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The Fuzzy Transformation and Its Applications in Image Processing

Vision Lab, Dept. of EE, NCTU Jui-Nan Chang 2009.4.6. The Fuzzy Transformation and Its Applications in Image Processing. Outline. Introduction Basic Concepts Properties of Fuzzy Transformation Filter Generalization Using the FZT and Applications Conclusion References.

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The Fuzzy Transformation and Its Applications in Image Processing

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  1. Vision Lab, Dept. of EE, NCTU Jui-Nan Chang 2009.4.6 The Fuzzy Transformation and Its Applications in Image Processing

  2. Outline • Introduction • Basic Concepts • Properties of Fuzzy Transformation • Filter Generalization Using the FZT and Applications • Conclusion • References

  3. Introduction (1/2) • Nonlinear signal processing methods - heavy tailed distribution or non-stationary statistics • Spatial & Rank (SR) orderings - center weighted median (CWM) - weighted median (WM) - permutation • Spatial correlation and rank order information crisp (binary) SR relations

  4. Introduction (2/2) • Fuzzy SR relations - crisp SR relations sample spread (diversity) - fuzzy spatial samples - fuzzy order statistics - fuzzy spatial indexes - fuzzy rank fuzzy SR space crisp SR space fuzzy transformation

  5. Basic Concepts (1/4) • crisp SR relations spatial sample order statistic rank index spatial index we get

  6. Basic Concepts (2/4) • Combined with spread information - membership functions Gaussian membership function Uniform membership function Triangular membership function Note: they are all monotonically non-decreasing function and

  7. Basic Concepts (3/4) • Combined with spread information - fuzzy SR relations we get They are represented the weighted averages of the crisp order statistics , spatial samples ,spatial indexes and rank indexes. column normalized row normalized

  8. Basic Concepts (4/4) • Example (Gaussian membership function) fuzzy SR space crisp SR space

  9. Properties of Fuzzy Transformation • Element Invariant Property - the crisp SR relations are fully preserved by the FZT • Order Invariant Property • the fuzzy SR space contains SR information consistent with that in the crisp SR space • Mean preserving an unbiased operator

  10. Filter Generalization Using the FZT and Applications • Fuzzy identity filer - remove the blocking artifact with preserving edge - use Gaussian membership function - use MSE criteria to estimate the parameter

  11. Filter Generalization Using the FZT and Applications • Fuzzy identity filer

  12. Filter Generalization Using the FZT and Applications • Fuzzy identity filer blocking artifact QF=10 result of fuzzy IF

  13. Filter Generalization Using the FZT and Applications • LUM filter – impulse noise removal (lower-upper-middle) The LUM smoother may cause over smoothing when there are no outliers, or under smoothing when corrupted samples have ranks within the range [k,N-k+1 ]

  14. Filter Generalization Using the FZT and Applications • FLUM filter – impulse noise removal (fuzzy lower-upper-middle) • The FLUM filter incorporates sample spread information, and thus more effectively identifies true outliers and improve filer performance

  15. Filter Generalization Using the FZT and Applications • FLUM filter – impulse noise removal

  16. Filter Generalization Using the FZT and Applications • FLUM filter – impulse noise removal

  17. Filter Generalization Using the FZT and Applications • FLUM filter – impulse noise removal fuzzy LUM filter crisp LUM filter 5% impulse noise

  18. Conclusion • FZT retains the consistent SR information of the samples • FZT effectively reflects sample spread information • The FZT is utilized to generalize conventional filters to exploit the joint spatial-rank-spread information • It has potential to be exploited in novel techniques for other signal processing applications

  19. References • Yao Nie and K. E. Barner, "The fuzzy transformation and its applications in image processing," Image Processing, IEEE Transactions on, vol. 15, pp. 910-927, 2006.

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