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),
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