Image Processing Reference
In-Depth Information
1th Tol class. subimage:5
2th Tol class. subimage:9
The original image
161
139
161
78
80
152
66
116
114
The tolerance class displayed on a white background
The tolerance class displayed on the image
3th Tol class. subimage:4
4th Tol class. subimage:8
(8.4a)
(8.4b)
FIGURE 8.4: (a) The image covering, (b) all classes
O / = B =
{x / = B | x ∈ O}
function
φ k ∈B
, a tolerance matrix
TM k
=[
t ij ] is defined as in equation 8.11,
where the elements
t ij
of the matrix will be zero if subimages
x i
and
x j
do not
belong to the same tolerance class which is defined by
x i .
t ij =
φ k (
x j )
if
x j ∈ x i/ = B
(8.11)
0
otherwise
OTM
) is defined by removing iden-
tical rows in the tolerance matrix (identical tolerance classes) and sorting out the
rows (classes) based on the average value of
Subsequently, an Ordered Tolerance Matrix (
φ k (
x
) among the perceptual objects of
each tolerance class.
Example 8.5
In example 8.4, there are 9 perceptual objects (equation 8.1) and 4 tolerance classes.
The tolerance matrix
1 (average gray value
between 0 and 255) will be a 9 × 9 matrix as follows with 4 non redundant rows:
TM
defined for the only probe function
φ
162 0 0 140 0 0 162 153 0
0 9 70 10000
0 9 70 10000
162 0 0 140 0 117 162 153 115
0 9 70 10000
0
TM φ 1 =
{t ij }
=
(8.12)
0
0
140
0
117
0
0
115
162
0
0
140
0
0
162
153
0
162
0
0
140
0
0
162
153
0
0
0
0
140
0
117
0
0
115
j th
The element
t ij
of the tolerance matrix is set to the average gray value of
th and
th subimages belong to the same tolerance class that is defined
subimage if
i
j
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