Image Processing Reference
In-Depth Information
Chapter 3
How Accurate Is the Logic-Based
Filter?
3.1 Optimum Filter Error
In most practical situations, even the optimal filter within a finite window is unable
to recover the original image exactly. However, the remaining error will be the
smallest possible for that window. Returning to the observations for the simple ex-
ample shown in Fig. 2.8, it can be seen that for the line of the table discussed,
x
= (1,
0, 1), the output of the filter was set to 1. While this gave the correct output value for
four of the pixels, it still left one in error. In general, each input
x
will make a contri-
bution to the error equivalent to the smaller of the two values of
N
0
or
N
1
. The error
from each input may be totaled to give the overall filter error.
The MAE arising from the optimum filter is therefore
=
∑
(
)
min
NN
RC
,
(
)
(
)
o
1
MAE
ψ
I
,
I
(3.1)
n
o
for an image containing
R
rows and
C
columns.
Figure 3.1
Calculation of error after filtering with the optimal filter. The shaded areas repre-
sent the error arising from each input.
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