Filtration

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Filtration

• Filtration methods for binary images
• Filtration methods for color images

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Binary image filtration

• Morphological filters
• Statistical filters

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Color image filtration

• Statistical
• Color distance based

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Morphological filters

• Based on basic morphological operations Erode
  Dilate
• Erosion
• Dilation
• X an image
• A Structural element

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Structural element

• Usual SEs are
• cross
• block
• Also could be any form

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Dilate increasingoperator
cross
block
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Erode reducingoperator
cross
block
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Open filter

• Sequential applying
• Erosion
• Dilation

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Open example
cross
block
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Close filter

• Sequential applying
• Dilation
• Erosion

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Close example
cross
block
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Sequential filters

• Open-close filter
• Close-open filter

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Rank operator

• A structural element of n cells
• boolean function of n variables
• where binary image

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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

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Median filter for binary images

• , where n is odd, and

cross
block
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Statistical filters

• Based on probability statistics of filtered
  pixel within a local neighborhood
• Better pixel prediction with extended
  templates

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Statistical filters

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

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Morphological vs. Statistical

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

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Statistics example 1
Nb 104 Nw 152 P(bc) 2.87 Threshold
5 Pixel will be changed to white
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10 threshold
Contexts in total 16, Pixels removed 377 of 40000
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Context tree filtering

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

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Color image filtration

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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

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Context tree filtration
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End of day 1

• Questions?