Image Processing Reference

In-Depth Information

Image 1

Image 2

X

Y

FIGURE 8.7: Two images and sample subimages with matching descriptions

Weak Tolerance Nearness Relation

DEFINITION 8.10

Let

O,
F

be a perceptual system and let

X, Y ⊆ O

and

∈

.A t

X

is

perceptually
almost
near to a set

Y

in a weak sense within the perceptual system

O,
F

F
, if and only if the following condition is satisfied:

∃ x ∈ X, ∃ y ∈ Y, ∃B⊆
F

and is shown with

x
=
B,ε
y

Consequently, weak tolerance nearness relation is defined on

such that

P

(

O

) as follows:

F
=
{
(
X, Y
)
∈P
(
O
)
×P
(
O
)

| X
F
Y }

(8.16)

.

Aset
X
is a near set iff there is
Y ⊆ O
such that
X
F
Y
. The family of near sets

of a perceptual system is denoted by

Near Sets

Let

O,
F

be a perceptual system and let

X ⊆ O

DEFINITION 8.11

Near
F
(

O

)

Tolerance Near Sets
Let
O,
F
be a perceptual system and

DEFINITION 8.12

let

X ⊆ O

.Aset

X

is a tolerance near set iff there is

Y ⊆ O

such that

X
F
Y

.

The family of tolerance near sets of a perceptual system is denoted by

Near

F
(

O

)

8.3

Analysis and Comparison of Images Using Tolerance

Classes

Tolerance classes as described in section 8.2.2, can be viewed as structural elements

in representing an image. The motivation for using tolerance classes in perceptual

image analysis is the conjecture that visual perception in the human perception is

performed in the class level rather than pixel level.

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