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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