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Filtration

Filtration. Filtration methods for binary images Filtration methods for color images. Binary image filtration. Morphological filters Statistical filters. Color image filtration. Statistical Color distance based. Morphological filters.

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Filtration

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  1. Filtration Filtration methods for binary images Filtration methods for color images

  2. Binary image filtration • Morphological filters • Statistical filters

  3. Color image filtration • Statistical • Color distance based

  4. Morphological filters • Based on basic morphological operations: Erode & Dilate • Erosion: • Dilation: • X – an image • A – Structural element

  5. Structural element • Usual SE’s are: • cross • block • Also could be any form

  6. Dilate – increasingoperator cross block

  7. Erode – reducingoperator cross block

  8. Open filter • Sequential applying • Erosion • Dilation

  9. Open example: cross block

  10. Close filter • Sequential applying • Dilation • Erosion

  11. Close example cross block

  12. Sequential filters • Open-close filter • Close-open filter

  13. Rank operator • A – structural element of n cells • boolean function of n variables • where binary image

  14. Rank operator • , where boolean function of n variables • Which have value of 1 if at least k variables equals to 1, and 0 otherwise • where is a complimentary part of A

  15. Median filter for binary images • , where n is odd, and cross block

  16. Statistical filters • Based on probability statistics of filtered pixel within a local neighborhood • Better pixel “prediction” with extended templates

  17. Statistical filters • First phase – determining statistical context of the image • Second phase – flipping pixels with low probability values, assuming they as noise.

  18. Morphological vs. Statistical • Statistical – 2 pass filters. • With big templates huge memory consumption. • Statistical filters adapt to the image.

  19. Statistics example 1 Nb = 104 Nw = 152 P(b|c) = 2.87% Threshold = 5% Pixel will be changed to white

  20. 10% threshold

  21. Context tree filtering • Fixed template • Huge memory consumption • , where k is the size of template • Not all context are used

  22. Color image filtration

  23. Statistical filters • Fixed template • Enormous memory consumption • , where k is the size of template, and n is amount of colors • Not all context are used

  24. Context tree filtration

  25. End of day 1 Questions?

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