The geometry of fractal sets
The Science of Fractal Images
Computer Vision, Graphics, and Image Processing
IEEE Transactions on Signal Processing
Estimation of fractal signals from noisy measurements usingwavelets
IEEE Transactions on Signal Processing
Wavelet analysis and synthesis of fractional Brownian motion
IEEE Transactions on Information Theory - Part 2
Fractal-Based Description of Natural Scenes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Synthesis and Estimation of Random Fields Using Long-Correlation Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
An EMD based simulation of fractional Gaussian noise
IMACS'08 Proceedings of the 7th WSEAS International Conference on Instrumentation, Measurement, Circuits and Systems
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We report here on image texture analysis and on numerical simulation of fractional Brownian textures based on the newly emerged Empirical Mode Decomposition (EMD). EMD introduced by N.E. Huang et al. is a promising tool to non-stationary signal representation as a sum of zero-mean AM-FM components called Intrinsic Mode Functions (IMF). Recent works published by P. Flandrin et al. relate that, in the case of fractional Gaussian noise (fGn), EMD acts essentially as a dyadic filter bank that can be compared to wavelet decompositions. Moreover, in the context of fGn identification, P. Flandrin et al. show that variance progression across IMFs is related to Hurst exponent H through a scaling law. Starting with these recent results, we propose a new algorithm to generate fGn, and fractional Brownian motion (fBm) of Hurst exponent H from IMFs obtained from EMD of a White noise, i.e. ordinary Gaussian noise (fGn with H=1/2).