Abstract
In this chapter, the moments-based multismoothlet transform was proposed. It is based on Custom-Built moments used to compute multiedge parameters. The transform was presented in the consecutive steps, starting from a linear beamlet computation. Further, smoothlet parameters are computed. And finally, multismoothlet parameters are determined. At the end of this chapter, the computational complexity of the presented transform was discussed followed by some numerical results.
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References
Lisowska, A.: Moments-based fast wedgelet transform. J. Math Imaging Vis. 39(2), 180–192 (2011). (Springer)
Donoho, D.L.: Wedgelets: nearly-minimax estimation of edges. Ann Stat 27, 859–897 (1999)
Romberg, J., Wakin, M., Baraniuk, R.: Multiscale wedgelet image analysis: fast decompositions and modeling. In: IEEE International Conference on Image Processing vol. 3, pp. 585–588 (2002)
Friedrich, F., Demaret, L., Führ, H., Wicker, K.: Efficient moment computation over polygonal domains with an application to rapid wedgelet approximation. SIAM J. Sci. Comput. 29(2), 842–863 (2007)
Walker, J.S.: Fourier analysis and wavelet analysis. Not. Am. Math. Soc. 44(6), 658–670 (1997)
Liao, S.X., Pawlak, M.: On image analysis by moments. IEEE Trans. Pattern Anal. Mach. Intell. 18(3), 254–266 (1996)
Teh, C.H., Chin, R.T.: On image analysis by the methods of moments. IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 496–513 (1988)
Mukundan, R., Ong, S.H., Lee, P.A.: Image analysis by Tchebichef moments. IEEE Trans. Image Process. 10(9), 1357–1364 (2001)
Chong, C.W., Mukundan, R., Raveendran, P.: A comparative analysis of algorithms for fast computation of Zernike moments. Pattern Recogn. 36, 731–742 (2003)
Popovici, I., Withers, W.D.: Custom-Built moments for edge location. IEEE Trans. Pattern Anal. Mach. Intell. 28(4), 637–642 (2006)
Lisowska, A.: Smoothlet transform: theory and applications. Adv. Imaging Electr. Phys. 178, 97–145 (2013). (Elsevier)
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Lisowska, A. (2014). Moments-Based Multismoothlet Transform. In: Geometrical Multiresolution Adaptive Transforms. Studies in Computational Intelligence, vol 545. Springer, Cham. https://doi.org/10.1007/978-3-319-05011-9_4
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DOI: https://doi.org/10.1007/978-3-319-05011-9_4
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