The Ellipselet Transform
DOI: 10.4103/jmss.JMSS_42_17
Abstract
Background: A fair amount of important objects in natural images have circular and elliptical shapes. For example, the nucleus of most of the biological cells is circular, and a number of parasites such as Oxyuris have elliptical shapes in microscopic images. Hence, atomic representations by two-dimensional (2D) basis functions based on circle and ellipse can be useful for processing these images. The first researches have been done in this domain by introducing circlet transform. Methods: The main goal of this article is expanding the circlet to a new one with elliptical basis functions. Results: In this article, we first introduce a new transform called ellipselet and then compare it with other X-let transforms including 2D-discrete wavelet transform, dual-tree complex wavelet, curvelet, contourlet, steerable pyramid, and circlet transform in the application of image denoising. Conclusion: Experimental results show that for noises under 30, the ellipselet is better than other geometrical X-lets in terms of Peak Signal to Noise Ratio, especially for Lena which contains more circular structures. However, for Barbara which has fine structures in its texture, it has worse results than dual-tree complex wavelet and steerable pyramid.
Keywords
Full Text:
PDFReferences
Daubechies I, Bates BJ. Ten Lectures on Wavelets. J Acoust Soc Am 1993;93:1671.
Candes EJ, Donoho DL. Ridgelets: A key to higher-dimensional intermittency? Philos Trans R Soc A Math Phys Eng Sci 1999;357:2495-509.
Alzubi S, Islam N, Abbod M. Multiresolution analysis using wavelet, ridgelet, and curvelet transforms for medical image segmentation. Int J Biomed Imaging 2011;2011:136034.
Starck JL, Candès EJ, Donoho DL. The curvelet transform for image denoising. IEEE Trans Image Process 2002;11:670-84.
Do MN, Vetterli M. The contourlet transform: An efficient directional multiresolution image representation. IEEE Trans Image Process 2005;14:2091-106.
Yang L, Guo BL, Ni W. Multimodality medical image fusion based on multiscale geometric analysis of contourlet transform. Neurocomputing 2008;72:203-11.
Chauris H, Karoui I, Garreau P, Wackernagel H, Craneguy P, Bertino L. The circlet transform: A robust tool for detecting features with circular shapes. Comput Geosci 2011;37:331-42.
Amini Z, Rabbani H. Classification of medical image modeling methods: A review. Curr Med Imaging Rev 2016;12:1. [Last cited on 2019 May 20].
Kingsbury N. The Dual-Tree Complex Wavelet Transform: A New Efficient Tool for Image Restoration and Enhancement; 1998.
Selesnick IW, Baraniuk RG, Kingsbury NC. The dual-tree complex wavelet transform. IEEE Signal Process Mag 2005;22:123-51.
Lambert P, Pires S, Ballot J, García RA, Starck JL, Turck-Chièze S. Curvelet analysis of asteroseismic data I: Method description and application to simulated sun-like stars. Astron Astrophys 2006;454:1021-7.
Satheesh S, Prasad K. Medical image denoising using adaptive threshold based on contourlet transform. Adv Comput Int J 2011;2:52-8.
Simoncelli EP, Freeman WT. The steerable pyramid: A flexible architecture for multi-scale derivative computation. In: Proceedings, International Conference on Image Processing. Washington, DC. IEEE Comput Soc Press; 1995. p. 444-7.
Simoncelli EP, Freeman WT, Adelson EH, Heeger DJ. Shiftable multiscale transforms. IEEE Trans Inf Theory 1992;38:587-607.
Wang J. Exposure fusion based on steerable pyramid for displaying high dynamic range scenes. Opt Eng 2009;48:117003.
Sarrafzadeh O, Dehnavi AM, Rabbani H, Ghane N, Talebi A. Circlet based framework for red blood cells segmentation and counting. In: 2015 IEEE Workshop on Signal Processing Systems (SiPS). IEEE; 2015. p. 1-6.
Comaniciu D, Meer P. Mean shift: A robust approach toward feature space analysis. IEEE Trans Pattern Anal Mach Intell 2002;24:603-19.
Hamdi M. A comparative study in wavelets, curvelets and contourlets as denoising biomedical Images. Image Process Commun 2011;16:13-20.
Rabbani H. Image denoising in steerable pyramid domain based on a local Laplace prior. Pattern Recognit 2009;42:2181-93.
Portilla J, Strela V, Wainwright MJ, Simoncelli EP. Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans Image Process 2003;12:1338-51.
Wang Z, Bovik AC, Sheikh HR, Simoncelli EP. Image quality assessment: From error visibility to structural similarity. IEEE Trans Image Process 2004;13:600-12.
Candès E, Demanet L, Donoho D, Ying L. Fast discrete curvelet transforms. Multiscale Model Simul 2006;5:861-99.
Refbacks
- There are currently no refbacks.
https://e-rasaneh.ir/Certificate/22728
ISSN : 2228-7477