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Dr. Chittaranjan Verma delivered this lecture for Digital Image Processing course at B R Ambedkar National Institute of Technology. It includes: Restoration, Noise, Only, Degradation, Colors, Pictures, Digital, Image, Processing, Harmonic, Mean, Filter
Typology: Slides
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N u v
3
Mean filters ^
^
^
^
^
Order statistics filters ^
^
^
^
5
Output is based on ordering (ranking) the pixels in asubimage ^
Replaces the value of a pixel by the median of thegray levels in the neighborhood of that pixel ^
Excellent
for
removing
both
bipolar
and
unipolar
impulse noise
( , )
xy
s t
S
6
Median filter: Example
8
Max and Min filters: Example
Input imageis corruptedwith peppernoise (left)and saltnoise (right)
9
Midpoint filter ^
Filter output is the midpoint between maximum andminimum values of the gray levels in a subimage ^
Combines order statistics and averaging ^
Midpoint filter works best for randomly distributednoise (Gaussian or uniform noise)
^
^
^
^
( , )
( , ) 1
( ,
)^
max
( , )
min
( , )
2
xy
xy^
s t
S
s t
S
f^
x y
g s t
g s t
^
^
^
12
Adaptive filters ^
The behavior of adaptive filters changes according to thestatistical
characteristics
of
the
image
in
the
filter
region
(subimage S
)xy^
^
This will enable the filters to have the desired response evenif the image has regions with totally different characteristics ^
Statistical
characteristics
considered:
Local
mean,
local
variance, local maximum, local minimum, local median, globalmean, global variance and noise variance ^
We study two adaptive filters: ^
Adaptive, local noise reduction filter ^
Adaptive median filter
14
The behavior of the filter ^
If^
2 = 0 (no noise)
f(x,y) = g(x,y)
, the filter should return
simply the value of
g(x,y)
^
If the local variance (
2 ) is high relative to noise variance
(^2)
the
filter
should
return
a^
value
close
to
g(x,y)
i.e. ^
High
local
variance
S
xy^
is^
associated
with
edges,
so
preserve the edges
^
If the two variances are equal , we want the filter to returnthe arithmetic mean value of the pixels in S
.xy
^
This condition occurs when local area has same properties asoverall image, and local noise is to be reduced by simpleaveraging (in this case, edges are not blurred)
15
Mathematical expression of the filter
^
2 2
( ,
)^
( ,
)^
( ,
)^
L
L
f^
x y
g x y
g x y
m
NOTE: In real situations, the exact knowledge of noise variance(
2 ) is not known a priori. ATTENTION: Negative gray levels occur when
(^2)
(^2) L
17
Suitable for higher level of salt and pepper noise(P
a^
= P
b^
0.2 as a rule of thumb)
^
AdvantagePreserve details while smoothing non-impulse noise(a traditional median filter is not capable of doing this) ^
Unlike previously discussed adaptive filter, theadaptive median filter changes (increases) the sizeof S
xy
during filter operation depending on certain
conditions
18
Adaptive median filter Suppose:
z^ min
and z
max
= minimum and maximum gray levels in S
xy
z^ med
= median of gray levels in S
xy
z^ xy
= gray level at coordiante (x,y) Smax
= maximum allowed size of S
xy
Algorithm:Level A:
A1 = z
med
min
A2 = z
med
max
if A1 > 0 AND A2 < 0, Goto Level BElse increase the window sizeif window size
≤ S
max
, repeat Level A
Else Output z
xy
Level B:
B1 = z
xy^
min
B2 = z
xy^
max
if B1 > 0 AND B2 < 0, output z
xy
Else Output z
med
