Image Processing Reference
In-Depth Information
allocated between
1i N
is considered as a set of the pixels correlated with adjacent
pixels. Considering periodic layout of filters (lattice filters - color filter array (CFA) the given
correlations will show periodicity. Being based on it in considered article the assumption
about identity of scales of pixel sets with different
x
and
y
that a set of the correlated pixels,
and according to their weight for each pixel in
I(
are identical.
Let's consider the right member of equation (1.1) as
filter F
applied to
I(
, designating
operation of a filtration
F( I( )
as well as summed averaged square errors from both sides
from
I(
, we receive:
WH N
1
2
MSE( F( I( )))
I( x
x , yy) (x y )|
(2)
i
i
i
WH
x1y1i1
Where H and W - height and width of an image accordingly. Adding the virtual correlated
pixel
αN+1
=-1,
ΔxN+1
= Δ yN+1=0, the equation (1.2) assumes more arranged air:
2
WH N
1
MSE( F( I(
)))
I( x
x , y
y )
.
(3)
i
i
i
WH
x1y1i1
The extension of the equation (1.3) gives the square form rather Х = {α
1
,
α2
, …,
αN+1
}
T
:
T
MSE( F( I(
)), I(
))
X
AX
,
Where
WH
1
A(i, j)
I( x
x ,y
y ) I(x
x ,y
y )
,
1 ,j N1
.
i
i
j
j
WH
x1y1
The coefficient of a matrix
A
contains the full information for determination of variable
vector
Х
, however, in article obtaining Х optionally and for the further analysis enough
matrix affirms that
A
.
It was empirically revealed that the correlated pixels mask shown in a figure 2, yields good
result (N=12).
On a following step the analysis of principal components is done.
Fig. 2. Correlated pixels mask, where — is a center and
Δ
— correlated pixels
Numerical values of elements
A
after obtaining are normalized:
*
Ai,j
A(i,j) A/A,
(1
i, j
N
1),