Abstract
We provide here some contributions for both the comprehension and theoretical modeling of the well known Empirical Mode Decomposition (EMD) method in 2D. This is achieved by reconsidering the so-called local mean which is formulated now with the morphological median operator. Doing this helps us derive curvature motion-like partial differential equations (PDEs) that mimic the 2D sifting process. In addition to the mathematical framework brought out herein, preliminary results show also that our proposed approach behaves like the 2D EMD and in a better way.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bhuiyan, S.M.A., Adhami, R.R., Khan, J.F.: A novel approach of fast and adaptative bidimensional empirical mode decomposition. In: IEEE ICASSP, pp. 1313–1316 (2008)
Boudraa, A.O., Cexus, J.C., Salzenstein, F., Beghdadi, A.: Emd-based multibeam echosounder images segmentation. In: IEEE ISCCSP (Marocco) (2006)
Damerval, C., Meignen, S., Perrier, V.: A fast algorithm for bidimensional emd. IEEE Sign. Process. Lett. 12(10), 701–704 (2005)
Diop, E.H.S., Alexandre, R., Boudraa, A.-O.: Analysis of intrinsic mode functions: a PDE approach. IEEE Sign. Process. Lett. 17(4), 398–401 (2010)
Diop, E.H.S., Alexandre, R., Perrier, V.: A PDE based and interpolation-free framework for modeling the sifting process in a continuous domain. Adv. Comput. Math. 38, 801–835 (2013)
Diop, E.H.S., Boudraa, A.O., Khenchaf, A., Thibaud, R., Garlan, T.: Multiscale characterization of bathymetric images by empirical mode decomposition. In: MARID III, Leeds, UK, 1–3 April 2008
Diop, E.H.S., Alexandre, R., Boudraa, A.-O.: A PDE model for 2D intrinsic mode functions. In: IEEE ICIP, Cairo, Egypt, pp. 3961–3964 (2009)
Diop, E.H.S., Alexandre, R., Moisan, L.: Intrinsic nonlinear multiscale image decomposition: a \(2{D}\) empirical mode decomposition-like tool. Comput. Vis. Image Underst. 116(1), 102–119 (2012)
Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.-C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis. Roy. Soc. 454, 903–995 (1998)
Linderhed, A.: 2-d empirical mode decompositions- in the spirit of image compression. In: Proceedings of SPIE, WICAA IXI, Florida, USA, vol. 4738, 1–5 April 2002
Linderhed, A.: Compression by image empirical mode decomposition. In: IEEE ICIP, Genoa, Italy, vol. I, pp. 553–556, 11–14 September 2005
Liu, Z., Peng, S.: Estimation of image fractal dimension based on empirical mode decomposition. In: ACIVS, Brussels, Belgium (2004)
Xu, Y., Liu, B., Liu, J., Riemenschneider, S.: Two-dimensional empirical mode decomposition by finite elements. The Royal Society A, 1–17 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Diop, E.H.S., Alexandre, R. (2015). Analysis of Intrinsic Mode Functions Based on Curvature Motion-Like PDEs. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2014. Lecture Notes in Computer Science(), vol 9213. Springer, Cham. https://doi.org/10.1007/978-3-319-22804-4_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-22804-4_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22803-7
Online ISBN: 978-3-319-22804-4
eBook Packages: Computer ScienceComputer Science (R0)