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Synthesis of bidimensional α -stable models with long-range dependence

This paper discusses the synthesis of bidimensional α-stable models with long-range dependence to model textures with impulsive and LRD behaviors. It explores the applications of this modeling technique in various fields such as medical imaging and computer graphics.

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Synthesis of bidimensional α -stable models with long-range dependence

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  1. Synthesis of bidimensional α-stable models withlong-range dependence xiaodong sun MESA (Mechatronics, Embedded Systems and Automation)Lab School of Engineering, University of California, Merced E: xsun7@ucmerced.edu Phone:209 201 1947 Lab: CAS Eng 820 (T: 228-4398) sep 22, 2014. Applied Fractional Calculus Workshop Series @ MESA Lab @ UCMerced

  2. The paper we talk about Synthesis of bidimensional α-stable models with long-range dependence Beatrice Pesquet-Popescu a, ∗, Jean-Christophe Pesquetb

  3. Why need 2D fractal model The motivation for modeling and synthesizing textures with impulsive and long-range dependence (LRD) behaviors are on the following: • Segmentationofsynthetic or satellite images( high-speckle SAR imagery ) • ultrasound medical imaging and astronomical imaging. • In computer graphic applications, the generation of 2-D picture realizations( create natural-looking night landscapes) • Underwater image modeling (Scattering effect caused by water molecule) • Camera internal noise modeling

  4. The way to bidimensional α-stable models Generate multivariate stable distribution noise Generate long-range dependence (LRD) behaviors bidimensional α-stable models with long-range dependence

  5. Generate multivariate α-stable driving noise According to the proposition 1.7.1 in paper [1]. The α-stable driving noise can be generated [1]G. Samorodnitsky, M.S. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman and Hall, New York, 1994.

  6. Generate long-range dependence (LRD) behaviors 'fractionally differenced' processes are capable of modelling long-term persistence. 2D discrete-spaceprocess with LRD properties can be achieved by a 2D fractional stable process passed a bidimensional filter system . the frequency response of the bidimensional filter can be expressed by

  7. Generate long-range dependence α-stable processes Generate 2D α-stableprocesses X Apply FFT to X ,W=fft(X) α-stable noise pass 2D filter Hd() . Generate S=W.Hd() α-stable process with LRD by using inverse . Ss=ifft2(S)

  8. Simulation pcolor α=1.4 d=0.25

  9. Simulation contour3 α=1.4 d=0.25

  10. Simulation pcolor α=1.6 d=0.3

  11. Simulation contour3 α=1.6 d=0.3

  12. Simulation pcolor α=1.8 d=0.35

  13. Simulation contour3 α=1.8 d=0.35

  14. Thank you!

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