Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 4
,
A
ugu
st
2016
, pp
. 16
27
~
1
636
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
4.1
029
1
1
627
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
RGB Medical Vi
deo Com
p
ressi
on Using Geom
etric Wavelet
and SPIHT Coding
Habc
hi Yassi
ne
1
,
Bela
dg
ham Mo
ha
mmed
1
, Ta
leb Abdelma
lik Ahmed
2
1
Department of
Electrical Eng
i
n
eering
,
LTIT Laborator
y
,
T
a
hri
M
oham
m
e
d Univers
i
t
y
of
Be
cha
r
, Be
char
, Alg
e
ri
a
2
LAMIH UMR CNRS 8530, Le
Mont Hou
y
, 593
13 Valen
c
iennes
,
France
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Feb 24, 2016
Rev
i
sed
May 26
, 20
16
Accepted
Jun 10, 2016
The
compression of medical
video r
e
pr
es
ent
s
a big
chal
le
nge. I
t
ge
ts
indispensable solution in field o
f
stor
age and tr
ansmission of
me
dical data.
This paper
intr
oduces an
algor
ithm for color
medical v
i
deo
compression
based on geometrical wav
e
let
coupled
with S
P
IHT coding algorithm. In
order to prov
e the efficiency
of
our algor
ithm,
comparativ
e stu
d
y
is made
between
other
c
l
as
s
i
ca
l tr
ans
f
orm
s
. Th
e peak signal- no
ise Rate (PSNR), it
us
ed as
an obje
c
tiv
e param
e
t
e
r
to m
eas
ure the
qualit
y of r
ecov
r
ed fram
e
s
.
The exp
e
rimental results show th
at th
e proposed
algorithm for lo
w bit rate is
superior to traditional methods;
this is
justified
with a high valus of PSNR
parameter
.
Keyword:
Geom
etric wavelet
M
e
di
cal
vi
de
o
codi
ng
SPIHT c
o
der
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Yassine
Ha
bc
h
i
,
Depa
rt
m
e
nt
of El
ect
ri
cal
Engi
neeri
n
g
,
LT
IT Lab
o
rat
o
ry
,
Tahri
M
o
ham
m
e
d U
n
i
v
e
r
si
t
y
of
B
echa
r
,
P.O
.
B
o
x 41
7,
08
0
0
0
,
B
e
c
h
ar,
Al
ge
ri
a.
Em
a
il: h
a
b
c
h
i
8j
ij
el@g
m
a
il.co
m
1.
INTRODUCTION
W
i
t
h
t
h
e
i
m
port
a
nt
i
n
c
r
easi
n
g
vol
um
es of
dat
a
i
n
t
h
e fi
el
d
of m
e
di
cal
i
m
agi
ng,
com
p
r
e
ssi
on
i
s
t
h
e
maj
o
r
ch
allenges in
h
ealth
care ser
v
ices.
In
teleh
ealth
, Magn
etic Reso
n
a
n
c
e I
m
ag
in
g
(
M
RI
)
,
U
ltr
asound
(U
S),
Co
m
p
u
t
ed
Tom
o
g
r
aph
y
(CT), etc need
t
o
be tran
sm
itted
t
o
ano
t
h
e
r m
e
d
i
cal ex
p
e
rt. Th
ese hu
g
e
d
a
ta cau
s
e a
hi
g
h
t
i
m
e t
r
ansm
i
ssi
on an
d st
ora
g
e c
o
st
. T
h
e pr
o
b
l
e
m
b
ecom
e
s even m
o
re critical with the ge
ne
ralisation
of
3D se
que
nce.
So i
t
i
s
necessary
t
o
use com
p
ressi
o
n
i
n
o
r
de
r t
o
red
u
ce t
h
e am
ount
o
f
m
e
d
i
cal
dat
a
t
o
be
st
or
e
d
an
d
t
r
an
sm
itte
d
.
In
th
e literat
u
re m
a
n
y
co
mp
ressi
on
sch
e
mes b
y
tran
sform
a
t
i
o
n
h
a
v
e
been
pro
p
o
s
ed
,
we can
ci
t
e
t
h
e st
anda
rds
M
P
EG
f
o
r
com
p
ressi
n
g
vi
de
o.
Al
l
o
f
t
h
ese st
a
nda
rd
s
are
based
o
n
t
h
e di
sc
ret
e
c
o
si
ne
trans
f
o
r
m
(DCT) [1]
.
Ov
er th
e
p
a
st ten
years, th
e
wav
e
lets (DWT) co
m
p
ression
h
a
s si
g
n
i
fican
tly b
e
tter p
e
rform
a
n
ce in
term
s
o
f
ob
j
ect
iv
e and
sub
j
ectiv
e p
a
ram
e
ters at lo
w b
it
rat
e
. To im
pro
v
e t
h
e codi
ng
efficiency, this trans
f
orm
i
s
sui
t
a
bl
e t
o
ho
ri
zo
nt
al
vert
i
cal
and di
ag
onal
di
rect
i
o
n
s
. These c
h
ar
act
eri
s
t
i
c
s per
m
i
t
a hi
gher
codi
ng
efficiency
i
n
isotropic regularity
along
various c
u
rves
. Unfort
unately,
th
ese sep
a
rately b
a
sis
presen
t
discontinuities in all recovered fram
es.
In fact,
the degra
d
ation of
qu
al
ity visual increases trem
endously.
Seve
ral
ri
go
ro
us t
r
ans
f
orm
s
have
been de
v
e
l
ope
d an
d ex
p
l
oi
t
t
o
encapsu
l
a
t
e
ani
s
ot
ro
pi
c regul
a
r
i
t
y
i
n
fram
e
s.
I
n
[2
] CA
ND
ES and
D
ONOH
O in
tro
d
u
c
ed r
i
dg
elet tr
an
sfo
r
m
as m
u
lt
id
imen
sio
n
a
l ex
ten
s
ion
o
f
th
e
wav
e
let
tr
an
sf
or
m
.
I
n
19
99
, C
A
ND
ES and
DO
NOH
O
i
n
tr
odu
ced
cur
v
elet tr
an
sfo
r
m
[
3
].
In [
4
] and
[5
] D
O
and
VETTER
ha
ve
propose
d
c
o
ntourlet tr
ans
f
orm
.
All
these represe
n
tations
are use
d
to e
x
ploit the
geom
etric
regu
larity b
u
t
d
o
n
o
t
allow to
exp
l
o
it co
mp
letely
. To o
v
e
rcom
e t
h
ese lim
it
at
i
ons, PE
NNEC
a
nd M
A
LL
AT
in
trodu
ced g
e
ometric wav
e
let to
represen
t di
ffe
rentes
re
gul
arity
[6]
a
n
d
[
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
27
–
1
636
1
628
To
im
p
r
ov
e the qu
ality o
f
fra
m
e
s in
v
i
d
e
o at h
i
gh
co
m
p
ression
rate, sev
e
ral co
ders
h
a
v
e
b
e
en
p
r
op
o
s
ed
and
repo
rted
i
n
the literatu
re. Th
e effectiv
en
ess
of
cod
i
ng
was first d
e
mo
n
s
t
r
ated
b
y
Sh
ap
i
r
o’s
Em
b
e
d
d
e
d
Zero
tree
Wav
e
let (EZW) [8
]. Later, research
b
y
Sai
d
and
Pearlm
an
on
Set Partition
i
ng
i
n
Hierarc
h
ical T
r
ees enc
o
der
(SPIHT)
[9]. SPIHT applie
d
success
f
ully to bot
h lossy a
n
d lossless c
o
mpressi
on
o
f
im
ag
e an
d im
p
r
o
v
e
d
u
pon EZW
.
Th
is
pap
e
r is
o
r
g
a
n
i
zed
as fo
llow
s
: Section
2
d
e
scr
i
b
e
s th
e
g
e
ometr
i
c
wavel
e
t
.
S
P
I
H
T code
r i
s
di
s
c
usse
d i
n
sect
i
on 3
.
Sect
i
o
n
4 desc
ri
bes s
t
eps of
pr
o
p
o
s
ed al
g
o
ri
t
h
m
.
The
per
f
o
r
m
a
nce and
t
h
e e
xpe
ri
m
e
nt
al
res
u
l
t
s
ar
e sh
ow
n i
n
sec
t
i
on
5. Fi
nal
l
y
, a co
ncl
u
si
on
s
u
m
s
up t
h
e
fi
n
d
i
n
gs
of
pa
per
.
2.
GEOMET
RIC WAVELET
Ove
r
the past
decade
s
, there
has bee
n
abundant in
terest on X_Lets fam
i
ly
for the compressi
on of
im
age. Pennec
and M
a
l
l
a
t
have pr
o
v
e
n
t
h
at
geom
et
ri
c
wavel
e
t
has n
on
separa
bl
e basi
s
,
unl
i
k
e t
h
e
w
a
vel
e
t
t
r
ans
f
o
r
m
,
t
h
i
s
adva
nt
age
i
s
v
e
ry
i
m
port
a
nt
i
n
m
a
ny
d
o
m
a
ins.
The
wa
vel
e
t
bases
ge
nerat
e
s a r
e
d
u
nda
nc
y
,
t
h
i
s
is tran
slated
in
th
e p
r
esen
ce
o
f
h
i
g
h
-m
ag
n
itud
e
co
efficien
ts
in
th
e sing
u
l
ari
ties o
f
th
e im
a
g
e [1
0
]
. To
m
a
in
tain
the re
gularity of the
fram
e
, each
fram
e
is decom
posed
through
wavelet t
r
ansfor
m
.
Afte
r decom
position we
obt
ai
n
f
o
ur spa
t
i
a
l
freq
u
e
n
cy
sub
b
a
n
ds. The
sub
b
a
n
ds
a
r
e g
i
ven
a
s
:
y
x
y
x
f
y
x
a
j
j
j
,
,
,
y
x
y
x
f
y
x
d
j
j
H
j
,
,
,
(
1
)
y
x
y
x
f
y
x
d
j
j
V
j
,
,
,
y
x
y
x
f
y
x
d
j
j
D
j
,
,
,
w
h
er
e
j
:repre
sent t
h
e s
cale factor.
y
x
j
,
:scalin
g
fun
c
tio
n.
y
x
j
,
:wavelet function.
Due
to the
re
dundancy
of t
r
an
sform
,
we can partition each
subba
nds into seve
ral
bloc
ks
with
diffe
re
nt size to take a best segm
entation of each scale.
We prese
n
t the support of the blocks as
S
, an
d
it is
di
vi
de
d
i
n
t
o
s
m
al
l
several
s
u
b-
regi
on
s.S
u
c
h
segm
ent
a
t
i
on
is re
prese
n
ted
as qua
d
-tree
.
T
h
e l
o
cal di
rections
in
whi
c
h f
r
am
es
have
re
gul
ar
v
a
ri
at
i
ons a
r
e s
h
o
w
n by
geom
et
ri
c fl
ow
. T
h
e
rel
a
t
i
ons
hi
p
b
e
t
w
een t
h
e
ge
o
m
et
ric
fl
o
w
a
n
d
cu
rve
i
n
eac
h
regi
on
o
f
bl
oc
ks ca
n
be
got
t
e
n
by
E
quat
i
o
n
2
[
11]
.
)
(
1
)
(
1
1
)
(
2
x
c
x
c
x
(
2
)
x
c
'
: Slo
p
e
of
op
tical f
l
ow
.
The
optim
a
l geom
etric flows
of each bl
ock a
r
e
determ
ined by
m
i
nimizing a
Lagrange cos
t
2
2
3
,
28
R
s
jG
j
B
j
j
L
fR
f
f
Q
R
R
R
(3)
To
op
timize al
g
o
rith
m
o
f
q
u
a
d
-
tree seg
m
en
tatio
n
,
Peyre and
Mallat p
r
op
osed
to
bu
ild
the b
e
st q
u
a
d-
tree seg
m
en
tati
o
n
, th
is co
rresp
ond
ing
to
mi
n
i
mize th
e La
gran
gi
an co
st
of
com
b
i
ng t
h
e fou
r
chi
l
d
ren t
o
get
h
e
r
.
For a
L
xL
bl
ock
S
, d
e
no
te its fo
u
r
ch
ild
ren
as
4
3
2
1
,
,
,
s
s
s
s
, t
h
e Lagra
nge
cost
of com
b
i
ng t
h
e
f
o
u
r
ch
ild
ren
t
o
g
e
t
h
er is:
2
01
0
2
0
3
0
4
0
3
28
L
sL
s
L
s
L
s
L
s
L
s
Q
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
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:
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RGB
Medi
c
al
Vi
deo
C
o
mp
re
ssi
on
Usi
n
g
Ge
omet
ri
c W
a
vel
et
an
d
SP
IH
T
C
odi
ng
(
H
a
b
c
h
i
Y
a
ssi
ne)
1
629
If there is
no geom
etric flow in
t
h
at
m
acro-
bl
ock
,
i
t
m
eans that
t
h
e m
acro-
bl
oc
k i
s
re
g
u
l
a
r u
n
i
f
orm
l
y
so we ca
n
use
wavel
e
t
ba
si
s. Ot
he
rwi
s
e
,
t
h
e su
b
-
bl
oc
k
m
u
st
be proce
ssed
by
ge
om
et
ri
c wavel
e
t
basi
s b
y
appl
y
i
n
g
t
h
e w
a
rp
o
p
erat
i
o
n,
whi
c
h i
s
defi
ne
d i
n
[
1
2]
.
Each im
age of sequence is com
p
ressed by codi
ng
of
se
gm
ent
a
t
i
on o
f
i
m
age an
d a geom
et
ri
c fl
ow i
n
each re
gion
of
the segm
entation. After
qua
nt
ization, th
e c
o
e
fficients are coded. T
h
e total num
ber
of
bits
R
is
decom
pose
d
i
n
t
o
jB
jG
js
j
R
R
R
R
R
,
w
h
er
e
s
R
is th
e
n
u
m
b
e
r
o
f
b
its to cod
e
th
e d
y
ad
ic sq
uare seg
m
en
tati
o
n
.
G
R
is the
num
ber
of bits to code
th
e di
rection in each
square
re
gion
B
R
is th
e
n
u
m
b
e
r
o
f
b
its to cod
e
th
e qu
a
n
tized
geom
etric wavelet coef
ficients.
The
wavel
e
t
c
o
ef
fi
ci
ent
s
a
r
e
pr
o
duct
s
bet
w
een
f
unct
i
o
n
,
f
xy
and
basi
s of
di
scret
e
se
para
bl
e
wav
e
let.
12
12
12
,,
,,
,,
,
,
jn
jn
jn
j
n
jn
j
n
xy
xy
x
y
(5)
Sepa
rable wa
velets are
warpe
d
with an operat
or
W
al
on
g fl
o
w
l
i
n
es,
de
fi
ne
d as
,,
Wf
x
y
f
x
y
c
x
fo
r th
e
v
e
rtical p
a
rallel flo
w
. Th
e
W
is an
o
r
t
h
ogo
n
a
l operato
r, its
ad
jo
in
t is equ
a
l to
its
in
v
e
rse,
1
,,
,
W
f
xy
W
f
xy
f
x
y
c
x
. Th
e warp
ed wav
e
let b
a
sis is
obt
ai
ne
d by
1
W
to each
sepa
rable
wa
velet basis.
2
2
2
,
,,
,,
,
,,
,
()
(
(
)
)
()
(
(
)
)
()
(
(
)
)
H
j
n
jn
jn
V
j
nj
n
j
n
D
jn
jn
j
n
xy
c
x
xy
c
x
xy
c
x
(6)
After
W
ope
rat
i
o
n
of
wa
vel
e
t
basi
s, t
h
e
ne
x
t
st
ep i
s
a
ba
ndel
e
t
i
zat
i
o
n
t
o
c
o
n
s
t
r
uct
ge
om
et
ri
c
wav
e
let. The
,
x
y
consi
s
t
s
o
f
hi
g
h
-
pass
fi
l
t
e
rs
a
n
d
has
va
ni
shi
n
g m
o
m
e
nt
s at
l
o
we
r
resol
u
t
i
o
ns,
t
h
i
s
i
s
v
a
lid
fo
r
V
n
j
,
and
D
n
j
,
, but
not
f
o
r
H
n
j
,
. Pr
obl
em
of reg
u
l
a
ri
t
y
al
ong t
h
e
fl
ow l
i
n
e i
s
d
u
e t
o
t
h
e scal
i
n
g
fu
nct
i
o
n
,
x
y
wh
ere it co
n
s
ists o
f
low-p
a
ss
fi
l
t
ers and
does
not
ha
ve va
ni
shi
n
g m
o
m
e
nt at
l
o
wer
reso
l
u
tio
ns. To tak
e
adv
a
n
t
age o
f
regu
larity alo
n
g
th
e fl
ow lin
es fo
r
H
n
j
,
, th
e d
e
form
ed
wav
e
let b
a
sis i
s
bandeletization
by replacing
t
h
e horizontal wavelet
H
n
j
,
with
new fun
c
tion
s
,,
()
(
(
)
)
jn
j
n
x
yc
x
(7)
The
ort
h
o
n
o
rm
al
basi
s
of
ge
o
m
et
ri
c wavel
e
t
o
f
fi
el
d
wa
r
p
i
n
g
i
s
defi
ne
d
b
y
:
,
,,
,,
,
,,
,
()
(
(
)
)
()
(
(
)
)
()
(
(
)
)
H
j
n
jn
jn
V
j
nj
n
j
n
D
jn
jn
j
n
xy
c
x
xy
c
x
xy
c
x
(8)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
27
–
1
636
1
630
Aft
e
r
wa
rpi
n
g
,
t
h
e
war
p
ed
regi
on i
s
reg
u
l
ar al
on
g t
h
e
vert
i
cal
o
r
h
o
ri
z
ont
al
(sam
e pre
v
i
o
us
ope
rat
i
o
ns)
di
r
ect
i
on.
T
h
e
ba
ndel
e
t
i
zat
i
o
n
r
e
m
oves t
h
e c
o
rrelatio
n th
at
ex
ists
b
e
tween
wav
e
let co
ef
fi
cien
ts
n
ear th
e si
n
gularity
. Lastly
, th
e resu
ltin
g
o
f
g
e
o
m
etric
wav
e
let co
ef
fi
cients are c
o
m
puted from
warpe
d
wav
e
lets with
1
D
d
i
screte wav
e
let
tran
sfo
r
m
th
an
ar
e
en
cod
e
d
using su
bb
and
coder
.
Th
e fu
ll detailed
descri
pt
i
o
n
s
of
t
h
e
geom
et
ri
c wavel
e
t
a
r
e s
h
ow
n i
n
Fi
gu
re
1.
Fi
gu
re
1.
B
l
oc
k
di
ag
ram
of g
e
om
et
ri
c wavel
e
t
fo
r m
e
di
cal
vi
de
o e
n
co
di
ng
3.
REVIEW
OF
SET PA
RTIT
IONI
NG
IN
HIER
AR
CHI
CAL T
R
EES
SPI
HT
[1
3]
i
s
con
s
i
d
ere
d
t
o
be one
o
f
t
h
e m
o
st
popular
wavelet im
age com
p
ression al
gorithm
s
.
The
su
ccess
of SPIHT
is
d
u
e
to
t
h
e
o
r
g
a
n
i
sation
o
f
wav
e
let co
ef
ficien
ts in
t
o
th
e sp
atial o
r
i
e
n
t
atio
n
t
r
ees.
Th
ree
typ
e
s o
f
trees:
,
Di
j
,
,
Oi
j
and
,
Li
j
, wi
t
h
ro
ot
at
co
or
di
nat
e
,
ij
, are
use
d
t
o
hol
d wa
vel
e
t
coef
ficients
as
sets:
,
Oi
j
is a sp
ecial case
o
f
,
Di
j
, and
,,
,
Li
j
D
i
j
O
i
j
. All
co
ef
ficien
ts are or
g
a
n
i
sed in
t
h
ree lists:
LIP
(Li
s
t
of
i
n
s
i
gni
fi
ca
nt
Pi
xel
s
).
LIS (Li
s
t
of I
n
si
gni
fi
ca
nt
Set
s
).
LSP
(List o
f
Sig
n
i
fican
t
Pi
x
e
ls).
During in
itiali
satio
n
,
th
e co
ef
ficien
ts in h
i
gh
frequ
en
cy
sub
b
a
nd
are pu
t
o
n
th
e
,
Di
j
t
y
pes
of
trees in LIS,
with
ro
o
t
s
,
ij
at t
h
e
coarse
st s
u
bba
n
d a
n
d leaves
on
t
h
e
fi
nest
s
u
bba
n
d
;
ot
he
r c
o
ef
fi
ci
ent
s
a
r
e
o
u
t
in
t
h
e LIP; th
e in
itial LSP
is e
m
p
t
y
.
Th
en b
it p
l
an
e cod
i
n
g
is tran
sm
itt
ed
b
y
so
rting
an
d
refi
n
e
m
e
n
t
p
a
sses.
In s
o
rting pas
s
,
the
c
o
ef
ficients i
n
LIP
a
r
e
scanned
a
n
d
c
ode
d
i
n
di
vi
dua
l
l
y
, and
si
gni
fi
cant
c
o
ef
fi
ci
en
t
s
ar
e
m
o
v
e
d
to LSP; th
e t
r
ees i
n
LIS are scan
n
e
d
an
d co
d
e
d
,
and sign
ifican
t t
r
ees are p
a
rtitio
ned
i
n
su
b
t
rees
an
d /
or indi
vidual coef
ficients,
which are
put
t
o
LIS, L
I
P
a
n
d L
S
P
res
p
ect
i
v
el
y
.
In
refi
nem
e
nt
pass, c
o
ef
fi
ci
ent
s
i
n
LSP
a
r
e sca
n
ne
d a
n
d
co
de
d.
Fi
gu
re
2.
B
l
oc
k
di
ag
ram
of g
e
neri
c
bi
na
ry
o
f
SP
I
H
T e
n
c
o
d
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
RGB
Medi
c
al
Vi
deo
C
o
mp
re
ssi
on
Usi
n
g
Ge
omet
ri
c W
a
vel
et
an
d
SP
IH
T
C
odi
ng
(
H
a
b
c
h
i
Y
a
ssi
ne)
1
631
4.
PROP
OSE
D
ALGO
RITH
M
The
pr
o
p
o
s
ed
al
go
ri
t
h
m
t
o
en
code
m
e
di
cal
fram
e
s devel
o
p
e
d as
f
o
l
l
o
w
s
:
Step 1:
Inpu
t th
e co
lor
m
e
d
i
cal sequ
en
ces of size 512
x51
2.
Step 2:
Decom
pos
e the
each input
Y, C
b
a
nd
Cr fram
e
through 2D DWT.
Step 3:
T
h
e
Y,
C
b
a
n
d C
r
o
f
e
ach
fram
e
of se
que
nces
are
re
cursi
v
ely segm
ented i
n
to
dya
d
ic s
qua
res.
Step 4:
G
e
o
m
etr
i
c f
l
ow
is constr
u
c
ted in
squar
e
for
each
Y
,
Cb
and
Cr.
Step 5:
T
h
e
w
a
vel
e
t
s
basi
s
i
s
wa
rpe
d
al
on
g
geom
et
ri
c fl
o
w
.
Step 6:
Th
e
b
a
n
d
e
letizatio
n op
eration
is applicated
to
th
e warp
ed
wav
e
let b
a
sis.
Step 7:
T
h
e
SPIHT
code
r is
used t
o
e
n
co
de
geom
etric wavelet coefficients.
Step 8:
C
o
llect all layers in
on
e m
a
trix
Ycbcr.
St
e
p
9
:
Th
e
resu
ltin
g
sequ
en
ce qu
alities are
measu
r
ed in
term
s o
f
PSNR
(d
B)
p
a
ram
e
ter
.
Fi
gu
re 3.
Pr
o
p
o
se
d bl
oc
k di
agram
fo
r
c
o
l
o
r
m
e
di
cal
vi
de
o com
p
ressi
o
n
5.
R
E
SU
LTS AN
D ANA
LY
SIS
In
t
h
i
s
pa
per
,
we a
r
e
i
n
t
e
rest
ed i
n
l
o
ssy
c
o
m
p
ressi
on
m
e
tho
d
s
ba
sed
on
geom
et
ri
cal
w
a
vel
e
t
be
cause
t
h
ei
r i
m
port
a
nt
es r
o
l
e
i
n
ca
pt
uri
ng a
n
i
s
ot
ro
pi
c re
gul
a
r
i
t
y
al
on
g
vari
o
u
s
cur
v
es.
The
p
r
op
ose
d
al
g
o
r
i
t
h
m
was
appl
i
e
d
t
o
e
n
c
ode t
e
st
nat
u
r
a
l
seque
nces
(
F
OR
EM
A
N
,
AK
IY
O
)
an
d
m
e
di
cal
seque
nces (
E
N
D
O
S
C
OP
Y
,
B
A
C
TER
I
A
-
G
R
O
W
T
H
)
o
f
si
ze 51
2
x
5
1
2
, t
h
ese nat
u
ral
an
d
m
e
di
cal
vi
deo
are t
a
ke
n f
r
o
m
dat
a
base [
1
4]
an
d
[1
5]
. F
o
r t
h
e
p
u
r
p
ose
of
eval
uat
i
o
n
,
t
h
e cl
as
si
cal
m
e
t
hods
(
d
i
s
cret
wavel
e
t
t
r
ans
f
orm
(D
WT)
[
1
6]
an
d
di
scret
cu
rv
elet tran
sfo
r
m
(DC
u
T))
[17
]
h
a
s
b
e
en u
s
ed
.
Th
e imp
o
rtan
ce
o
f
ou
r work lies i
n
t
h
e
po
ssib
ility o
f
reducing
t
h
e bit-rates for whic
h
the
vi
deo quality
re
mains accepta
ble. The e
ffic
i
ency of the
propose
d
algorithm
is ev
aluated according t
o
the objec
tive param
e
te
rs. In ge
neral, a
higher
Pea
k
-Signal-t
o
-Noise
-Ratio
(PSNR) v
a
l
u
e sh
ou
l
d
co
rrelate
to
a h
i
gh
er qu
ality
fram
e
.
1
0
1
0
2
2
2
10
1
255
log
10
N
i
N
j
ij
ij
R
C
N
PSNR
(9)
Whe
r
e:
:
N
Size param
e
ter.
:
,
j
i
Po
sition
informatio
n
.
:
ij
C
Cur
r
ent fram
e
.
:
ij
R
Refere
nce
fr
am
e.
Fig
u
re
4
sho
w
n
b
e
low illu
strates th
e co
m
p
ressed
resu
lts fo
r d
i
f
f
eren
t
b
it-rate
v
a
lu
es.
T
o
sho
w
the
p
e
rf
or
m
a
n
ce of
t
h
e
pr
opo
sed
m
e
th
o
d
(
g
eo
m
e
tr
ic w
a
v
e
l
e
t cou
p
l
ed w
i
th
SPIH
T
coder
)
,
w
e
sugg
est to
appl
i
cat
ed
t
o
a
set
of
nat
u
ral
and
m
e
di
cal
vi
deo
.
W
e
not
e t
h
at
ou
r al
go
ri
t
h
m
i
s
adapt
e
d
fo
r t
h
e m
e
di
cal
vi
de
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
27
–
1
636
1
632
com
p
ressi
o
n
.
Al
so,
we ca
n
obs
er
ve t
h
at
c
o
m
p
ressi
o
n
de
gra
d
es
f
o
r
l
o
w
com
p
ressi
o
n
bi
t
-rat
e
.
H
o
we
ver
,
f
o
r
hi
g
h
c
o
m
p
ressi
on
bi
t
r
at
e,
o
u
r
al
go
ri
t
h
m
achive a
high
val
u
s
of PSNR
(dB
)
.
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
28
28
.
5
29
29
.
5
30
30
.
5
31
31
.
5
32
BI
T
R
AT
E
(
M
b
p
s
)
P
S
NR(
d
B
)
FOR
E
M
A
N
AK
I
Y
O
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
30
31
32
33
34
35
36
37
BI
T
R
A
T
E
(
Mb
p
s
)
PSN
R
(
d
B
)
EN
D
O
SC
O
P
Y
B
A
CT
E
R
I
A
-
G
RO
W
T
H
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
28
29
30
31
32
33
34
35
36
37
B
I
T
R
AT
E(
M
b
p
s
)
PSN
R
(
d
B
)
AK
I
Y
O
B
A
CT
E
R
I
A
-
G
RO
W
T
H
Fi
gu
re
4.
PS
N
R
(dB
)
val
u
es
achi
e
ve
d
fo
r
n
a
t
u
ral
a
n
d
m
e
di
cal
t
e
st
fram
e
s usi
n
g
t
h
e
pr
o
p
o
se
d m
e
t
hods
To s
h
o
w
t
h
e p
e
rf
orm
a
nce o
f
t
h
e p
r
o
p
o
se
d
m
e
t
hod,
we m
a
ke a c
o
m
p
ari
s
o
n
bet
w
ee
n di
ff
erent
t
y
pes
o
f
trans
f
o
r
m
D
W
T, DCu
T
a
n
d GEOM
E
T
RIC
W
A
V
E
L
E
T
(
G
W)
co
up
led
with
th
e SPIHT.
Fo
r each app
licatio
n
we
vary
t
h
e
bi
t-rate f
r
o
m
e
(0
.3,
0
.
9
a
n
d
2
M
bps
),
an
d
we calcu
late th
e PSNR
(d
B
)
param
e
ter. Th
e
resu
lts
obt
ai
ne
d a
r
e
g
i
ven i
n
Ta
bl
e
1.
Acc
o
r
d
i
n
g
t
o
t
h
e
PS
NR
(dB
)
val
u
es
,
we
not
e t
h
at
vi
de
o r
eco
nst
r
uct
i
on
becom
e
s alm
o
st perfect wit
h
propo
sed
al
g
o
rith
m
fo
r all b
itrate v
a
lu
es. Also
from th
is resu
lts, o
u
r
ex
p
e
rim
e
n
t
al r
e
su
lts sho
w
that th
e p
r
o
p
o
s
ed
algo
rith
m
fo
r lo
w
b
it rate (0.3
M
b
p
s
) is ab
le to
red
u
ce
u
p
t
o
37
.1
9% an
d 2
8
.
2
0
% o
f
t
h
e co
m
p
l
e
x geom
et
ri
cs det
ect
i
on com
p
ared t
o
t
h
e
D
W
T+S
P
I
H
T
and DC
uT+S
PIH
T
alg
o
rith
m
.
Th
e q
u
a
lity v
i
su
al d
e
grad
atio
n
o
f
fram
e
s is
less
in
lo
w b
it rate
th
an
in
h
i
gh
b
i
t rate. Also
,
we can
see th
at th
e PSNR (d
B) v
a
l
u
e
d
e
p
e
nd
o
n
th
e
d
eco
m
p
o
s
ition
th
resh
o
l
d
s
(T)
as it sho
w
n
i
n
F
Fig
u
re 5
.
Th
e q
u
a
lity
v
i
su
al o
f
d
e
co
m
p
ressed
fram
e
s
(for first,
ten
t
h,
twen
tie
th
an
d th
i
r
tieth
fram
e)
using al
goritm
of GE
OMETR
IC
W
A
VELET
-SP
I
HT
at
2Mbps
are
s
h
own
in Figure
6.
Tabl
e 1.
T
h
e
P
S
NR
(dB
)
val
u
es
o
f
reco
nst
r
u
c
t
e
d
B
A
CTER
IA GR
OWTH sequence
fo
r var
i
ou
s
b
itr
ate valu
es
using WAVE
L
ET-S
P
IHT,
CURVE
LET-SP
IHT
and
GE
OMETRIC
W
A
VELET
-S
PIHT
BITRAT
E (Mb
p
s
)
WAV
E
L
E
T
-
SPI
H
T
CURVEL
ET
-SPI
HT
PROPOSE
D
A
L
G
O
RITH
M
0.
3 24.
694
7
26.
425
4
33.
879
9
0.
9 24.
583
0
26.
721
9
35.
962
7
2
30.
4890
30.
9402
36.
332
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
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S
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8-8
7
0
8
RGB
Medi
c
al
Vi
deo
C
o
mp
re
ssi
on
Usi
n
g
Ge
omet
ri
c W
a
vel
et
an
d
SP
IH
T
C
odi
ng
(
H
a
b
c
h
i
Y
a
ssi
ne)
1
633
10
30
50
10
0
0
10
20
30
40
T
H
R
ESH
O
L
D
S
(
T
)
P
S
NR[
d
B
]
Fi
gu
re
5.
PS
N
R
(dB
)
val
u
es
of
rec
o
n
s
t
r
uct
e
d B
A
C
TER
I
A
GR
O
W
T
H
se
q
u
ence
v
s
t
h
res
hol
ds
(T=
1
0
,
3
0
,
5
0
an
d 100
) u
s
i
n
g pr
opo
sed m
e
t
h
od
a.
b.
Fig
u
re
6
.
V
i
sual q
u
a
lity of
d
e
co
m
p
ressed BAC
TERIA
GR
OWTH fram
es
u
s
i
n
g GEOM
ETRIC
W
A
VELET
-
SPIHT
at
2
M
bp
s
for
first, tenth
,
twen
tieth
an
d th
irtie
th
fra
m
e
: (a).O
r
igi
n
al fram
e
s; (b)
.
Decom
p
resse
d
fram
e
s
B
e
fo
re a
ppl
y
i
n
g
pr
o
pose
d
al
go
ri
t
h
m
on t
h
e col
o
r
vi
de
o,
t
h
e R
G
B
col
o
r
f
r
am
es are conve
r
ts int
o
YC
bC
r
f
o
rm
, and
t
h
e
n
a
ppl
y
i
ng
p
r
o
p
o
se
d al
go
ri
t
h
m
on eac
h l
a
y
e
r i
n
de
pe
nde
nt
l
y
, t
h
i
s
m
eans eac
h l
a
y
e
r f
r
om
YC
bC
r
are c
o
m
p
ressed as a
gray
scal
e
fram
e
. YC
bC
r
refe
r
s
t
o
t
h
e
col
o
r
r
e
sol
u
t
i
o
n
of
di
gi
t
a
l
com
pone
nt
vi
de
o
si
gnal
s
,
whi
c
h i
s
based o
n
sa
m
p
li
ng rat
e
s. T
h
i
s
pr
ocess i
s
r
e
peat
ed f
o
r e
v
ery
fram
e
and resol
u
t
i
on i
n
t
h
e case
of l
e
vel
5 dec
o
m
posi
t
i
ons.
R
G
B
col
o
r a
n
d YC
bC
r fo
rm
of reco
v
r
ed f
r
a
m
e
s i
n
cl
udi
n
g
nat
u
ral
and
m
e
di
cal
f
r
a
m
e
s b
y
th
e pr
opo
sed m
e
t
h
od
ar
e
pr
esen
ted in
Figu
r
e
8
.
Reco
v
e
r
e
d BA
CTER
I
A
G
R
OW
TH
sequ
en
ces
yielded
by t
h
e
using
GE
OM
ETRIC
W
A
VE
LET+SP
IHT,
DCuT+
SPIHT
a
nd DWT+
S
P
IHT a
r
e
shwons
i
n
Fi
gu
re 9.
Fi
gu
re 7.
V
i
de
o
c
o
m
p
ressi
o
n
st
eps usi
n
g Ge
om
et
ri
c
W
a
vel
e
t
t
r
ans
f
o
r
m
coupl
e
d
wi
t
h
S
P
I
H
T
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 6
,
N
o
. 4
,
Au
gu
st 2
016
:
16
27
–
1
636
1
634
Orig
in
al
De
co
m
p
ressed
Orig
in
al
Deco
m
p
ressed
Y
Cb
Cr
RGB
(a).
A
K
I
Y
O
(b).
E
N
D
O
SC
OP
Y
Fi
gu
re
8.
R
eco
vere
d c
o
l
o
r
fra
m
e
s usi
n
g
pr
o
p
o
se
d al
g
o
ri
t
h
m
at
0.
9M
bps
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
RGB
Medi
c
al
Vi
deo
C
o
mp
re
ssi
on
Usi
n
g
Ge
omet
ri
c W
a
vel
et
an
d
SP
IH
T
C
odi
ng
(
H
a
b
c
h
i
Y
a
ssi
ne)
1
635
Y
Cb
C
r
R
G
B
O
r
igi
n
al
(
a
)
(
b
)
(c
)
Figure
9. Recovere
d B
A
CTE
R
IA
GROWT
H
se
quence
usi
ng: (a). GE
OMETRIC
W
A
VE
LET+SP
IHT, (b).
DC
uT+
SPI
HT
and
(c
). D
W
T
+
SPI
HT
at
0.
9
M
bps
6.
CO
NCL
USI
O
N
Th
e
ob
j
ectiv
e
o
f
th
is
p
a
p
e
r i
s
to
im
p
r
ov
e t
h
e en
h
a
n
cem
en
t of co
lor m
e
d
i
cal v
i
d
e
o quality after th
e
appl
i
cat
i
o
n o
f
t
h
e p
r
o
p
o
se
d al
go
ri
t
h
m
t
o
ai
d
di
ag
no
si
s (st
o
r
a
ge o
r
t
r
an
sm
i
s
si
on
) i
n
m
e
di
cal
im
agi
ng.
We use
d
th
e g
e
o
m
etr
i
c
w
a
v
e
let coup
led
w
ith
SPIH
T co
d
i
n
g
. Af
ter
sev
e
r
a
l
app
licatio
n
s
, w
e
fo
und
th
at
t
h
is
al
g
o
rith
m
g
i
v
e
s
b
e
tter resu
lts th
an
t
h
e
o
t
h
e
r trad
itional alg
o
r
ith
m
s
. To
d
e
v
e
l
o
p
our algo
rith
m
,
we h
a
v
e
app
lied th
is
t
echni
q
u
e
o
n
d
i
ffere
nt
t
y
pes
of c
o
l
o
r
vi
de
o.
W
e
have
n
o
t
i
ced t
h
at
fo
r l
o
w bi
t
-
rat
e
, t
h
e
pr
o
pose
d
al
go
ri
t
h
m
pr
o
v
i
d
es
very
i
m
port
a
nt
PSN
R
(dB
)
val
u
es
fo
r col
o
r m
e
di
cal
vi
deo a
n
d i
t
i
s
m
o
re sui
t
a
bl
e fo
r B
A
C
T
ER
IA
-
GR
O
W
T
H
vi
d
e
o. I
n
pers
pect
i
v
e, we as
pi
re t
o
ap
pl
y
ou
r al
g
o
ri
t
h
m
t
o
com
p
ress
vi
de
o se
que
nces
wi
t
h
a
not
her
efficient tra
n
s
f
orm
s
and code
rs.
ACKNOWLE
DGE
M
ENTS
We w
oul
d l
i
k
e t
o
t
h
ank t
h
e
Edi
t
o
r a
nd a
n
o
n
y
m
ous revi
e
w
ers f
o
r t
h
ei
r com
m
e
nt
s and
sug
g
est
i
o
ns
,
also
we
would like to tha
n
k t
h
e m
e
m
b
ers a
n
d the
dire
ctor
s o
f
L
T
IT
La
b
o
rat
o
ry
of
U
n
i
v
ersity
o
f
Bec
h
ar
f
o
r
t
h
ei
r e
n
co
ur
an
gem
e
nt
and
f
o
r
t
h
ei
r
preci
o
u
s
hel
p
.
REFERE
NC
ES
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V
.
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e
lier
, “Progressive coding of
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.
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, 2005
.
[2]
E. J. Candes
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d D. L
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,
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i
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nsional inter
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ittency
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ef
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ad
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S
SN
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2
088
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08
I
J
ECE
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l. 6
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N
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05–120, 1999
.
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.
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e
tter
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ont
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u
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”
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f
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N. Do,
et al.
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T
h
e
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ef
fici
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u
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ec
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a
ll
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m
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ge
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t
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,”
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ec
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”
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r
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an,
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ci
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e
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”
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e
nne
c,
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B
andel
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tt
es
e
t
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ent
a
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é
om
étri
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at
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y
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echn
i
que
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ud
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e
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id
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.
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an
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ag
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3.
BIOGRAP
HI
ES
OF AUTH
ORS
Yassine HABC
H
I was born in
Mechria,
Algeri
a. He rec
e
iv
ed t
h
edipl
.
El-Ing fr
om
the Univers
i
t
y
of Saïda University
, Algeria, in
2010, the Magi
stere degr
ee in digital communication and signal
processing from University
of B
echar
,Alger
ia.in
2013. Actu
elly
,
he prep
are th
e d
o
ctoral deg
r
ee
Es
s
c
ienc
e
at Uni
v
ers
i
t
y
of
Be
cha
r
, Alge
ria
.
His
m
a
in int
e
res
t
ed
are Im
ag
e
and v
i
deo pro
ces
s
i
ng
,
1
st
G and 2
nd
G
wavelets tr
ansform and optimal enco
d
e
r.
Correspondence address: Bech
ar
Universit
y
,
Dep
a
rtm
e
nt of
E
l
ec
tr
onic,
Be
char
,Alg
eria
,E-m
ai
l: h
a
b
c
hi8ar
tic
le@gm
a
il
.com
Mohammed BELADGHA
M was born in
Tl
emcen,
Algeria; he received
the electrical
engineering
diploma from university
of
Tlemcen, Alger
i
a,
and
the
n
a
Ma
giste
r
in signals and s
y
ste
m
s from
Univers
i
t
y
o
f
T
l
em
cen, Alg
e
ria
and the P
h
D. degree in E
l
e
c
t
r
onics
from
the Univers
i
t
y
of
Tlemcen (Alg
er
ia),
in 2012.
His research in
terests ar
e Image processing,
Medical imag
e
compression, wavelets transfor
m and optimal
encoder
.
Correspondence
ad
dress: Bechar
Uni
v
e
r
si
ty
,
De
pa
rt
me
nt
of E
l
e
c
t
r
ic
a
l
E
ngi
nee
r
i
ng,
Be
c
h
a
r
,
Al
ge
ri
a
,
E
m
a
il:
beladgh
am
.tlm
@gm
a
il.com
Abdelm
alik TALEB-AHMED
was born in Rou
b
aix,
Franc
e
, in
1962. He receiv
e
d a post graduat
e
degree and
a Ph. D. in
Electron
ics and Microw
aves from the University
of Lille1 in
1988
and
1992. From 1992 to 2004, He
was an Associate Profe
ssor at the University
of
Littoral, Calais
.
Since 2004, He is currently
a Pro
f
essor at the Univ
ersity
of Valen
c
ienn
es
in the department GE2I,
and does his research at the LA
MIH FRE C
N
R
S
3304 UVHC,
His research interests includ
es
signal and
imag
e processing. Imag
e segmentatio
n, Prior knowled
g
e in
tegration
in
image analy
s
is,
Partial Diff
eren
tial Equ
a
tions an
d Variation
a
l
M
e
thods in image analy
s
is, Image compression,
Multim
odal signal processing
, Medic
a
l im
age
an
al
y
s
is, inc
l
uding
m
u
ltim
odal im
age registra
tion
,
etc. Correspondance address: Lamih Umr-Cnrs
8
530 Valenciennes Mont-Houy
University
59313
,
Valenc
iennes
,
Fr
ance
.
E-m
a
il:
taleb@univ-valenciennes.fr
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