Image Processing Reference
In-Depth Information
is represented by an array S b
S b
= [H i
: i∈G b ], where G b
= [g a , . . . , g b , . . . , g max ]
H i
= H i when (i = g a or i≥g b ), H i
= 0 elsewhere.
In a similar manner, the dark region after the association is represented by an array S d
S d
= [H i
: i∈G d ], where G d
= [g min , . . . , g d , . . . , g a ]
H i
= H i when (i = g a or i≤g d ), H i
= 0 elsewhere.
In order to decide whether the graylevel bin corresponding to the gray value g a belongs to
the bright or dark region, we need to determine the corresponding errors Err d and Err b .
As mentioned earlier, our measure of an association error (Err) comprises of a proximity
error measure (e p ) and a change error measure (e c ). We represent an association error as
Err = (α + βe c ) + e p
where α and β are constants such that α + βe c and e p take values from the same range,
say, [0, 1].
In order to determine the errors e p and e c corresponding to the bright and dark regions,
let us consider the arrays S b and S d , respectively. We define the change error due to the
association in the bright region as
GA(S b )−GA( S b )
GA(S b ) + GA(
e c
S b )
where the array S b is obtained by replacing H g a by 0 in S b and GA(S ) gives the grayness
ambiguity in the image region represented by the graylevel bins in an array S . The grayness
ambiguity in the image region is calculated using the expression in (3.30) or (3.31). Note
that, the grayness ambiguity is calculated for a region in an image here and not for the
whole image as presented in Section 3.3. Now, in a similar manner, the change error due
to the association in the dark region is given as
GA(S d )−GA( S d )
GA(S d ) + GA( S d )
e c
where the array S d is obtained by replacing H g a by 0 in S d . It is evident that the expressions
in (3.37) and (3.38) measure the change in grayness ambiguity of the regions due to the
association of g a and hence we refer the measures as the change errors. The form of these
expressions is chosen so as to represent the measured change as the contrast in grayness
ambiguity, which is given by the ratio of difference in grayness ambiguity to average grayness
ambiguity. As can be deduced from (3.37) and (3.38), the change errors would take values
in the range [−1, 1]. It is also evident from (3.37) and (3.38) that the change error may
take a pathological value of 0/0. In such a case we consider the change error to be 1.
Next, we define the proximity errors due to the associations in the bright and dark regions
respectively as
1−GA( S b )
e p
S d )
e p
In the above, we take e p = 0, if C×GA( S d ) > 1. It will be evident later from the
explanation of the function GA(·), that the grayness ambiguity measures in (3.39) and
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