TELKOM
NIKA
, Vol. 11, No. 12, Decem
ber 20
13, pp.
7564
~75
7
0
e-ISSN: 2087
-278X
7564
Re
cei
v
ed
Jun
e
28, 2013; Revi
sed Aug
u
st
15, 2013; Accepted Sept
em
ber 3, 201
3
A Study on Sub-pixel Interpolation Filtering Algorithm
and Hardware Structural Design Aiming at HEVC
Wang G
a
ng
1,
2
, Chen Hexi
n
1
, Chen Mia
n
shu
*
1
, Liu Yuan
y
u
an
1,3
1
School of Co
mmunicati
on E
ngi
neer
in
g, Jili
n Univ
ersit
y
, C
han
gch
un,Ch
in
a
2
School of Mec
han
ical En
gi
ne
erin
g, Baich
e
n
g
Normal C
o
l
l
e
ge, Baich
e
n
g
, Chin
a
3
School of Infor
m
ation T
e
chno
log
y
, Jin
lin Agr
i
cultura
l
Univ
er
sit
y
, Cha
ngc
hu
n, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: haoh
eh
e53
0
@
16
3.com
A
b
st
r
a
ct
Aiming
at th
e
new
-gen
erati
o
n vid
e
o
co
mpr
e
ssi
o
n
stan
dar
d b
e
in
g for
m
u
l
ated-HEV
C
, a
kind
of
sub-p
i
xel i
n
ter
pol
ation fi
lteri
ng al
gor
ith
m
i
s
pr
opos
ed (l
umin
ance: 1/4
precis
i
on, ch
romina
nce: 1/
8
precisi
on). B
a
sed
on t
he
al
gorith
m
,
a h
a
r
d
w
a
re d
e
si
gn w
i
th
pip
e
li
ne
structure
a
n
d
hig
h
d
egr
ee o
f
para
lle
lis
m is p
u
t forw
ard. T
he hardw
are over
hea
d is re
d
u
ce
d by multip
lex
W
i
ener
filter a
n
d
the reducti
on
of the si
z
e
of r
egister
array. A
nd th
e int
e
rpo
l
ation
ord
e
r of v
e
rtical
prio
r
i
ty i
s
ado
pted
to re
duce t
he r
ead
i
n
g
ban
dw
idth of the storag
e. It i
s
indi
c
a
ted fro
m
the p
e
rformance a
nalys
is
that this interp
olati
on structur
e
possess
es b
e
tter perfor
m
anc
e an
d s
m
a
ller
hardw
are
over
hea
d. T
h
is d
e
s
i
gn
also
takes
full co
nsid
erati
o
n
of the
bal
anc
e
betw
een s
p
e
e
d
a
nd
area,
meetin
g the
req
u
i
re
ments
of pr
o
c
essin
g
stan
da
rd defi
n
iti
on
an
d
hig
h
defi
n
itio
n vide
o i
m
ag
e.
Ke
y
w
ords
:
s
u
b
-pix
el inter
pol
ation, har
dw
are framew
ork, HEVC, H.264
Co
p
y
rig
h
t
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
HEVC [1, 2] (Hig
h Efficiency Vide
o Codi
ng) i
s
a
younge
r-g
en
eration vide
o
codin
g
stand
ard b
e
i
ng formulate
d
by joint vid
eo codi
ng group JCT-VT
(Joi
nt Colla
b
o
rative Team
on
Video Co
ding
) con
s
i
s
ting o
f
the experts of IS
O/IEC MPEG and ITU-T/VCEG. It
mainly geare
d
toward
high
-d
efinition TV
(HDTV
)
and
video
co
ding
system. Th
e g
oal of
HEV
C
i
s
to
re
du
ce
th
e
cod
e
rate of the video stre
aming to 50
% of
H.264 standard und
e
r
the con
d
itio
n of same pe
ak
sign
al to noise ratio
(PSNR). With th
e increa
se of
comp
re
ssi
on
efficiency, the com
putati
on
c
o
mplexity of
HEVC may be three
to fou
r
times of H.2
64 stan
dard, thus the comp
lexity of code
r
and de
cod
e
r of the hardwa
r
e is al
so increa
sed.
Aiming at
the heavy computation i
n
interpol
ation pro
c
e
ss, an
i
m
pleme
n
tatio
n
sche
ma
of i
n
terpol
ation
h
a
rd
wa
re
stru
cture b
a
sed o
n
pipeline i
s
put
forwa
r
d in thi
s
pap
er.
2. Principles of the Sub
-
p
i
xel Interpol
ation of
Algo
rithm HEVC
2.1. Interpol
ation Proce
s
s
of Lumina
n
ce Sample
Figure 1 sho
w
s the
po
sitio
n
s of the inte
ger pixel
sam
p
le, 1/2 pixel sampl
e
an
d 1
/
4 pixel
sampl
e
of th
e lumin
a
n
c
e
comp
one
nts
of the refere
nce
imag
e. It is
sup
p
o
s
ed
that lumin
a
n
c
e
sampl
e
point
A
i,j
is locat
ed at the p
o
sition of int
eger
sam
p
le
point (xA
i,j
, yA
i,j
), then the
predi
cate
d va
lue from
lumi
nan
ce p
o
int ‘
a
0,0
’ to ‘r
0,0
’ at non-i
n
tege
r
sampl
e
p
o
int
positio
ns ca
n
be obtai
ned
by the filter
with the
co
efficient of
(-1,4
,
-10,58,17,
-5,
1
,
-1,4,-1
1
,40,40,-1
1,4,-1),
(1,-5,1
7
,58,-1
0,4,-1).
(1)
Hori
zo
ntal
and Vertical Interpol
ation F
iltering of Integer Pixel
The value
s
o
f
1/2 pixel po
ints b
0, 0
, h
0, 0
and 1/4 pix
e
l point a
0,0
, c
0,0
;d
0,0
,n
0,0
can be
obtaine
d by using the filter
interpol
ation
ment
ione
d in the pape
r on
the nearest i
n
teger pixel i
n
the hori
z
ontal
and vertical
dire
ction
s
. Th
e
whol
e com
puting process is a
s
followi
ng:
a
0,0
=(
−
A
−
3,0
+4
*A
−
2,0
−
10*A
−
1,0
+58*A
0,0
+1
7*
A
1,0
−
5*A
2,0
+A
3,0
)/64
(1)
b
0,0
=(
−
A
−
3,0
+4
*A
−
2,0
−
11*A
−
1,0
+40*A
0,0
+4
0*
A
1,0
−
11*A
2,0
+4*A
3,0
−
A
4,0
)/64
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
A Study on Sub-pi
xel Inte
rpolation Filte
r
ing
Algorithm
and Hard
wa
re Structu
r
al…
(Wa
ng Ga
ng
)
7565
c
0,0
=(A
−
2,0
−
5*
A
−
1,0
+17*A
0,0
+58*A
1,0
−
10*
A
2,0
+4*A
3,0
−
A
4,0
)/64
(3)
d
0,0
=(
−
A
0,
−
3
+4
*A
0,
−
2
−
10*A
0,
−
1
+58*A
0,0
+1
7*
A
0,1
−
5*A
0,2
+A
0,3
)/64
(4)
h
0,0
=(
−
A
0,
−
3
+4
*A
0,
−
2
−
11*A
0,
−
1
+40*A
0,0
+4
0*
A
0,1
−
11*A
0,2
+4*A
0,3
−
A
0,4
)/64
(5)
n
0,0
=(A
0,
−
2
−
5*
A
0,
−
1
+17*A
0,0
+58*A
0,1
−
10*
A
0,2
+4*A
0,3
−
A
0,4
)/64
(6)
(2) Ve
rtical In
terpolatio
n Fil
t
ering of 1/2
Pixel and 1/4 Pixel
The value
s
of 1/2 pixel po
int j
0, 0
and 1/4 pixel point e
0,0
,i
0,0
, p
0,0
, f
0,0
, q
0,
0
, g
0,
0
, k
0,0
and
r
0,0
ca
n b
e
o
b
t
ained
by u
s
i
ng the
filter i
n
terpol
at
ion
mentione
d in
the pa
per on
the ne
are
s
t
1
/
2
pixel or 1/4 pi
xel in vertical dire
ction.
The
whole
comp
uting pro
c
e
ss is as follo
win
g
:
e
0,0
=(
−
a
0,
−
3
+4
*a
0,
−
2
−
10*
a0,
−
1
+58*
a
0,0
+17
*
a
0,1
−
5*a
0,2
+a
0,3
)/64
(7)
i
0,0
=(
−
a
0,
−
3
+4*
a
0,
−
2
−
11*a
0,
−
1
+40*
a
0,0
+40
*
a
0,1
−
11*a
0,2
+4*a
0,3
−
a
0,4
)/64
(8)
p
0,0
=(a
0,
−
2
−
5*
a
0,
−
1
+17*a
0,0
+58*a
0,1
−
10
*
a
0,
2
+4*a
0,3
−
a
0,4
)/64
(9)
f
0,0
=(
−
b
0,
−
3
+4
*
b
0,
−
2
−
10*b
0,
−
1
+58*
b
0,0
+17
*
b
0,1
−
5*b
0,2
+b
0,3
)/64
(10)
j
0,0
=(
−
b
0,
−
3
+4*
b
0,
−
2
−
11*b
0,
−
1
+40*
b
0,0
+40
*
b
0,1
−
11*b
0,2
+4*b
0,3
−
b
0,4
)/64
(11)
q
0,0
=(b
0,
−
2
−
5*
b
0,
−
1
+17*b
0,0
+58*b
0,1
−
10
*
b
0,
2
+4*b
0,3
−
b
0,4
)/64
(12)
g
0,0
=(
−
c
0,
−
3
+4
*c
0,
−
2
−
10*
c
0
,
−
1+5
8
*c
0,0
+17*
c
0,1
−
5*
c
0,2
+c
0,3
)/64
(13)
k
0,0
=(
−
c
0,
−
3
+4
*c
0,
−
2
−
11*
c
0,
−
1
+40*
c
0,0
+40*
c
0,1
−
11*
c
0,2
+4*
c
0,3
−
c
0,4
)/64
(14)
r
0,0
=(
c
0,
−
2
−
5*
c
0,
−
1
+17*c
0,0
+58*c
0,1
−
10*
c
0,2
+4*
c
0,3
−
c
0,4
)/64
(15)
F
i
gure 1. Positi
on of Integer S
a
mpl
e
Point a
n
d
N
on-
integ
e
r Sampl
e
Point i
n
the Interpo
l
at
ion of
Lumi
nanc
e
2.2. Interpol
ation Proce
s
s
of Chr
o
minance Samp
le
Figure 2 sho
w
s th
e po
sitions
of the integer
pixel sa
mple, 1/2 pix
e
l sam
p
le, 1/
4 pixel
sampl
e
, 1/8 pixel sam
p
le
of the chro
minan
ce
co
mpone
nts of
the referen
c
e ima
ge. It is
sup
p
o
s
ed tha
t
chromi
nan
ce sam
p
le poi
nt B
i, j
is locat
ed at the inte
ger
sampl
e
p
o
int (xB
i, j
, yB
i,
j
),
then the p
r
e
d
icted valu
e
from ch
rom
i
nan
ce poi
nt ‘ab
0,0
’ to ‘hh
0,0
’ at non-i
n
teger
sam
p
l
e
positio
ns
ca
n
be obtai
ned
by the 4-beat
filter with the
coeffici
ent of
(-2,5
8,10,-2),
(-4,5
4,16,-2),
(-6,4
6,28,-4
), (-4,3
6,36,-4
), (-4,2
8,46,
-6
), (-2,1
6,54,-4
), (-2,1
0,58,-2
).
A
-1,
-
1
A
0,
-
1
a
0,
-1
b
0,
-
1
c
0,
-1
A
1,
-
1
A
-1
,
0
A
0,
0
A
1,
0
A
-1
,
1
A
0,
1
A
1,
1
a
0,
1
b
0,
1
c
0,
1
a
0,
0
b
0,
0
c
0,
0
d
0,
0
h
0,
0
n
0,
0
e
0,
0
i
0,
0
p
0,
0
f
0,
0
j
0,
0
q
0,
0
g
0,
0
k
0,
0
r
0,
0
d
-1
,
0
h
-1
,
0
n
-1
,
0
d
1,
0
h
1,
0
n
1,
0
A
2,
-
1
A
2,
0
A
2,
1
d
2,
0
h
2,
0
n
2,
0
A
-1
,
2
A
0,
2
A
1,
2
a
0,
2
b
0,
2
c
0,
2
A
2,
2
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 12, Dece
mb
er 201
3: 756
4 – 7570
7566
Figure 2. Positions of Integ
e
r Sample Po
int and
No
n-i
n
teger Sam
p
l
e
Point in the Interpolatio
n
o
f
C
h
r
o
min
anc
e
(1)
Hori
zo
ntal
and Vertical Interpol
ation F
iltering of Integer Pixel
The value
s
of 1/2 pixel points ae
0,0
, ea
0,0
;1/4 pixel point ac
0,0
, ag
0,0
, ca
0,0
, ga
0,0
; and 1/8
pixel point a
b
0,0
, ad
0,0
, af
0,0,
ah
0,0
, ba
0,0
, da
0,0
, f
a
0,0
, ha
0,0
can be obtain
ed
by using filter
interpol
ation
mentione
d in
the pape
r on
the neares
t i
n
teger
pixel in the hori
z
o
n
tal and vertical
dire
ction
s
. Th
e whol
e com
puting process is a
s
followi
ng:
ab
0,0
=(
−
2*B
−
1,
0
+58*B
0,0
+1
0*
B
1,0
−
2*B
2,0
)/64
(16)
ac
0,0
=(
−
4*B
−
1,0
+54*B
0,0
+1
6*
B
1,0
−
2*B
2,0
)/64
(17)
ad
0,0
=(
−
6*B
−
1,
0
+46*B
0,0
+2
8*
B
1,0
−
4*B
2,0
)/64
(18)
ae
0,0
=(
−
4*B
−
1,
0
+36*B
0,0
+3
6*
B
1,0
−
4*B
2,0
)/64
(19)
af
0,0
=(
−
4*B
−
1,0
+28*B
0,0
+46*
B
1,0
−
6*B
2,0
)/64
(20)
ag
0,0
=(
−
2*B
−
1,
0
+16*B
0,0
+5
4*
B
1,0
−
4*B
2,0
)/64
(21)
ah
0,0
=(
−
2*B
−
1,
0
+10*B
0,0
+5
8*
B
1,0
−
2*B
2,0
)/64
(22)
ba
0,0
=(
−
2*B
0,
−
1
+58*B
0,0
+1
0*
B
0,1
−
2*B
0,2
)/64
(23)
ca
0,0
=(
−
4*B
0,
−
1
+54*B
0,0
+1
6*
B
0,1
−
2*B
0,2
)/64
(24)
da
0,0
=(
−
6*B
0,
−
1
+46*B
0,0
+2
8*
B
0,1
−
4*B
0,2
)/64
(25)
ea
0,0
=(
−
4*B
0,
−
1
+36*B
0,0
+3
6*
B
0,1
−
4*B
0,2
)/64
(26)
fa
0,0
=(
−
4*B
0,
−
1
+28*B
0,0
+46*
B
0,1
−
6*B
0,2
)/64
(27)
ga
0,0
=(
−
2*B
0,
−
1
+16*B
0,0
+5
4*
B
0,1
−
4*B
0,2
)/64
(28)
ha
0,0
=(
−
2*B
0,
−
1
+10*B
0,0
+5
8*
B
0,1
−
2*B
0,2
)/64
(29)
(2) Ve
rtical In
terpolatio
n Fil
t
ering of 1/2
Pixel and 1/4 Pixel
The value
of sub
-
pixel
sa
mple poi
nt b
X
0,0
, c
X
0,0
, dX
0,0
, eX
0,
0
, f
X
0,0
, gX
0,
0
and hX
0,0
(amo
ng which, X presents any one in
b
,
c, d, e,
f, g
and h
)
can b
e
obtaine
d by
the 4-b
eat filter
interpol
ation i
n
the vertical
dire
ction. Th
e
whole
comp
uting pro
c
e
ss is as follo
win
g
:
B
0,
0
ae
0,
0
ag
0,
0
ah
0,
0
ab
0,
0
ac
0,
0
ad
0,
0
af
0,
0
B
1,
0
B
1,
1
B
0,
1
be
0,
0
bg
0,
0
bh
0,
0
bb
0,
0
bc
0,
0
bd
0,
0
bf
0,
0
ba
0,
0
ce
0,
0
cg
0,
0
ch
0,
0
cb
0,
0
cc
0,
0
cd
0,
0
cf
0,
0
ca
0,
0
de
0,
0
dg
0,
0
dh
0,
0
db
0,
0
dc
0,
0
dd
0,
0
df
0,
0
da
0,
0
ee
0,
0
eg
0,
0
eh
0,
0
eb
0,
0
ec
0,
0
ed
0,
0
ef
0,
0
ea
0,
0
fe
0,
0
fg
0,
0
fh
0,
0
fb
0,
0
fc
0,
0
fd
0,
0
ff
0,
0
fa
0,
0
ge
0,
0
gg
0,
0
gh
0,
0
gb
0,
0
gc
0,
0
gd
0,
0
gf
0,
0
ga
0,
0
he
0,
0
hg
0,
0
hh
0,
0
hb
0,
0
hc
0,
0
hd
0,
0
hf
0,
0
ha
0,
0
ah
-1
,
0
bh
-1
,
0
ch
-1
,
0
dh
-1
,
0
eh
-1
,
0
fh
-1
,
0
gh
-1
,
0
hh
-1
,
0
he
0,
-
1
hg
0,
-
1
hh
0,
-
1
hb
0,
-
1
hc
0,
-
1
hd
0,
-
1
hf
0,
-
1
ha
0,
-
1
ba
1,
0
ca
1,
0
da
1,
0
ea
1,
0
fa
1,
0
ga
1,
0
ha
1,
0
ae
0,
1
ag
0,
1
ah
0,
1
ab
0,
1
ac
0,
1
ad
0,
1
af
0,
1
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
A Study on Sub-pi
xel Inte
rpolation Filte
r
ing
Algorithm
and Hard
wa
re Structu
r
al…
(Wa
ng Ga
ng
)
7567
bX
0,0
=(
−
2*aX
0
,
−
1
+58*aX
0,0
+10*
aX
0,1
−
2*
aX
0,2
)/64
(30)
cX
0,0
=(
−
4*
aX
0
,
−
1
+54*aX
0,0
+16*aX
0,1
−
2*
a
X
0,2
)/64
(31)
dX
0,0
=(
−
6*aX
0,
−
1
+46*aX
0,0
+28*aX
0,1
−
4*
a
X
0,2
)/64
(32)
eX
0,0
=(
−
4*aX
0
,
−
1
+36*aX
0,0
+36*
aX
0,1
−
4*
aX
0,2
)/64
(33)
fX
0,0
=(
−
4*
aX
0,
−
1
+28*aX
0,0
+4
6*aX
0,1
−
6*aX
0,2
)/64
(34)
gX
0,0
=(
−
2*aX
0,
−
1
+16*aX
0,0
+54*aX
0,1
−
4*
a
X
0,2
)/64
(35)
hX
0,0
=(
−
2*aX
0,
−
1
+10*aX
0,0
+58*aX
0,1
−
2*
a
X
0,2
)/64
(36)
It is indicated
from the above algorithm
analys
i
s
that the interpola
t
ion of certai
n sub
-
pixel points
can b
e
pro
c
essed only
after so
m
e
other sub
-
pixel points a
r
e
obtained. F
o
r
example, th
e inte
rpolati
on of
lumin
ance at
1/2
pixel
point
j
0,0
and
1/
4 pixel
poi
nt
e
0,0
,i
0,0
,p
0,0
,f
0,0
q
0,0
,g
0,0
,k
0,0
,r
0,
0
depend
s o
n
1/2 pixel poi
nt b
0,0
and 1/4pixel point
s a
0,0
and c
0,0
. In
summ
ary, the
computatio
n seq
uen
ce i
s
shown in Tabl
e 1.
Table 1. Co
m
putation Seq
uen
ce of Interpolation at Su
b-Pixel Point
Sequence Sub-pixel
Point
Step1 b
0,0
, a
0,0
, c
0,
0
Step2 d
0,0
, e
0,0
, f
0,0
, g
0,0
Step3 h
0,0
, i
0,
0
,
0,0
, k
0,0
Step4 n
0,0
, p
0,0
, q
0,0
, r
0,0
3. Design an
d Realizatio
n of Har
d
w
a
r
e
Frame
w
o
r
k
3.1. Structu
r
e of Lumina
n
ce Inter
polation
Sub-pixel i
n
te
rpolatio
n filtering dem
and
s
the
expan
sio
n
of refe
ren
c
e ma
cro
-
blo
c
k. The
orde
r of filter
deci
d
e
s
the read
am
ount
of the referen
c
e d
a
ta [3-5].
Whe
n
the si
ze of the macro-
block i
s
M
×
N, the refe
ren
c
e data
amo
u
n
t req
u
ired
to
be
rea
d
i
s
(M+7
)
× (N+7
). For
exampl
e,
the interpol
ation of an 8×8 referen
c
e blo
ck a
dopt
s 8-o
r
de
r filter, whi
c
h re
qui
re
s e
x
pansi
on of 3
integer
pixel
points i
n
the l
e
ft and at the
top of
the 8
×
8 blo
ck, a
nd
expan
sion
of 4 intege
r pixe
ls
points in the
right and at
the bottom of the bl
ock, thus 15
×15
refere
nce d
a
ta amount
are
requi
re
d to
b
e
re
ad, a
s
it
can b
e
see
n
in
Figu
re
3. Th
e 1/2
pixel val
ue a
nd
1/4 pi
xel value i
n
th
e
algorith
m
ca
n be obtaine
d by horizo
n
tal interpol
at
ion filtering, and then vertical interpol
atio
n
filtering. Overall stru
ctu
r
e
of
the sub-pixel interpol
ation pro
c
e
s
s of luminan
ce is sho
w
n
in
Figure 4.
Figure 3. Ref
e
ren
c
e Pixel
s
Requi
red at
Sub-
pixel Interpol
ation Position
Figure 4. Overall Structu
r
e
of Sub-Pixel
Interpolatio
n Process of Lu
minan
ce
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 12, Dece
mb
er 201
3: 756
4 – 7570
7568
Thre
e o
p
e
r
at
ors a
r
e
ado
p
t
ed in
this p
aper to
co
nd
uct the
1/2
pixel an
d 1/
4 pixel
interpol
ation f
iltering in h
o
rizontal a
nd v
e
rtic
al
dire
cti
ons. Th
e first
operator, se
con
d
ope
rato
r
and thi
r
d
ope
rator are 8
-
ta
pping
finite i
m
pulse
re
spo
n
se
filter
(FIR) of
weig
ht co
efficient (-1,4,
-
10,58,17,-5,1
)
(-1,4,-1
1,4
0
,40,-11,4,
-1)
(1,-5,1
7
,58,
-10,4,-1). Fig
u
re
5 shows
the stru
cture of
1/2 pix
and
1/4 pixel
inte
rpolatio
n filte
r
ing. T
h
e
first
ope
rato
r
an
d third o
p
e
r
a
t
or
con
d
u
c
t 1
/
4
pixel interpol
ation filtering
and the seco
nd ope
rato
r condu
cts 1/2 p
i
xel interpolati
on filtering.
Figure 5. 1/2 Pixel and 1/4 Pixel In
terpol
ation Filterin
g
Structure
Whe
n
the si
ze of data storage unit is (M
+7)×
(N+7
), input buffering
unit inclu
d
e
s
(M+7)
line regi
ste
r
s
whi
c
h are used to
store the data line co
nsi
s
ting of
(N+7) pixel
s
, in
put by the data
stora
ge unit a
c
cordi
ng to pi
xel storag
e. And multiple d
a
ta items bel
ongin
g
to different line
s
a
r
e
store
d
in re
sp
ective line re
gisters.
(a)
(b)
Figure 6. 1/2 Pixel Hori
zon
t
al Interpolat
i
on Ope
r
ation
of the Secon
d
Operator
Among which
C1, C2, C3,
C4, C5, C6, C7, C8 i
s
the input data ite
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
A Study on Sub-pi
xel Inte
rpolation Filte
r
ing
Algorithm
and Hard
wa
re Structu
r
al…
(Wa
ng Ga
ng
)
7569
By analyzing
Figure 6, 7
and 8, after inpu
tting the
7 line data items into the
input
buffer, the fi
rst op
erato
r
u
s
e
s
7
intege
r
pixel
value
s
(su
c
h as C1,
C
2,C3,C4,C5,
C
6 and C7
) with
the arra
ngem
ent of a
shifted pixel
to
condu
ct
inte
rp
olation
ope
ra
tion on
the
1
/
4 pixel “a
0,0
”.
Mean
while th
e first op
erat
or cond
uct
s
9
times of 1/4
pixel interp
ol
ation ope
ratio
n
s in h
o
ri
zont
al
dire
ction. Th
en, the
re
sult
s of inte
rp
ola
t
ion H_
pel1
′
…H_
pe1
9
′
are sto
r
ed
in th
e data
bufferi
ng
unit. When t
he first op
erator cond
uct
s
1/4 pixel
i
n
terpol
ation f
iltering, the seco
nd an
d third
operator
con
duct inte
rpol
a
t
ion ope
ratio
n
on 1/2 pixe
l “b
0,0
” and 1/
4 pixel “c
0,0
”
and 8 time
s
of
hori
z
ontal i
n
terpol
ation filtering, a
nd th
e obt
ain
ed in
terpolatio
n re
sults
(H_pel
1
…
H_
pe1
8 an
d
H_p
e
l1
″
…
H
_
pe18
″
) are st
ored in the d
a
t
a buffering u
n
it.
(a)
(b)
Figure 7. 1/2 Pixel Hori
zon
t
al Interpol
ati
on Ope
r
ation
of the first Op
erato
r
(a)
(b)
Figure 8. 1/2 Pixel Hori
zon
t
al Interpol
ati
on Ope
r
ation
of the Third O
perato
r
From th
e ab
ove analy
s
is,
the value
s
of 1/2 pixel
point an
d 1/4
pixel point b
e
twee
n
integer pixel
line
s
in
the
ho
rizontal
d
i
rectio
n are
obtaine
d
by interpol
ation filtering on
t
h
e
nearest inte
g
e
r pixel
s
u
s
in
g 3 ope
rato
rs. Similarl
y, the value
s
of
the 1/2 pixel
point and
1/4
pixel point b
e
twee
n integ
e
r pixel line
s
in the ve
rtical dire
ction a
r
e obtain
ed
by interpolati
o
n
filtering on the nearest integer pixel
s
u
s
ing 3 op
er
at
ors. After obt
aining the val
ues of 1/2 pi
xel
point a
nd 1/4
pixel poi
nt b
e
twee
n the
in
teger
pixel
lin
es i
n
the
ho
ri
zontal
directi
on, the val
ue
of
sub
-
pixel b
e
twee
n the no
n
-
intege
r pixel
lines
and li
sts (su
c
h
as: 1/2
pixel j
0,0
and
1/4 pixel e
0,0
,
i
0,0
, p
0,
0
, f
0,0
, q
0,0
, g
0,0
, k
0,0
and r
0,0
) can
be obtaine
d by interpolati
on filtering o
n
the nearest
1/2
pixel and 1/4
pixel in vertical dire
ction
u
s
ing
3 ope
rat
o
rs. T
he p
r
in
ciples
of interp
olation p
r
o
c
e
s
s
in
ho
rizontal dire
ction and
vertic
al
ho
rizontal a
r
e th
e
same, th
us
th
e ha
rd
ware
structu
r
e
chart
of
the sub
-
pixel
interpol
ation
pro
c
e
ss in ve
rtical di
re
ctio
n is not given
in the paper.
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 12, Dece
mb
er 201
3: 756
4 – 7570
7570
3.2. Structu
r
e of Chr
o
minance Interp
olation
7 op
erat
ors
are
ado
pted
to co
ndu
ct 1
/
2 pixe
l, 1/4
pixel an
d 1/8
pixel inte
rp
o
l
ation
filtering of horizontal an
d
vertical ch
rominan
ce. S
e
ven ope
rato
rs a
r
e 4-bea
t finite impulse
respon
se
(FI
R
) filter
with
weig
ht coefficient (-
2,58,1
0
,
-2), (-4,5
4,16
,-2), (-6,4
6,28
,-4), (-4,3
6,36
,-
4), (-4,2
8,46,
-6), (-2,16,54
,-4), (-2,10,5
8
,-2). T
he p
r
i
n
cipl
es a
r
e the sam
e
with those of sub-
pixel interpol
ation pro
c
e
s
s of luminan
ce, thus
the
hard
w
a
r
e structu
r
e chart of sub-pix
e
l
interpol
ation
pro
c
e
ss of
ch
romin
a
n
c
e is
not pre
s
ente
d
in details.
4. Performan
ce Analy
s
is
The de
sign
e
d
interpol
atio
n stru
cture in th
is paper i
s
capabl
e of condu
cting 1/
2 pixel
and 1/4
pixel interpol
ation
filtering; be
si
des, the
stored data in
re
gisters
can
b
e
shifted i
n
the
unit of line t
o
co
ndu
ct su
b-pixel inte
rp
olation. As
th
e re
giste
r
is
shifted, different ope
ration
s
related
to int
e
rpol
ation
ca
n be
co
ndu
ct
ed. Except
fo
r the initial
6
hours
delay, for the
adja
c
e
n
t
8×8 bl
ock in vertical di
re
ction,
con
s
tant
input of data is avail
able, whi
c
h do
es n
o
t requi
re th
e
filling of the pipeline. T
h
is
can not
only
accelera
te the computation and
reduce delay, but al
so
increa
se
th
e reu
s
e of
interpolat
ion data,
thus
26% of the
cl
oc
k peri
od can
be sa
ved.
Re
giste
r
sup
port
s
the
sub m
a
cro
-
bl
ock with
ch
a
nging
si
ze
s,
and the
pixel is shifted u
p
in the sam
e
dire
ction, thu
s
the 1/2 pixe
l and 1/4 pixe
l interpol
at
ion
can b
e
ap
pli
ed to blo
c
ks
of all sizes, a
n
d
the stru
cture of the interpol
at
ion circuit can be sim
p
lified.
5. Conclusio
n
Similar to
H.2
64/AVC, HEV
C
al
so a
dopt
s sub
-
pixel in
terpolatio
n al
gorithm
(lumi
nan
ce:
1/4 pre
c
i
s
ion,
chromin
ance: 1/8 pre
c
i
s
i
on).
Th
e lum
i
nan
ce an
d chromi
nan
ce
adopt filters
of
different o
r
de
rs to
re
alize
the interpolat
ion of
the
pi
xel at desi
r
e
d
po
sition. Di
fferent filterin
g
algorith
m
s wit
h
variou
s pre
c
isi
o
n
s
in the interpol
ation
pro
c
e
ss of HEVC ar
e di
scussed in deta
ils
in this pa
per.
Aiming at the larg
e co
mp
utati
on amo
u
n
t of interpol
ation ope
rati
on process, a
hard
w
a
r
e fra
m
ewo
r
k de
si
gn of interp
ol
ation ba
s
ed
on pipeli
ne structu
r
e is
pu
t forward. Th
e
desi
gn ta
ke
s con
s
id
eratio
n
of the balan
ce b
e
twe
en p
r
ocessin
g
sp
eed a
nd a
r
ea
. It is indicate
d
from the
pe
rforma
nce an
a
l
ysis th
at the
stru
cture i
s
capabl
e of d
e
c
re
asi
ng th
e
band
width
an
d
increa
sing th
e handli
ng
capa
city, meeting the
re
q
u
irem
ent of dealin
g with
high-definiti
on
image.
Ackn
o
w
l
e
dg
ements
This work wa
s su
ppo
rted
by the national
natural
sci
ence foundati
on of China (Gran
t
No. 611
710
7
8
), and Impo
rtant Project o
f
Baicheng
Normal
University.
Referen
ces
[1]
Ugur, Kem
a
l,
Anderss
on, Ke
nneth, F
u
l
d
set
h
, Arild, et a
l
. Lo
w
c
o
mpl
e
xit
y
vi
de
o cod
i
ng a
nd th
e
emergi
ng HEV
C
standar
d.
Picture Cod
i
ng S
y
mp
osi
u
m (PC
S
)
. 2010: 47
4~
477.
[2]
Wiega
nd T
,
Ohm JR, Su
lliv
a
n
GJ. et a
l
. S
peci
a
l S
e
ctio
n
on t
he J
o
int
Call
for Pro
p
o
s
als o
n
H
i
g
h
Efficienc
y Vi
de
o Cod
i
n
g
(HE
V
C) Stand
ardi
zation.
IEEE Transactions on Circuits and
System
s for
Vide
o T
e
chn
o
l
ogy,
201
0;12; (
20):16
61~
1
666
.
[3]
Bi Ho
u-ji
e. A n
e
w
g
ener
atio
n
of vide
o co
din
g
st
and
ard (
H
.264/AVC). Be
ij
ing:
Post &T
elecom Press
.
200
5.
[4]
Z
H
AO Z
i
-lia
ng,
Z
H
ENG Sh
i-b
ao. D
e
sig
n
an
d Impl
em
ent
ati
on of
Quarter-
pi
xel
Inter
pol
ati
on
in
H. 2
6
4
/AVC.
Journal
of Imag
e an
d Graphics
. 20
07
: 1740~
17
44.
[5]
LAI Xi
ao-l
i
n
g
, SANG Hong-s
h
i, et al. Sub-
Pixe
l Moti
on E
s
timation Inter
pol
ation M
e
tho
d
and
its High-
efficient VLSI Impl
ementation for H.264
. C
o
m
p
u
t
e
r
En
gi
nee
ri
ng
. 200
7: 18
7~
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