Image Processing Reference
In-Depth Information
where P is a non-linear function of pixel's value, its coordinates and its neighborhood
N(y ) .
Structure noise can be suppressed by subtracting additive noise
ij
c
, then dividing pixels
ij
value by normalized frame's values:
x'
( y
c)/f '
,
ij
ij
ij
ij
where
i x' is a corrected pixels value,
i f ' is an approximation of
f
by averaging multiple
ij
(k)
flat-exposure frames
f
, k ..K
:
ij
(k)
f
ij
k
f '
m n
.
ij
(k)
ij
f
i,j,k
This operation cannot be done on
i p , only over raw data from photosensitive matrix
y
ij
prior successive image processing.
Properties of pixel non-uniformity noise
To get better understanding influence of structural noise onto resulted images and
determine its characteristics in the following experiments were done:
Using ambient light 118 images were made on Canon camera with automatic exposure and
focused on infinity. White balance was set to create neutral gray images.
All obtained images possessed pronounced brightness gradient (vignetting). To eliminate
that low-frequency distortion the HF-filter with cutoff frequency at (150/1136)  . Then
images were averaged thus random noise was suppressed and structural noise summed.
Spectrum of the signal resembles white spectrum with decrease of HF-components area,
which is explainable as consequences of color interpolation over pixel neighborhood. PNU-
noises are not presented in saturated and completely dark areas where FPN prevails. Owing
to noise-like of the PNU-components of matrix noise, it is natural to use correlation method
for its detection [16].
2.3 Identification based on non-uniformity of pixels sensitivity
In the absence of access in consumer-grade cameras to sensors output i y , usually it is
impossible to extract PNU from gray-frame. However it is possible to approximate noise by
averaging multiple images p(k) k= 1,…,Np. Process speed-up is performed by filtering and
averaging of residual noise n(k) :
(
k
)
(
k
)
(
k
)
n  .
Other advantage of operation with residual noise that low-frequency component of PRNU is
automatically suppressed. It is obvious that, the more the number of images (N> 50), the less
influence of the single source image will take place. Originally, the filter based on wavelet
transform was used. So advantages of this method are:
-
p
F
(
p
)
No access to internals of camera is required;
-
Applicable to all cameras built on the basis of photosensitive matrixes.
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