F-transform basics. Presentation describe basics ideas of fuzzy transform. decomposition of fuzzy partitions.

1. F-transform for data processing
Babii Andrii
Kharkiv National University of Radioelectronics
Senior lecturer,
Department of software engineering
andrii.babii@nure.ua

2. Fuzzy logic. Membership functions

3. Ruspini partitions
Ruspini, Enrique H. "A new approach to clustering." Information and control 15.1
(1969): 22-32.

4. 1D data. Crisp partitions

5. Fuzzy partitions
http://www.atlantis-press.com/php/download_paper.php?id=8437

6. 1D data. Fuzzy partitions on X
Uniform Fuzzy partitions

7. Equations
Direct fuzzy transform
Inverse fuzzy transform

8. Fuzzy partition approximation.

9. 2D fuzzy partitions
=
For each partition!

10. Real image

12. Result of approximationInput
F-transform (5x5, triangle)
Gaussian blur(5x5)

13. How it works
Find sharp parts (the best parts)
extract
create better image
Fuzzy transform used here

14. Main idea
Fuzzy transform smoothing edges
So, the more fuzzy image –
the lower compression error after fuzzy transform !
1. Recursively transform image via fuzzy transformation
2. Good parts will have high difference between origin and reconstruction
3. Use it to reconstruct sharp image
Steps

15. Step 1. Direct + Inverse Fuzzy Transform

16. Step 2. Calculate error for pixels and areas

17. Apply the threshold to areas

18. Result

19. Example

20. References
http://www.earthview3d.net/about/
http://dsp.etfbl.net/mif/
http://eijournal.com/print/articles/data-fusion-empowers-geospatial-analysis
https://publications.mpi-cbg.de/Swoger_2007_1403.pdf
https://www.semanticscholar.org/paper/Multi-temporal-optical-VHR-image-fusion-for
-Land-Paget-Gressin/8730aed1036c9ad2512724cfda6cc1c43690c720
http://www.atlantis-press.com/php/download_paper.php?id=8437
http://www.hindawi.com/journals/afs/2012/125086/
http://www.math.sk/fsta2012/presentations/dankova-perfilieva.pdf

21. Direct 2D fuzzy transform

22. Inverse 2D fuzzy transform

23. Thank you!