yuan.Y. Tang and L.H. Yang, Edge extraction of images by reconstruction using wavelet decomposition details at di®erent resolution levels, Int.J. Pattern Recogn. Artif. Intell. 14 (2000) 779-793
28. R. Fjortoft, P. Marthon, A. Lopes and A. Lop Es, Multiresolution edge detection in sar images (1997), available at http://citeseerx.ist.psu.edu/ viewdoc/download?doi=10.1.1.47-6767&rep=rep1&type=pdf
29. C.C. Fung and P.C. Shi, Multiscale edge representation applied to image fusion, in Proc. SPIE, Vol. 4119 (International Society for Optical Engineering, 2000), pp. 894-901
30. C.C. Fung and P.C. Shi, Design of compactly supported wavelet to match singularities in medical images, in SPIE Proc., Vol. 4790 (2002), pp. 358-369
31. X. Gao, F. Sattar, A. Quddus and R. Venkateswarlu, Multiscale contour corner detection based on local natural scale and wavelet transform, Image Vis. Comput. 25 (2007) 890-898 (Pubitemid 46528585)
32. T. N.T. Goodman, D.P. Hardin, S.L. Lee and W.S. Tang, Wavelets of multiplicity r, Trans. Am. Math. Soc. 338 (1993) 639-654
33. K. Guo and D. Labate, Optimally sparse multidimensional representation using shearlets, SIAM J. Math. Anal. 39 (2007) 298-318 (Pubitemid 351271316)
34. K. Guo, D. Labate and W. Lim, Edge analysis and identīcation using the continuous shearlet transform, Appl. Comput. Harmon. Anal. 27 (2009) 24-46
35. W. He and M.J. Lai, Examples of bivariate nonseparable compactly supported continuous wavelets, IEEE Trans. Image Process. 9(5) (2000) 949-953
36. Q. He, X.G. You, P. S.P. Wang and Y.Y. Tang, An image watermarking scheme using non-Tensor product wavelets, in Proc. Int. Conf. Wavelet Analysis and Pattern Recognition, Beijing, China, November 2007, pp. 350-355
37. J.W. Hsieh, M.T. Ko, H. Y.M. Liao and K.C. Fan, A new wavelet-based edge detector via constrained optimization, Image Vis. Comput. 15 (1997) 511-527
38. http://www.shearlab.org
39. J. Hua and Q. Liao, Wavelet-based multiscale corner detection, WCCC-ICSP 2000. 5th Int. Conf. Signal Processing Proc., Vol. 1 (2000), pp. 341-344
40. W.L. Hwang and F. Chang, Character extraction from documents using wavelet maxima, Image Vis. Comput. 16 (1998) 307-315 (Pubitemid 128393580)
41. L.M. Kennedy and M. Basu, A gaussian derivative operator for authentic edge detection and accurate edge localization, Int.J. Pattern Recogn. Artif. Intell. 13(3) (1999) 367-380
42. N. Kingsbury, Complex wavelets for shift invariant analysis and ̄ltering of signals, Appl. Computat. Harmon. Anal. 10 (2001) 234-253 (Pubitemid 33675919)
43. G. Kutyniok and D. Labate, The construction of regular and irregular shearlet frames, J. Wavelet Theory Appl. 1 (2007) 1-10
44. G. Kutyniok and D. Labate, Resolution of the wavefront set using continuous shearlets, Trans. Am. Math. Soc. 361 (2009) 2719-2754
45. G. Kutyniok and T. Sauer, From wavelets to shearlets and back again, Approximation Theory XII, San Antonio, TX, 2007, (Nashboro Press, Nashville, TN, 2008), pp. 201-209
46. D. Labate G. Easley and W. Lim, Optimally sparse image representations using shearlets, in Proc. 40th Asilomar Conf. on Signals, Systems and Computers, Monterey (2006
47. D. Labate, W. Lim, G. Kutyniok and G. Weiss, Sparse multidimensional representation using shearlets, SPIE Proc., Wavelets XI, Vol. 5914 (SPIE, Bellingham, WA, 2005), pp. 254-262
48. L. Lam, S.W. Lee and C.Y. Suen, Thinning methodologies a comprehensive survey, IEEE Trans. Pattern Anal. Mach. Intell. 14 (1992) 869-885
49. J.S. Lee, Y.N. Sun and C.H. Chen, Multiscale corner detection by using wavelet transform, IEEE Trans. Image Process. 4(1) (1995) 100-104
50. J. Li, A wavelet approach to edge detection, Master's thesis, Sam Houston State University (2003
51. T. Lindeberg, Edge detection and ridge detection with automatic scale selection, in Proc. Int. Conf. Computer Vision and Pattern Recognition (San Francisco, California), pp. 465-470
52. H.C. Liu and M.D. Srinath, Partial shape classīcation using contour matching in distance transformation, IEEE Trans. Pattern Anal. Mach. Intell. 12(11) (1990) 1072-1079
53. S. Mallat, Multiresolution approximations and wavelet orthonormal bases of L2(R), Trans. Am. Math. Soc. 315 (1989) 69-87
54. S. Mallat, Wavelet Tour of Signal Processing (Academic Press, San Diego, CA, 1998
55. S. Mallat and W.L. Hwang, Singularity detection and processing with wavelets, IEEE Trans. Inf. Theory 38(2) (1992) 617-643
56. S. Mallat and S. Zhong, Characterization of signals from multiscale edges, IEEE Trans. Pattern Anal. Mach. Intell. 14(7) (1992) 710-732
57. D. Marr and E. Hildreth, Theory of edge detection, Proc.R. Soc. Lond. B 207 (1980
58. Y. Meyer, Wavelet and Operators, Advanced mathematics (Cambridge University Press, 1992
59. M. Nabti, L. Ghouti and A. Bouridane, Multiscale edge detection using wavelet maxima for iris localization, IET Int. Conf. Visual Information Engineering (VIE 2006) (2006), pp. 62-67
60. M.T. Orchard and H.F. Ates, Nonlinear modeling of wavelet coe±cients around edges, in Proc. IEEE Int. Conf. Image Processing (2003), pp. 641-644
61. D.D. Po and M.N. Do, Directional multiscale modeling of images using the contourlet transform, IEEE Trans. Image Process. 15(6) (2006) 1610-1620 (Pubitemid 43778938)
62. A. Quddus and M.M. Fahmy, Fast wavelet wavelet-based corner detection technique, IEE Elect. Lett. 35 (1999) 287-288
63. A. Quddus and M. Gabbouj, Wavelet-based corner detection technique using optimal scale, Pattern Recogn. Lett. 23 (2002) 215-220 (Pubitemid 33119514)
64. A. Rattarangsi and R.T. Chin, Scale-based detection of corners of planar curves, IEEE Trans. Pattern Anal. Mach. Intell. 14 (1992) 430-449
65. Y. Shen, G.R. Easley D. Labate and H. Krim, A shearlet approach to edge analysis and detection, IEEE Trans. Image Process. 18(5) (2009) 929-941
66. Y. Shen, D. Labate, G.R. Easley and H. Krim, Edge detection and processing using shearlets, Proc. IEEE Int. Conf. Image Processing, San Diego (2008
67. J.X. Sun, D.B. Gu, Y.Z. Chen and S. Zhang, A multiscale edge detection algorithm based on wavelet domain vector hidden markov tree model, Pattern Recogn. 37 (2004) 1315-1324 (Pubitemid 38653363)
68. W. Sweldens, The lifting scheme: B custom-design construction of biorthogonal wavelets, Appl. Comput. Harmon. Anal. 3 (1996) 186-200 (Pubitemid 126375198)
69. Y.Y. Tang, Status of patternition with wavelet analysis, Front. Comput. Sci. China 2(3) (2008) 268-294
70. Y.Y. Tang, L.H. Yang and L. Feng, Characterization and detection of edges by Lipschitz exponent and masw wavelet transform, in Proc. of the 14th Int. Conf. on Pattern Recognition, Brisbane, Australia (1998), pp. 1572-1574
71. Y.Y. Tang, L.H. Yang and L. Feng, Contour detection of handwriting by modular-Angleseparated wavelets, in Proc. of the 6th Int. Workshop on Frontiers of Handwriting Recognition (IWFHR-VI), Taejon, Korea (1998), pp. 357-366
72. Y.Y. Tang, L.H. Yang, and J.M. Liu, Wavelet-based edge detection in Chinese document, Proc. the 17th Int. Conf. on Computer Processing of Oriental Languages, Vol. 1, 1997, pp. 333-336
73. Y.Y. Tang, L.H. Yang and J.M. Liu, Characterization of Dirac-structure edges with wavelet transform, IEEE Trans. Sys. Man Cybern. B, Cybern. 30(1) (2000) 93-109 (Pubitemid 30588339)
74. Y.Y. Tang, L.H. Yang, J.M. Liu and H. Ma, Wavelet Theory and its Applications to Pattern Recognition (World Scientīc Publishing Co. Pte, Ltd., Singapore, 2000
75. Y.Y. Tang and X.G. You, Skeletonization of ribbon-like shapes based on a new wavelet function, IEEE Trans. Pattern Anal. Mach. Intell. 25(9) (2003) 1118-1133
76. P. Tchamitchian and B. Torresani, Ridge and skeleton extraction from the wavelet transform, in Wavelets and Their Applications (Jones and Bartlett, MA, 1992), pp. 123-151
77. C.-H. Teh and R.T. Chin, On the detection of dominant points on digital curves, IEEE Trans. Pattern Anal. Mach. Intell. 11 (1989) 859-872
78. D. Ch. Tseng and M.Y. Shih, A wavelet-based multiresolution edge detection and tracking, Image Vis. Comput. 23 (2005) 441-451
79. C.L. Tu, W.L. Hwang and J. Ho, Analysis of singularities from modulus maxima of complex wavelets, IEEE Trans. Inf. Theory 51(3) (2005) 1049-1062 (Pubitemid 40377565)
80. Y. Wang and Y.L. Cai, Construction and properties of b-spline wavelet ̄lters for multiscale edge detection, in Proc. Int. Conf. Image Processing, Washington, DC, October 1995, pp. 145-148
81. L.H. Yang, C.Y. Suen and Y.Y. Tang, A width-invariant property of curves based on wavelet transform with novel wavelet function, IEEE Trans. Syst. Man Cybern. B, Cybern. 33(3) (2003) 541-548
82. L.H. Yang, Z.H. Yang and X.M. Sun, Construction of wavelets for width-invariant characterization of curves, Pattern Recogn. Lett. 24(15) (2003) 2751-2760
83. X.G. You and Y.Y. Tang, Wavelet-based approach to character skeleton, IEEE Trans. Image Process. 16(5) (2007) 1220-1231 (Pubitemid 46629551)
84. X.G. You, Q.H. Chen, P. S.P. Wang and D. Zhang, Nontensor-product- wavelet-based facial feature representation, in Image Pattern Recognition-Synthesis and Analysis in Biometrics, eds. S.N. Yanushkevich, M. Gavrilova, P. Wang, and S. Srihari (WSP, 2007), pp. 207-224
85. X.G. You, D. Zhang, Q.H. Chen, P. S.P. Wang and Y.Y. Tang, Face representation by using non-Tensor product wavelets, in Proc. Int. Conf. Pattern Recognition, Hong Kong, China, August 2006, pp. 503-506 (Pubitemid 46531951)
86. T.Y. Zhang and C.Y. Suen, A fast parallel algorithm for thinning digital patterns, Commun. ACM 27 (1984) 236-239 (Pubitemid 14581473)
87. Z. Zhang, S.L. Ma, H. Liu and Y.X. Gong, An edge detection approach based on directional wavelet transform, Comput. Math. Appl. 57 (2009) 1265-1271
88. D. Zhang, X.G. You, P. S.P. Wang, S.N. Yanushkevich and Y.Y. Tang, Facial biometrics using non-Tensor product wavelet and 2D discriminant technique, Int.J. Pattern Recognit. Artif. Intell. 23(4) (2009) 421-543
89. P. Zhao, C. Zhao and P.G. Casazza, Perturbation of pegular sampling in shift invariant spaces for frames, IEEE Trans. Inf. Theory 52(10) (2006) 4643-4648 (Pubitemid 46445300)
90. D. Ziou and S. Tabbone, Edge detection techniques -An overview, Int.J. Pattern Recogn. Image Anal. 8 (1998) 537-559