Abstract

This paper proposed an edge detection using Skewed and Elongated Basis functions (SEBF). In an image, edges present at any directions and any scale. Common edge detection algorithms are single scale, and limited in directions. The proposed method efficiently removes these difficulties by using SEBF that are having multiscale and non separable properties. The two dimensional non separable properties of SEBF provide multiple directions, whereas the multiscale to explore the hidden edge information at various scales. The SEBF are derived from anisotropic directionlets are applied for edge detection to effectively preserving edges in all orientations and scales. This paper uses Figure of Merit (F), accuracy, sensitivity, specificity characteristics to analyze the performances. The experimental results showed that the proposed algorithms provide improvement in all performance measure.

References

• Mallat S, HW ANG W L 2002 .Singularity Detection and Processing with Wavelets. IEEE Trans on Info Theory, 617-643
• Mitra Basu, 2002. Gaussian-Based Edge-Detection Methods—A Survey. IEEE Transactions on Systems, Man, and Cybernetic, 252-260
• Castleman K. R., 1996. Digital Image Processing. Englewood Cliffs, NJ: Prentice-Hall
• Donoho D. L., Vetterli M., DeVore R. A., and Daubechies I., 1998. Data compression and harmonic analysis. IEEE Trans. Inf. Theory, 2435–2476
• Vetterli M. and Kova?cevic´ J.,1995. Wavelets and Subband Coding. EnglewoodCliffs, NJ: Prentice-Hall
• Pennec E. L. and Mallat S.,2000. Image compression with geometric wavelets. IEEE Int. Conf. Image Processing, 661–664
• Stephane Mallat,Gabriel Peyre 2005. Sparse geometric image representations with bandelets, IEEE Trans. Image Process.,. 423–438.
• Donoho D. L.,1999. Wedgelets: Nearly-minimax estimation of edges. Ann.Statist., 859–897
• Romberg J. K.,.Wakin M, and Baraniuk R.,2002. Multiscale wedgelet image analysis: Fast decompositions and modeling. IEEE Int. Conf. Image Processing, 585–588
• Romberg J. K., Wakin M., and Baraniuk R 2003. Approximation and compression of piecewise smooth images using a wavelet/wedgelet geometric model. IEEE Int. Conf. Image Processing, Barcelona, Spain, 49–52.
• Wakin M., Romberg J., Hyeokho C., and Baraniuk R.,2002. Rate-distortion optimized image compression using wedgelets. IEEE Int. Conf. Image Processing, 237 -240.
• Wakin M., Romberg J., Choi H., and Baraniuk R., 2006. Wavelet-domain approximation and compression of piecewise smooth images. IEEE Trans. Image Process, 1071–1087
• Candès E. J. and Donoho D. L.,1999. Curvelets – A surprisingly effective nonadaptive representation for objects with edges, in Curve and Surface Fitting, A. Cohen, C. Rabut, and L. L. Schumaker, Eds. Nashville, TN: Vanderbilt Univ. Press
• Candès E. J. and Donoho D., 1999. Curvelets and curvilinear integrals, Tech. Rep., Dept. Statist., Stanford Univ., Stanford, CA
• Candès E. J. and Donoho D. L. 2002. New tight frames of curvelets and optimal representations of objects with smooth singularities, Tech. Rep., Dep. Statist., Stanford Univ., Stanford, CA
• Do M. N. and Vetterli M.,2005. The contourlet transform: An efficient directional multiresolution image representation, IEEE Trans. Image Process., 2091–2106
• Skodras A., Christopoulos C., and Ebrahimi T., 2001. The JPEG 2000 still image compression standard, IEEE Signal Processing Mag., 36–58
• Cohen A. and Daubechies I.,1993. Non-separable bidimensional wavelet bases, Revista Mat. Iberoamer., 51–137
• J.Kova?cevic´ 1991, Filter Banks andWavelets: Extensions and Applications,” Ph.D. dissertation, Graduate School of Arts and Sciences, Columbia Univ., New York.
• Kova?cevic´ J. and Vetterli M.,1992. Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for , IEEE Trans. Inf. Theory, 533–555
• Rosenfeld A, and Thurston M, 1970. Edge and Curve Detection for Visual Scene Analysis, IEEE Trans. Computer,562-569
• Sadler B M, Pham T, and Sadler L C, 1998. Optimal and wavelet based Shock Wave Detection and Estimation, J Acoust. Soc. Am., 955-963
• Ziou D, and Tabbone S, 1993.A Multiscale Edge Detector, PR, 26(9), 1305-1314
• Park D J, Nam K N, and Park R H, 1995.Multiresolution Edge Detection Techniques, Pattern Recognition, 211-219
• Canny J., 1986.A computational approach to edge detection, IEEE Trans. Pattern Anal. Mach. Intell., 679–698
• Bowyer K., Kranenburg C., and Dougherty S.,2001. Edge detector evaluation using empirical ROC curves,Comput. Vis. Image Underst 77–103
• Wei Jiang, Kin-Man Lam, and Ting-Zhi Shen,2009. Efficient Edge Detection Using Simplified Gabor Wavelets, IEEE Transactions On Systems, Man, and Cybernetics- Part B: Cybernetics