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 Based on basic morphological operations: Erode & Dilate Erosion: Dilation: X – an image A – Structural element

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

Dilate – increasing operator cross block

Erode – reducing operator cross block

Open filter Sequential applying Erosion Dilation

Open example: cross block

Close filter Sequential applying Dilation Erosion

Close example cross block

Sequential filters Open-close filter Close-open filter

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

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

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

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

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

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

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

10% threshold Contexts in total: 16, Pixels removed: 377 of 40000

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

Color image filtration

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

Context tree filtration

End of day 1 Questions?