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 – increasing operator
cross
block

7. Erode – reducing operator
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
Contexts in total: 16, Pixels removed: 377 of 40000

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?