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the segments of same size is noticeable. Each of the gray s
e
gments is a Bezier
a
rc and is represented by its three param
e
ters, namely
v
o
,
v
1
and
v
2
. Of them,
v
1
may not be an integer. So, instead of
v
1
, we consider the integer part of the
reconstructed data point
d
1
(say) at
t
=
2
for the segment. We designate this
pixel by
v
d
.Thus,
v
o
,v
d
,v
2
,and
n
completely specifies an approximated data
segment, where
v
o
,v
d
,and
v
2
are the three pixel brightness values on the arc.
These brightness values (approximation parameters) in an image are found to
frequently occur for different segments. Consequently, Huffman coding for all
the parameters provide good results for compression of images. Furthermore,
v
o
,v
d
,and
v
2
being the brightness values, they are found to be indistinguish-
able from their neighboring values when they differ by small values. This fact
can be used to reduce the number of independent brightness values to be en-
coded. The number of parameters drastically decreases when all the arcs are
replaced by horizontal line segments. This increases the compression ratio at
the cost of quality of the reconstructed image in terms of PSNR value. We,
therefore, have the following two different situations for compression:
(a) when the segments are all quadratic arc segments,
(b) when the segments are all replaced by horizontal line segments.
Let
θ
l
,
θ
v
o
,
θ
v
d
,and
θ
v
2
be the average number of bits/pixel for the length
of segments, and the parameters
v
o
,
v
d
,and
v
2
, respectively. The total number
of bits
N
b
, when the segments are all arcs, is given by,
(
N
b
)
A
=
N
s
(
θ
l
+
θ
v
o
+
θ
v
2
+
θ
v
d
)
,
(3.18)
where,
N
s
=number of segments.
When all the segments are lines, the number of bits reduces to
(
N
b
)
L
=
N
s
(
θ
l
+
θ
bl
)
(3.19)
where
θ
bl
is the average number of bits/pixel for the pixel values on line
segments.
3.5.1 Discriminating Features of the Algorithms
Below we provide the discriminating features of the two proposed algorithms.
For Algorithm 1:
•
Segmentation of pixels does not need any separate algorithm. The approx-
imation scheme itself selects the specific segments.
•
The method of approximation depends on the selection of
max
and
min
.
The values of these parameters are the same for all segments in the im-
age. The resulting performance in reconstruction, therefore, is parameter
dependent.
•
For large
max
, the possibility of long homogeneous segments of pixels for
satisfying the approximation criterion increases. This may introduce visual
disparity (smearing effect) between the original and the reconstructed seg-
ments. This, in turn, may affect the overall picture quality. For a raster
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