Graphics Reference
In-Depth Information
scanned image, this effect may become formidable if
max
exceeds a certain
value. However, for a Hilbert scanned image, this effect is almost negligible
even for a very high value
max
.
For Algorithm 2:
•
A separate algorithm selects only those segments that are homogeneous
in some sense. For this, an image is considered as an intensity surface
and the homogeneity concept of pixels over segments is viewed as a small
deformation space curve on this intensity surface.
•
Length of a homogeneous segment of pixels depends on the standard error
of deformation of the segment from its equilibrium position.
•
Different homogeneous segments in an image are approximated with dif-
ferent values of
max
, which are automatically determined in the process
of approximation. The performance of the algorithm, therefore, does not
depend on
max
as in algorithm 1, but on the chosen value for the standard
error.
3.6 Regeneration
Reconstruction of the image during decoding is done using quadratic B-B
polynomial. We use here the recursive computation algorithm based on New-
ton's forward difference scheme as described in [27, 26]. Let
y
=
at
2
+
bt
+
c
be
a polynomial representation of the equation (3.4) where the constant param-
eters a, b, and c are determined by the three pixels (two end pixels and one
mid pixel) of the arc segment. The usual Newton's method for evaluating the
polynomial results in multiplications and does not make use of the previously
computed values to compute new values.
Assume the parameter
t
ranges from 0 to 1. Let the incremental value be
q
. Then the corresponding
y
values will be
c
,
aq
2
+
bq
+
c
,4
aq
2
+2
bq
+
c
,
9
aq
2
+3
aq
+
c
,
···
. It is observed from [27, 26] that
2
y
j
=2
aq
2
2
y
j
+1
+
y
j
=2
aq
2
and
y
j
+2
−
j
≥
0
.
This leads to the recurrence formula
y
o
+2
aq
2
y
2
=2
y
1
−
(3.20)
that involves just three additions to get the next value from the two preceding
values at hand. Since the gray segment size is known, the increment
q
can be
obtained from
q
=
1
segment size −
1
The regenerated gray value
y
2
can therefore
be determined from equation (3.20).
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