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22
EugeniuszKornatowski
evennumberofelementsissuggestedinthiswork.Thealgorithmconceptisbased
onthefollowingassumptions:
1.TheresultofenlarginganMxNsizepictureisapicturehaving(2M-1)x(2N-1)
pixels.
2.Originalpicturepixelsareinterpolationalgorithmnodsandwillbepassedtothe
outputpicturewithoutanychanges.
3.Thetopleftandthebottomrightpixelonboththeoriginalandtheoutput
pictureremainthesame.
4.Inputpicturehasinterference.
5.Interpolationalgorithmmustenabletocalculatethreesetsofnewpointsin
outputpicture,i.e.:Y(m,n+q),Y(m+p,n),Y(m+p,n+q).
Asonlytwiceresamplingissueisconsidered,thenp=q=0.5.
Meetingtheaboveassumptions,whenapplyinginterpolationalgorithmthe
followingwindowdefinitionsformedianfilterarerecommended:
a)Y(m,n+0.5)pointgenerating:horizontalwindow:
Wb1'
=
{X(m,
n
+
l),
-
L
≤
l
≤
L
+
1}
(11)
b)Y(m+0.5,n)pointgenerating:verticalwindow:
Wb2'
=
{X(m
+
l,
n),
-
L
≤
l
≤
L
+
1}
(12)
c)Y(m+0.5,n+0.5):pointgenerating:squarewindow:
Wb3'
=
{X(m
+
l
1
,
n
+
l
2
),
-
L1
≤
l
1
,
l
2
≤
L1
+
1}
(13)
Interpolationfiltermedianalgorithmgoesaccordingtothefollowingequations:
Y(m,
n
+
0.5)
=
Med{X(m,
n)
∈
Wb
1
'
}
(14)
Y(m
+
0.5,
n)
=
Med{X(m,
n)
∈
Wb
2
'
}
(15)
Y(m
+
0.5,
n
+
0.5)
=
Med{X(m,
n)
∈
Wb
3
'
}
(16)
andaccordingtotheassumptions2and3:
Y(m,
n)
=
X(m,
n)
(17)
Equationsfrom(14)to(16)describemedianfilteringprocesshavingawindow
withtheevennumberofelements.Therefore,determinationofanoutputsampleis
ambiguous.Oneofpossiblesolutionsisadoptingaconceptionpreviously
presented,i.e.theequation(10),whichhasjustbeenusedinthepresented
algorithm.
4.PRACTICALANALYSEOFMEDIANINTERPOLATION
ALGHORIYHMEFFECTIVENESS
Themedianinterpolationalgorithmshownherehasbeenpracticallytestedon
picturematrixdensityincreasingprocessappliedtoapicturewith256shadesof
grey.Inexamplesshownbelow,interpolationmedianfilterhadwindowswiththe
parametersofL=1andL1=0.
