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d
d
c
c
e
b
b
k
1
k
3
−→
k
1
k
3
a
k
2
a
k
2
(
a
)
(
b
)
Fig. 1.14.
Undesirable loop: (a) Before cleaning; (b) After cleaning.
1.7 Approximation Capability and Effectiveness
So far, we have dealt with different approximation techniques based on Bezier-
Berntein spline polynomial. Here we show their approximation capability.
Consider the Figures 1.15 and 1.17(a) of two different digital contours, namely
a butterfly and a chromosome. Key pixels and the points of inflection detected
on them are marked by “3” and “
I
” respectively. Images regenerated by Meth-
3
oo3oo
I o
ooo
oooo
3
o
ooo
oo
o
o
o
o
o
o
o
3
ooo
3
oo
o
o
ooo
o
o
o
o
o
o
3
3
o
o
o
o
o
3
3
o
o
o
o
3
o
3
o
o
I
I
o
o
o
o
oo
o
o3
3
o
o
3
3
o
o
3
o
o
o
o
o
3
o
I
o
o
3
o
o
o
3
o
o
o
o
o
o
o
o
I
o
o
o
I
o
o
o
o
3
o
I
o
o
o
3
3
o
o
o
3
o
o
3
3
3
Fig. 1.15.
Butterfly input.
ods 1 and 2 corresponding to the butterfly and chromosome images are shown
in Figures 1.16(a), (b), and (c), and 1.17(b) and (c), respectively. Positions of
key pixels in both the input and output remain unaltered.
As a typical illustration, section 1.6.4 shows the effectiveness of the clean-
ing operations on the generated points for the butterfly image. Figure 1.16(b)
shows such an intermediate state for Method 1 before its final reconstructed
output. Here,
d
denotes a pixel to be deleted and
X
corresponds to the posi-
tion where a pixel is to be inserted to keep connectivity.
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