Image Processing Reference
In-Depth Information
j . Notice, also, that
we can formulate a relationship between the description-based intersection
i
Let i, j∈I X , I Y be distinct indices used to identify the classes
C
,
C
i T
j
C
= B C
and
the product of the class sizes C
i · C
j .
Proposition 1
X
i \
X
i∈I X ,
j∈I Y
C
i · C
j .
X
Y
j
X
Y
C
= B,ε C
i∈I X ,
j∈I Y
A measure of the resemblance (i.e., image nearness measure N M
= B (X, Y )) between a pair
of images X, Y is then formulated in Def. 6.
Definition 6 Tolerance Class Intersection-Based Nearness Measure (Peters and
Henry, 2009)
LethO,
ibe a perceptual system and assume X, Y⊆O with coverings defined using the
tolerance relation = B .
F
j denote tolerance classes in X / = B , Y / = B , respectively.
Then a tolerance class intersection-based nearness measure (tiN M
i
Let
C
,
C
= B (X, Y )) is given in
(12.9) to measure the degree of nearness of X, Y is computed using
C
P
i T
j
= B,ε C
i∈I X ,
j∈I Y
C
i · C
j
tiN M
= B,ε (X, Y ) =
P
.
(12.9)
i∈I X ,
j∈I Y
A tolerance class overlap distribution (TOD) nearness measure is based on statistical com-
parison of overlaps between tolerance classes at each subimage. The method is as follows:
Suppose X, Y∈O are two images (sets of perceptual objects). The sets of all tolerance
classes for images X and Y are shown as follows and form a covering for each image.
X /∼ B,ε ={x /∼ B,ε | x∈X},
(12.10)
Y /∼ B,ε ={y /∼ B,ε | y∈Y}.
(12.11)
Subsequently, the set of all overlapping tolerance classes corresponding to each object
(subimage) x is named as Ω X /∼ B,ε (x) and is defined as follows:
X /∼ B,ε (x) ={z /∼ B,ε ∈X /∼ B,ε | x∈z /∼ B,ε }.
(12.12)
Consequently, the normalized number of tolerance classes ω in X /∼ B,ε
which are overlap-
ping at x is defined as follows:
X /∼ B,ε (x)
X /∼ B,ε
ω X /∼ B,ε (x) =
.
(12.13)
Similarly, the set of all overlapping tolerance classes at every subimage y∈Y is denoted by
ω Y /∼ B,ε (y). Assuming that the set of probe functionsBand the value of are known, we use
the more simplified notation of Ω X (x) and ω X (x) for the set X /∼ B,ε
and the notations Ω Y (y)

Search WWH ::

Custom Search