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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