Image Restoration - Old Dominion Universityww2.odu.edu/~kiftekha/ECE783_883/handout...
27
Image Restoration Reference Gonzalez and Woods, Digital Image Processing, 2 nd Ed, Prentice Hall, 2002. Khan Iftekharuddin ISIP Lab
Transcript of Image Restoration - Old Dominion Universityww2.odu.edu/~kiftekha/ECE783_883/handout...
Image Restoration
ReferenceGonzalez and Woods, Digital Image
Processing, 2nd Ed, Prentice Hall, 2002.
Khan IftekharuddinISIP Lab
ISIP Lab/KMI
Image RestorationImage Restoration
ISIP Lab/KMI
•pdf of Gausssian random variable z:
70% of values are in [(µ-σ),(µ+σ)]
95% of values are in [(µ-2σ),(µ+2σ)]
•pdf of Rayleigh noise:
Noise ModelsNoise Models
22 2/)(
21)( σµ
σπ−−= zezp
44(4/
:var,0
,)(2)(
2
/)( 2
πσπµ −=+=
≤
≥−=−−
bandba
areianceandmeanTheazfor
azforeazbzp
baz
ISIP Lab/KMI
Noise ModelsNoise Models
Erlang (Gamma) noise pdf:2
2
1
;0,0
0,)!1()(
aband
ab
zfor
zforebza
zpaz
bb
==
<
≥−=
−−
σµ
Uniform noise pdf:12
)(,2;,0
,1)(
22 abba
otherwise
bzaifabzp −
=+=
≤≤
−= σµ
Impulse (salt-and-pepper) noise pdf:
.;,0,,
)( dotlightaasappearwillblevelgrayabIfotherwise
bzforPazforP
zp b
a
−>
==
=
ISIP Lab/KMI
Noisy ImagesNoisy Images
ISIP Lab/KMI
Noisy ImagesNoisy Images
ISIP Lab/KMI
Noisy ImagesNoisy Images
ISIP Lab/KMI
Additive Noise RemovalSpatial Filtering
Additive Noise RemovalSpatial Filtering
Arithmetic Mean filter
∑∈
=xySts
tsgmn
yxf),(
),(1),(
Similar to convolution mask. Sxy is the nxn filter
Geometric mean filtermn
Sts xy
tsgyxf
1
),(
),(),(
= ∏
∈
Harmonic filter
∑∈
=
xySts tsg
mnyxf
),( ),(1),(
ISIP Lab/KMI
Additive Noise RemovalSpatial Filtering
Additive Noise RemovalSpatial Filtering
Contraharmonicmean filterQ ->order of filter
For +ve->removes pepper noise
For –ve->removes salt noise
For Q=0 ->arithmetic
For Q=-1 -> mean
∑
∑
∈
∈
+
=
xy
xy
Sts
QSts
Q
tsg
tsgyxf
),(
),(
1
),(
),(),(
ISIP Lab/KMI
Spatial FilteringSpatial Filtering
ISIP Lab/KMI
Order-Statistics FiltersOrder-Statistics Filters
Filters
Median
Max and Min
Midpoint
ISIP Lab/KMI
Spatial FiltersSpatial Filters
ISIP Lab/KMI
Spatial FiltersSpatial Filters
Alpha trimmed mean filter
levelsgraytotaldtsgdmn
yxfxyStsr ;),(1),(
),(∑∈−
=
ISIP Lab/KMI
Adaptive Spatial FilteringAdaptive Spatial Filtering
ISIP Lab/KMI
Frequency filtersFrequency filters
ISIP Lab/KMI
Butterworth FilteringButterworth Filtering
ISIP Lab/KMI
Frequency FiltersFrequency Filters
ISIP Lab/KMI
Frequency filteringFrequency filtering
ISIP Lab/KMI
Interference noiseInterference noise
ISIP Lab/KMI
Degraded ImpulseDegraded Impulse
ISIP Lab/KMI
Turbulence NoiseTurbulence Noise
6/5)^2^2^{exp( vuk +−Turbulence Model
ISIP Lab/KMI
Blurred Image Restoration - IFBlurred Image Restoration - IF
ISIP Lab/KMI
Motion Blur onlyMotion Blur only
ISIP Lab/KMI
Inverse and least mean square (wiener) FilteringInverse and least mean square (wiener) Filtering
ISIP Lab/KMI
Motion Blur+ noiseIF and wiener filteringMotion Blur+ noise
IF and wiener filtering
ISIP Lab/KMI
Constrained least square filteringConstrained least square filtering
ISIP Lab/KMI
Iterative Constrained least square filteringIterative Constrained least square filtering
