S.
Zhu
et
al.
/
Int.
J.
Electron.
Commun.
(AEÜ)
68
(2014)
795–805
797
Fig.
2.
The
proposed
fractal
video
sequence
codec
structure.
Fig.
3.
Sketch
map
of
the
vertical
and
horizontal
boundaries.
the
boundary
formed
by
block
effect
(false
boundary)
of
the
image.
If
the
pixels
meet
the
following
conditions,
the
filtering
process
will
be
implemented.
⎧
⎪
⎨
⎪
⎩
abs(P
0
−
Q
0
)
<
(2
QP/6
−
1)
×
0.8
abs(P
0
−
P
1
)
<
(QP
>>
1)
−
7
abs(Q
0
−
Q
1
)
<
(QP
>>
1)
−
1
(1)
The
QP
means
the
quantization
parameter
used
in
the
codec.
If
the
true
boundary
happens
to
occur
at
the
boundary
of
two
mac-
roblocks
that
is
intra-coded,
the
adjacent
pixels
will
not
satisfy
the
conditions.
Then
the
true
boundary
will
not
be
filtered.
While
for
the
false
boundary,
strength
of
the
filter
depends
on
the
coding
modes
of
neighboring
blocks
and
the
gradient
of
image
samples
across
the
boundary.
Otherwise,
the
worse
coding
performance
will
be
got.
In
this
paper,
the
proposed
loop
filter
is
used
for
fractal
video
coding.
As
shown
in
Fig.
4,
it
makes
a
more
faithful
reproduction
of
the
original
frame
than
a
blocky
and
unfiltered
image,
so
the
visual
quality
of
the
decoded
image
increases.
2.1.3.
Sub-pixel
block
matching
In
order
to
obtain
more
accurate
motion
vectors,
sub-pixel
motion
compensation
is
brought
into
fractal
coding
algorithm.
For
an
inter-coded
macroblock,
a
better
motion
compensated
predic-
tion
may
be
formed
by
predicting
from
sub-pixel
positions
in
the
reference
block.
Since
the
values
at
sub-pixel
positions
do
not
exist
in
the
reference
picture,
it
is
necessary
to
create
them
by
using
interpolation
from
nearby
image
pixels.
Fig.
5
is
the
comparison
of
peak
signal
to
noise
ratio
(PSNR)
and
compression
ratio
(CR)
for
“foreman”
sequence
(352
×
288
pix-
els).
Table
1
provides
the
average
PSNR
and
CR
performances.
From
Table
1,
we
can
observe
that
the
proposed
algorithm
yields
up
to
0.207
dB
and
5.139
CR
gain
over
the
original
algorithm.
Therefore,
it
is
quite
effective
in
improving
the
coding
performance.
2.2.
An
efficient
searching
algorithm
2.2.1.
Pre-searching
limitation
condition
In
general,
there
are
several
ways
to
determine
the
coefficients
(i.e.,
contrast
scaling
factor
and
brightness
offset)
of
intensity
affine
mapping
for
an
input
range
block.
In
this
paper,
RMS
(root
mean
square)
is
used
as
the
error
between
R
block
and
the
matching
D
block.
Given
two
blocks
containing
m
pixel
intensities,
d
1
.
.
.d
m
(from
D
i
)
and
r
1
.
.
.r
m
(from
R
i
),
and
appropriate
values
for
s
and
o,
we
can
seek
s
and
o
to
minimize
RMS:
RMS
=
1
m
m
j=1
(s
·
d
j
+
o
−
r
j
)
2
(2)
where
s
is
a
scaling
factor
and
o
is
an
offset.
When
the
partial
deriva-
tives
with
respect
to
s
and
o
are
both
zero,
the
minimum
RMS
can
be
obtained.
And
the
equations
to
compute
s
and
o
are
as
follows:
s
=
⎡
⎣
m
m
j=1
d
j
r
j
−
m
j=1
d
j
m
j=1
r
j
⎤
⎦
⎡
⎢
⎣
m
m
j=1
d
2
j
−
⎛
⎝
m
j=1
r
j
⎞
⎠
2
⎤
⎥
⎦
(3)
Table
1
Comparison
of
average
results
by
using
the
original
algorithm
and
the
proposed
algorithm.
Algorithms
PSNR/dB
CR
Original
algorithm
32.660
65.408
Proposed
32.867
70.547
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