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INTRODUCTION
INTRODUCTION


Median is a quite popular non-linear filter in image processing.
Median is a quite popular non-linear filter in image processing. Most often it is used to remove impulsive noise, like "salt & pepper" noise, "dead" and "hot" pixels, dirt on film, etc. This is because it behaves kind of "inversely" compared to linear denoisers. The more a bad pixel stands out from the surrounding area, the bigger residual it will leave with a linear filter - but the more probably it will be eliminated by the median.
Most often it is used to remove impulsive noise, like
"salt & pepper" noise, "dead" and "hot" pixels, dirt on film, etc.
This is because it behaves kind of "inversely" compared to
linear denoisers. The more a bad pixel stands out from the
surrounding area, the bigger residual it will leave with a linear
filter - but the more probably it will be eliminated by the median.
 
The down side is that the median operation is quite slow. As an
order-statistic filter, it is similar to sorting, that must be
done for each pixel, so using a fast algorithm is very important. For the small medians, the algorithms of the type described in [1] are used here, with some small modifications for a further slight improvement in speed.
For the "Variable size" median, code from [2] is used.
The compound filters (ArceBI, ML3D, ML3dEX) are made
according to the formulas given in [3].
For more info on median filtering see
http://en.wikipedia.org/wiki/Median_filter
 


The down side is that the median operation is quite slow. As an order-statistic filter, it is similar to sorting, that must be done for each pixel, so using a fast algorithm is very important. For the small medians, the algorithms of the type described in [http://ndevilla.free.fr/median/median/src/optmed.c this page] are used here, with some small modifications for a further slight improvement in speed. For the "Variable size" median, code from <ref>Simon Perreault, Patrick Hebert: Median filtering in constant time, [http://nomis80.org/ctmf.pdf PDF version], [http://nomis80.org/ctmf.html HTML version]</ref> is used. The compound filters (ArceBI, ML3D, ML3dEX) are made according to the formulas given in the corresponding work<ref name="anil">[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.36.9618&rep=rep1&type=pdf Anil Christopher Kokaram: Motion Picture Restoration, Ph.D. thesis]</ref>. For more info on median filtering see [http://en.wikipedia.org/wiki/Median_filter Wikipedia article].


IMPLEMENTED ALGORITHMS
IMPLEMENTED ALGORITHMS


Cross5:
;Cross5
Median of the pixel with its top, bottom, left and right neighbor.
:Median of the pixel with its top, bottom, left and right neighbor.
 
Square3x3:
Median of the pixel with the surrounding 8 pixels. (3x3 box)
 
Bilevel:
First, make cross5 median, then make median of the pixel with its
four diagonal neighbors, and finally take the median of the pixel
and the two previously calculated medians.
Slightly better preserves detail than the simple medians above.


Diamond3x3:
;Square3x3
Takes median of the pixel with 12 neighboring pixels arranged in a
:Median of the pixel with the surrounding 8 pixels. (3x3 box)
diamond pattern.


Square5x5:
;Bilevel
Median of the pixel with the 5x5 surrounding box.
:First, make cross5 median, then make median of the pixel with its four diagonal neighbors, and finally take the median of the pixel and the two previously calculated medians. Slightly better preserves detail than the simple medians above.


Temp3:
;Diamond3x3
Temporal only median of three frames. Can be used to reduce
:Takes median of the pixel with 12 neighboring pixels arranged in a diamond pattern.
single frame time-impulsive noise like photoflash.
Delays the video by 1 frame.


Temp5:
;Square5x5
Temporal only median of five frames. Can be used to reduce
:Median of the pixel with the 5x5 surrounding box.
double frame time-impulsive noise, but the artifacts on fast moving
objects are stronger than with temp3.
Delays the video by 2 frames.


ArceBI:
;Temp3
Spatio-temporal multilevel median, as described by Arce. See [3].
:Temporal only median of three frames. Can be used to reduce single frame time-impulsive noise like photoflash. Delays the video by 1 frame.
Delays the video by 1 frame.


ML3D:
;Temp5
Spatio-temporal multilevel median, as described by Alp. See [3].
:Temporal only median of five frames. Can be used to reduce double frame time-impulsive noise, but the artifacts on fast moving objects are stronger than with temp3. Delays the video by 2 frames.
Delays the video by 1 frame.


ML3dEX:
;ArceBI
Spatio-temporal multilevel median. Further development of ML3D
:Spatio-temporal multilevel median, as described by Arce. See the corresponding work<ref name="anil" />. Delays the video by 1 frame.
by Kokaram, see [3].
Delays the video by 1 frame.


VarSize:
;ML3D
Simple spatial only median in a user selected size square box
:Spatio-temporal multilevel median, as described by Alp. See the corresponding work<ref name="anil" />. Delays the video by 1 frame.
around each pixel.
The effect could be described as "quasi edge preserving, corner
rounding, small stuff eliminator".
Or maybe just an "artsy blur".


;ML3dEX
:Spatio-temporal multilevel median. Further development of ML3D by Kokaram, see the corresponding work<ref name="anil" />. Delays the video by 1 frame.


;VarSize
:Simple spatial only median in a user selected size square box around each pixel. The effect could be described as "quasi edge preserving, corner rounding, small stuff eliminator". Or maybe just an "artsy blur".


PARAMETERS:
PARAMETERS:


Type:
;Type
selects one of the eleven algorithms
:Selects one of the eleven algorithms


Size:
;Size
Only active when "VarSize" type is selected. Determines the
:Only active when "VarSize" type is selected. Determines the size of the square area over which the median is taken.
size of the square area over which the median is taken.


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REFERENCES
REFERENCES


[1] http://ndevilla.free.fr/median/median/src/optmed.c
<references/>
 
[2]  Simon Perreault, Patrick Hebert: Median filtering in
constant time
http://nomis80.org/ctmf.pdf
http://nomis80.org/ctmf.html
 
[3]  Anil Christopher Kokaram: Motion Picure Restoration
phd disertation

Latest revision as of 11:32, 15 August 2023

Medians

This filter implements several median type filters.

INTRODUCTION

Median is a quite popular non-linear filter in image processing. Most often it is used to remove impulsive noise, like "salt & pepper" noise, "dead" and "hot" pixels, dirt on film, etc. This is because it behaves kind of "inversely" compared to linear denoisers. The more a bad pixel stands out from the surrounding area, the bigger residual it will leave with a linear filter - but the more probably it will be eliminated by the median.

The down side is that the median operation is quite slow. As an order-statistic filter, it is similar to sorting, that must be done for each pixel, so using a fast algorithm is very important. For the small medians, the algorithms of the type described in this page are used here, with some small modifications for a further slight improvement in speed. For the "Variable size" median, code from [1] is used. The compound filters (ArceBI, ML3D, ML3dEX) are made according to the formulas given in the corresponding work[2]. For more info on median filtering see Wikipedia article.

IMPLEMENTED ALGORITHMS

Cross5
Median of the pixel with its top, bottom, left and right neighbor.
Square3x3
Median of the pixel with the surrounding 8 pixels. (3x3 box)
Bilevel
First, make cross5 median, then make median of the pixel with its four diagonal neighbors, and finally take the median of the pixel and the two previously calculated medians. Slightly better preserves detail than the simple medians above.
Diamond3x3
Takes median of the pixel with 12 neighboring pixels arranged in a diamond pattern.
Square5x5
Median of the pixel with the 5x5 surrounding box.
Temp3
Temporal only median of three frames. Can be used to reduce single frame time-impulsive noise like photoflash. Delays the video by 1 frame.
Temp5
Temporal only median of five frames. Can be used to reduce double frame time-impulsive noise, but the artifacts on fast moving objects are stronger than with temp3. Delays the video by 2 frames.
ArceBI
Spatio-temporal multilevel median, as described by Arce. See the corresponding work[2]. Delays the video by 1 frame.
ML3D
Spatio-temporal multilevel median, as described by Alp. See the corresponding work[2]. Delays the video by 1 frame.
ML3dEX
Spatio-temporal multilevel median. Further development of ML3D by Kokaram, see the corresponding work[2]. Delays the video by 1 frame.
VarSize
Simple spatial only median in a user selected size square box around each pixel. The effect could be described as "quasi edge preserving, corner rounding, small stuff eliminator". Or maybe just an "artsy blur".

PARAMETERS:

Type
Selects one of the eleven algorithms
Size
Only active when "VarSize" type is selected. Determines the size of the square area over which the median is taken.


REFERENCES

  1. ↑ Simon Perreault, Patrick Hebert: Median filtering in constant time, PDF version, HTML version
  2. ↑ 2.0 2.1 2.2 2.3 Anil Christopher Kokaram: Motion Picture Restoration, Ph.D. thesis
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