TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.1, Jan
uary 20
14
, pp. 724 ~ 7
3
3
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i1.3364
724
Re
cei
v
ed Ma
y 29, 201
3; Revi
sed
Jul
y
8, 2013; Accept
ed Augu
st 18
, 2013
Multiple-feature Trackin
g
Based on the Improved
Dempster-Shafer Theory
Jie Cao
1
,
Lei
l
ei Guo*
1
,
Xing Meng
1
,
Di Wu
2
1
School of Co
mputer an
d Co
mmunicati
on, L
anzh
ou U
n
iv
er
sit
y
of T
e
chnol
og
y, Lanz
ho
u, 730
05
0, PR Chin
a
2
Colle
ge of Ele
c
trical an
d Information En
gin
e
e
rin
g
, Lanz
hou
Universit
y
of T
e
chn
o
lo
g
y
, Lan
zhou, 73
00
50,
PR China
*Corres
p
o
ndi
n
g
author: L
e
il
ei
Guo, e-mail: 7
455
41
228
@qq
.
com
A
b
st
r
a
ct
De
mpster-S
haf
er evid
enc
e theory is w
i
de
ly used i
n
the fie
l
ds of decis
ion
l
e
vel i
n
for
m
ati
o
n fusion.
In order to ov
erco
me th
e pr
obl
e
m
of the
counter-
i
ntuitiv
e
results e
n
co
untere
d
w
hen
usin
g De
mpster
’s
combi
natio
n ru
le to combin
e
the evide
n
ce
s w
h
ich ex
ist
hig
h
conflict, a mo
difie
d
se
que
ntial w
e
ig
h
t
ed
evid
ence
co
mb
inati
on
is pr
op
osed. F
i
rstly, t
he cre
d
i
b
il
ity of
each
evi
d
e
n
c
e
can
b
e
o
b
tai
ned
bas
ed
on
K-L
distanc
e, besi
des, the u
n
c
e
rtaint
y of e
a
c
h evid
enc
e
can o
b
tain
ed
base
d
on i
n
formati
on
entr
opy.
Si
mu
l
t
an
e
o
u
s
l
y
, u
s
i
n
g th
e
u
n
c
e
r
ta
i
n
ty o
f
e
a
c
h
e
v
id
en
ce
to
im
p
r
o
v
e
the
cre
d
i
b
i
li
ty o
f
e
a
c
h
e
v
id
en
ce
, then
the w
e
ig
hts of the b
o
d
i
es of
e
v
ide
n
ce
are o
b
t
aine
d b
a
sed
o
n
the i
m
prov
ed
credi
bil
i
ty of e
a
ch ev
id
ence, t
h
e
w
e
ights gen
er
ated are us
ed
to mod
i
fy the bod
ies of ev
id
ence i
n
clu
d
in
g
the previo
us combi
natio
n re
sult,
the prev
io
us e
v
ide
n
ce
and
the n
e
w
arrivi
n
g
bo
dy of
evid
ence
at curre
n
t
step. F
i
nal
ly, accord
in
g to t
h
e
De
mpster
’
s
co
mb
in
ation ru
le
, the w
e
ighted avera
ge co
mb
in
ation res
u
lts can be
obtai
ne
d. In th
e
exper
imenta
l
p
a
rt, the i
m
pr
ov
ed
meth
od
is
used t
o
fuse
v
i
deo
multi
p
le f
e
atures i
n
targ
e
t
tracking syst
em
and
co
mp
are
d
the res
u
lts w
i
th the st
and
ard
D-S the
o
ry.
T
he si
mul
a
tion
r
e
sults s
how
th
at the
prop
ose
d
meth
od h
a
s be
tter performanc
e.
Key wo
rd
s
: ob
ject tracking, p
a
rticle filter, D-
S
evidence theory, m
u
lti-feature fusion
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Obje
ct tracki
ng ha
s many
application
s
in the
field of comp
uter
vision, su
ch
as visu
al
surveill
an
ce,
Intelligent meeting
syst
em, autom
at
ic navigatio
n
of robots,
human
-comp
u
ter
intera
ction, m
u
lti-medi
a system and so o
n
[1]. In
t
he real trackin
g
p
r
ocess,
different feature
s
are
use
d
to represe
n
ted o
b
je
ct, su
ch
as
colo
r hi
stog
rams [2], ed
g
e
[3] and m
o
tion. Du
e to
the
unpredi
ctable
compl
e
x ch
ange of b
a
ckgroun
d an
d
object’
s fea
t
ure can
cha
nge ove
r
time.
Hen
c
e,
usin
g
a
single
fea
t
ure
can
'
t tra
c
k obj
ect
ro
bustly. The
fusio
n
of m
u
l
t
i-feature
is
an
effective mea
n
s to solve th
e probl
em
s.
Re
cently, ma
ny tracking
algorith
m
s
b
a
se
d
on m
u
l
t
i-feature fu
si
on are prop
ose
d
by
resea
r
chers.
The mai
n
differen
c
e
s
of al
gorithm
s
i
s
th
at the feature
extraction
a
nd the differe
nt
fusion st
rate
gies. The
D-S evidence theory fusi
on
has attra
c
ted
many rese
a
r
ch
ers’ attent
ion.
Evidence
the
o
ry, also
kno
w
n a
s
Dem
s
p
t
er-Shafe
r
(D-S), first p
r
op
o
s
ed i
n
1
967
b
y
the De
mpst
er
[4], later be
improve
d
a
nd p
r
omote
d
in 19
76 by
Shafte [5]. Evidence
the
o
ry is a u
s
e
f
ul
uncertainty re
aso
n
ing the
o
ry and provid
e
s
a po
we
rful
method fo
r the expre
s
sion
and synth
e
si
s
of uncertai
n
informatio
n. Given the
s
e
advantag
es
, it
has
b
een
su
ccessfully applie
d
to
d
a
ta
fusion, ta
rget
recognitio
n
a
nd intellig
ent
deci
s
io
n-m
a
ki
ng
system [6]
.
In the
frame
w
ork of
pa
rticle
filter, the ide
a
of Eviden
ce theo
ry is
use
d
to fu
se
the bl
ock
color
histo
g
ra
m and
Di
sta
n
ce
measure of the maximum
gradi
ent by Z
ou [7]. The id
ea of eviden
ce theory i
s
al
so u
s
e
d
to fuse
pluralitie
s fea
t
ures of targ
e
t
by Cao [8,
9]. Although these method
s adopt
s evid
ence theory to
fuse target’s
multiple featu
r
es,
D-S evid
ence t
heo
ry is se
nsitive to
noise a
nd h
a
s lo
w tra
cki
ng
robu
stne
ss in
stro
ng
noi
se
enviro
n
ment
. Simult
aneo
usly, D-S evi
den
ce h
a
s “o
ne ticket vet
o
”,
“poo
r ro
bu
stn
e
ss”a
nd othe
r defects.
In orde
r to so
lve the pro
b
l
e
ms of
D-S e
v
idence, man
y
algorithm
s
have bee
n i
m
prove
d
by schol
ars,
whi
c
h
ca
n b
e
divided
into
three
ca
tego
ries. T
he fi
rst
method
is a
amend
ment
of
combi
nation
rule
s of
D-S
eviden
ce th
eory, an
d
its essen
c
e
is
to remove
n
o
rmali
z
atio
n
step
whi
c
h d
eal
s
with the
redi
stributio
n of
confli
ct
information in
co
mbination
rul
e
s. Th
e typical
improve
d
alg
o
rithm
by [10
]
assign
ed th
e conflict
s
inf
o
rmatio
n of e
v
idence to th
e focal ele
m
ent
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
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TELKOM
NIKA
TELKOM
NIKA
Vol. 12, No
. 1, Janua
ry 2014: 724 – 7
3
3
725
whi
c
h is
assi
gned a
gre
a
ter ba
si
c pro
bability as
sig
n
ment amo
n
g
the focal e
l
ements,
whi
c
h
calle
d ab
so
rp
tion method.
This al
go
rith
m is
simple
i
n
appli
c
ation,
but lost the
combi
nation
of
multi-source
data
inte
rcha
nge ability.
The se
con
d
method i
s
o
n
ly to modif
y
the source
of
eviden
ce, a
n
d
do
esn't mo
dify the comb
ination
ru
le.
The typi
cal i
m
prove
d
met
hod
s a
r
e: M
u
rphy
[11] usi
ng
a
method
of
si
mple ave
r
a
g
i
ng, the
disad
v
antage
of thi
s
m
e
thod
do
esn't
con
s
ide
r
the
relation
shi
p
b
e
twee
n the evidences. On
the basis
of
Murply, Den
g
[12] introduced the eviden
ce
distan
ce
fun
c
tion to
obta
i
n the
credib
ility of
evide
n
ce. It
conv
erge
s fa
ste
r
than M
u
rph
y
’s
averagi
ng m
e
thod. The
third metho
d
is to modify
the
rules
of evide
n
ce
co
mbin
ation on
the
ba
sis
of handin
g
the eviden
ce source. T
he typical imp
r
ove
d
algorith
m
is Li [13]. This algorith
m
first
l
y
discou
nted the pro
c
e
ssi
ng
of t
he evidence source, a
nd then used
Demp
ster co
mbination rul
e
s
whi
c
h re
mov
e
the norm
a
lization fa
ctor
to combin
e a
nd allo
cated
confli
ct information acco
rding
to the su
ppo
rt of focal el
e
m
ent. The m
e
thod
can
de
alt with the e
v
idences
und
er hig
h
confli
ct
situation. Th
ese imp
r
ove
d
method
s were lack
of
practi
cal ap
plicatio
n, onl
y used num
erical
example
s
to
verify their va
lidity. However, for
the
m
u
lti-se
nsor da
ta fusio
n
, the
ch
ang
e of
d
a
ta
sou
r
ce is sust
ained a
nd the
environm
ent is more com
p
lex.
For the
co
mp
lexity and instability of targ
et tr
ackin
g
sy
stem; this
pa
per
pro
p
o
s
ed
a ne
w
tracking al
go
rithm of multi-feature
s
fusi
o
n
based
the improve
d
evid
ence theory. But currently the
fusion of evid
ence theori
e
s is base
d
on
batch fu
sion.
In the actual time, the time of obtainin
g
informatio
n with se
nsor
su
ccessively
divided.
Th
e sen
s
o
r
s
can't re
ceive
all the evide
n
ce
sou
r
ces at th
e same
time. Thu
s
thi
s
pa
per ado
pts seque
ntial fu
si
on m
e
thod.
Whe
n
the
sy
stem
colle
cts
a ne
w evide
n
ce, u
s
ing K
-
L di
sta
n
ce
and th
e e
v
idence un
ce
rtainty to mod
i
fy the previo
us
combi
nation
result, the p
r
e
v
ious evid
en
ce and th
e
ne
w arriving
bo
dy of evi
den
ce at cu
rrent st
ep;
according
to
Dem
s
pte
r
co
mbination
rules to
comp
let
e
the
cu
rrent
step
evide
n
ce combin
atio
ns.
On the o
ne h
and, we u
s
e
nume
r
ical ex
ample
s
to
de
monst
r
ate the
effectivene
ss of the propo
se
d
algorith
m
. On the other ha
nd, the algori
t
hm is in
trod
uce
d
to video multi-features fusi
on, wh
ich
has a
signifi
cant pra
c
tical
meanin
g
.
In the re
st of
this pa
per,
we expl
ain th
e sh
ortcomin
gs a
nd o
u
r al
gorithm i
n
Se
ction 2.
Experimental
re
sults
and
analysi
s
a
r
e re
porte
d i
n
Sectio
n 3.
We
con
c
lu
de this
pap
e
r
in
Section 4.
2. The Propo
sed Algori
t
h
m
The ba
si
c co
nce
p
ts of
D-S evidence theory
can
be
see
n
in the
referen
c
e
s
[1
,2]. This
se
ction firstly
introdu
ce
s the sh
ortcomi
ngs of
D-S e
v
idence theo
ry, and then
our alg
o
rithm
is
given.
2.1 D-S Ev
id
ence Th
eor
y
’s Shortcomi
ngs
The
ration
ality of com
b
ina
t
orial the
o
ry i
s
p
r
oved
in t
heory
by De
mpste
r
a
nd
Shafer.
Other
algo
rithms in
deali
ng with
un
ce
rtainty can
n
o
t be compa
r
ed
with D-S
eviden
ce th
eory.
Actually
the utilization of D-
S evidence theory may cause
some problems. We often
use
example
s
to analyze the insuffici
ent of D-S evide
n
ce
theory.
Table 1. The
BPA for EX1
Table 2. The
BPA for EX2
Table 3. The
BPA for EX3
EX1: Two
groups of Basi
c Proba
bility Assignment (BPA) evi
dence reports
are show in
table 1. After eviden
ce co
mbination fo
rm
ula, we can
obtain the fusion results a
s
:
m(A)=m(B
)=0
.
m(C)=1, K=0.9999.
Re
sults sho
w
that fu
sion
ta
rget i
s
C, T
h
i
s
i
s
obviou
s
ly
agai
nst
with
our no
rmal
co
gnition
.
In D-S eviden
ce, K reflect
s
the confli
ct betwee
n
ev
ide
n
ce
s. In this example it is con
c
lu
ded th
at K
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
Multiple-fe
a
tu
re Tracking B
a
se
d on the Im
prov
e
d
De
m
p
ster-Sh
a
fe
r Theo
ry (Leil
e
i Guo)
726
is 0.99
99, it mean
s that th
e co
nflict bet
wee
n
two
gro
ups
of eviden
ce i
s
con
s
ide
r
able. T
he fu
sion
result is not a
d
visabl
e in this situatio
n.
EX2: Two groups of Basi
c Probability Assignme
nt(BPA) evidence r
eports are show in
table 2. After eviden
ce co
mbination fo
rm
ula, we can
obtain the fusion results a
s
:
m(A)
=m(B
)= m(C
)
=
m
(
D)
=m(E)=0.2, K=0.8.
Although the
two eviden
ce
s are exactly same in ta
ble
2, it is concl
uded that K is 0.8, it
mean
s that the coeffici
e
n
t K can n
o
t really
rep
r
esent the relation
ship b
e
twee
n the two
eviden
ce
s.
EX3: We
give
so
me
eviden
ce
s g
r
ou
ps a
nd ma
ke
the
fusio
n
a
c
cordi
ng the
D-S e
v
idence
theory. The groups
of
Basi
c Probability Assignme
nt (BPA) evidence report
s
are
show i
n
tabl
e 3.
After evidence combi
natio
n formula,
we
can o
b
tain th
e fusion resul
t
s as:
m(A)=m(B
)=0
.
m(C)=1, K=0.9999
99.
The fu
sion
re
sults cl
early
n
o
t fit to peopl
e’s
nor
mal lo
gic, the
re
aso
n
of thi
s
ki
nd
probl
em
is that the ba
sic tr
ust di
stri
bution of
A
is 0
whi
c
h from th
e se
con
d
evi
den
ce. The
result of
A
alway
s
eq
ual
to ze
ro, n
o
matter h
o
w
much
the
ba
sic tru
s
t di
stribution from
other
eviden
ce
s
sup
port
A
. Own
i
ng the cha
r
a
c
teri
stics of one ticket
veto, this short
c
o
m
ing for D-S evidence
theory is very
deadly.
2.2. Weighte
d
Ev
idence Amendmen
t Based o
n
K-L
Dista
n
c
e
and Ev
idence Un
cer
ta
int
y
Measur
e
Weig
hted eviden
ce ame
n
d
ment ba
sed
on K-
L distance whi
c
h
prop
osed by
[14] and
evidence uncertainty measure
consi
s
ts of two
steps. The fi
rst
step obtains t
he credibility of
eviden
ce
s base
d
on K-L
distan
ce. The se
con
d
step further a
m
endm
ents t
he credibility
of
eviden
ce ba
sed on evide
n
c
e un
ce
rtaint
y measu
r
e to
stren
g
th the effects of excellent eviden
ce
s
and to su
ppre
ss the effe
cts of interferen
ce eviden
ce
s.
K-L di
stan
ce
is al
so
calle
d
the rel
a
tive e
n
tr
opy, it is a
measure of t
he di
stan
ce b
e
twee
n
prob
ability di
stributio
n P
and p
r
ob
abili
ty dist
ributio
n Q. Assumi
ng P and
Q
are p
r
o
babi
lity
distrib
u
tion fu
nction
s, the relative entrop
y
of P with respe
c
t to Q ca
n be define
d
in equatio
n (1
):
n
i
i
i
i
q
p
p
Q
P
D
1
lg
)
||
(
(1)
K-L di
stan
ce
can
mea
s
u
r
e inform
ation
distan
ce
an
d ha
s the n
a
ture of
asy
mmetric.
Ho
wever, it
will hap
pen th
e
situatio
n of
0
lg
whe
n
u
s
ing
K
-
L di
stan
ce
di
rectly m
e
a
s
ure the
distan
ce of e
v
idences. Th
en the modifi
ed K-
Ldi
stan
ce can b
e
defi
ned in eq
uati
on (2
):
k
i
i
i
i
A
m
A
m
A
m
m
m
d
1
2
1
1
2
1
)
(
)
(
lg
]
)
(
[
)
,
(
(2)
In equation (2
),
0.
0001
,
1
m
and
2
m
are basi
c probabilit
y assignment
.
Establishing
the re
co
gniti
on fr
am
ework of fu
sion
system is
U
.
12
,
n
mm
m
as
th
e
basi
c
proba
bi
lity assignm
e
n
t on the re
co
gnition fram
e
w
ork.
Defin
e
1
: Th
e distan
ce b
e
t
ween evid
en
ce
1
m
and
2
m
can be
defined in eq
uation (3
):
)
,
(
)
,
(
)
,
(
1
2
2
1
2
1
m
m
d
m
m
d
m
m
D
(3)
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Vol. 12, No
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3
3
727
Defin
e
2
: After o
b
taine
d
t
he di
stan
ce
of all evide
n
c
e
s
, the
su
p
port of
i
m
can
be d
e
fined i
n
equatio
n (4
):
1,
1
(,
)
0
.
0
0
0
1
i
n
ij
jj
i
Dm
m
(4)
Defin
e
3
:
Th
e cre
d
ibility of evidence
i
m
ca
n be define
d
by equation (5):
n
i
n
i
i
m
Crd
1
)
(
(5)
()
i
Cr
d
m
reflects the
credibility proportion of
evi
dences. It can al
so
reduce the i
n
fluence
of
fusion result by low credibi
lity evidence.
Funda
mentall
y
spea
king, the essen
c
e
of ev
idence
combi
nation i
s
the integra
t
ion of
inco
nsi
s
tent i
n
formatio
n, d
e
riving
a mo
re definit
ive
concl
u
si
on fro
m
the p
r
o
c
e
s
s of
com
b
inat
ion
.
Each
re
ceive
d
evide
n
ce h
a
s
un
certai
nty, but so
me e
v
idences which
have ve
ry
small
un
ce
rta
i
nty
have high
co
nflict with oth
e
r eviden
ce.
Therefore,
th
e eviden
ce which h
a
ve small uncertai
n
ty
sho
u
ld a
ssi
gn
small wei
ght
.
In orde
r to measure evid
e
n
ce u
n
certain
t
y,
we apply the pro
p
o
s
ed
equatio
n by Klir [15].
Defin
e
4
:
Th
e eviden
ce’
s
non
spe
c
ific
can be defin
ed
by equation (6):
A
A
A
m
m
N
2
log
)
(
)
(
(6)
Defin
e
5
:
Th
e eviden
ce’
s
inco
nsi
s
ten
c
y can b
e
define
d
by equation
(7):
AB
B
A
B
A
B
m
A
m
m
ST
)
(
log
)
(
)
(
(7)
Defin
e
6
:
T
he evide
n
ce’
s
u
n
ce
rtainty
factor ba
se
d on th
e evi
den
ce’
s
no
n
s
pe
cific
and
th
e
eviden
ce’
s
incon
s
i
s
ten
c
y can be defin
ed
by equation (8):
)
(
)
(
)
(
m
ST
m
N
m
(8)
Whe
n
the fo
cal elem
ent
A
is
a sin
g
le
point
set, the
evid
ence’s
non
sp
ecific is
ze
ro,
the
overall
un
ce
rtainty is i
n
con
s
iste
ncy. T
h
e
n
the
eviden
ce’s
un
certai
nty can
be
defi
ned
by eq
uati
on
(9):
A
A
m
A
m
m
)
(
2
log
)
(
)
(
(9)
The credi
bility of evidence
s
ba
sed o
n
K-L dista
n
ce only con
s
id
er the relative distan
ce
betwe
en
evidence, it do
n’t co
nsi
der the
inhe
rent
un
certainty of ev
iden
ce. Fo
r t
h
is
defe
c
t, we
apply the eviden
ce’
s
un
ce
rtainty to
amend the credibi
lity of evidences.
Defin
e
7
:
Regarding th
e
eviden
ce’
s
uncertainty a
s
qu
estio
ned
factor fo
r t
he cre
d
ibility of
eviden
ce. Th
en the amen
d
ed credibility of
evidence can be defin
ed
by equation (10):
)
(
)
(
)
(
i
i
i
m
m
Cred
m
Credm
(10
)
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ISSN: 2302-4
046
Multiple-fe
a
tu
re Tracking B
a
se
d on the Im
prov
e
d
De
m
p
ster-Sh
a
fe
r Theo
ry (Leil
e
i Guo)
728
Defin
e
8:
Th
e weig
hts of eviden
ce
s ca
n be define
d
by equation (11):
n
i
i
i
i
m
Credm
m
Credm
m
1
)
(
)
(
)
(
(11
)
Amende
d re
sults ma
ke th
e
eviden
ce
s which
hav
e hi
g
h
un
certai
nty get greater
weights,
and ma
ke the
evidences
which h
a
ve lower un
ce
rtainty have smalle
r weight
s.
Evidence
of
traditional
co
rre
ction
meth
od i
s
batch-t
ype, it mea
n
s
that
the
eviden
ce
s
whi
c
h
wait fo
r combin
ation
are m
odified
whe
n
t
he system colle
ct all
eviden
ce. Ho
wever,
in
the
actual a
pplica
t
ion, obtainin
g
ev
iden
ce
s are sequ
entia
l. So this paper propo
se
s
a new
sequ
e
n
tial
weig
hted evi
den
ce
com
b
i
nation a
p
p
r
o
a
ch. T
he
sp
ecific ste
p
s
of eviden
ce
s com
b
inatio
n
as
follows
:
Step 1: for
o
b
tained fi
rst
eviden
ce a
n
d
se
con
d
evid
ence:
1
new
m
and
2
new
m
, and
reg
a
rd
11
co
mb
n
e
w
mm
as the re
sult
combi
nation
of step 1.
The re
sult
s of modified eviden
ce
s as:
21
1
2
2
()
(
)
w
mm
m
m
m
.
The eviden
ce
s co
mbinatio
n results of st
ep 2 as:
22
2
co
m
b
w
w
mm
m
.
Step 2: for i=3:k: Assu
min
g
combi
natio
n results
of at current step
is related to previou
s
combi
nation
result,
previo
us coll
ecte
d eviden
ce
an
d the
ne
w a
rriving
bo
dy
of eviden
ce
a
t
cur
r
e
n
t
st
ep a
s
:
11
1
1
()
(
)
(
)
w
c
om
b
c
om
b
n
ew
new
n
ew
new
ii
i
i
i
i
i
mm
m
m
m
m
m
Then the result of combin
ation at curre
n
t step ca
n b
e
defined by:
comb
w
w
ii
i
mm
m
.
Algorithm flowchart is
s
h
own on the right.
Figure
1
sho
w
s that the combinatio
n re
sults of ea
ch step are not
only related to the new arri
ving
body of evide
n
ce
at curren
t step, but al
so
relate
d
to previou
s
coll
ected eviden
ce
a
nd previ
o
u
s
combi
nation
result. Besi
de
s, In each
co
mbinati
on
ste
p
, not only the distan
ce of
evidence an
d
but also the
uncertainty m
easure i
s
utili
zed to
dete
r
mine the
wei
ghts of t
he
b
odie
s
of evid
ence.
Then th
e wei
ghts g
ene
rat
ed a
r
e u
s
e
d
t
o
modify
the
bodie
s
of
eviden
ce in
clu
d
i
ng the
previo
us
combi
nation
result, the
pre
v
ious
colle
cte
d
evide
n
ce a
nd the
ne
w a
rriving
bo
dy
of eviden
ce
at
cur
r
e
n
t
st
ep.
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TELKOM
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TELKOM
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Vol. 12, No
. 1, Janua
ry 2014: 724 – 7
3
3
729
Figure 1. Algorithm flowch
art
3. Results a
nd Analy
s
is
In ord
e
r to
fu
lly verify the
validity of pro
posed al
go
rithm, on th
e o
ne h
and,
we
applie
d
nume
r
ical example to ana
lysis pr
opo
se
d algorith
m
a
nd som
e
cla
s
sic
D-S theo
ry algorithm. On
the other ha
nd, our ne
w
algorith
m
is applie
d to
the video targ
et tracki
ng. Furthe
rmo
r
e,
our
tracking
re
sul
t
s are
comp
ared with t
he tracking results used
D-S the
o
ry.
3.1. Fusion Modeling Ba
sed on D-S Ev
idence
In this pape
r,
we esta
blish
a D-S fusio
n
model for
video multipl
e
feature
s
u
nder the
frame
w
ork of
the particle
filter. The particle f
ilter ca
n solve the probl
em tra
c
king un
de
r the
nonlin
ear, no
n-Ga
ussia
n
model [16, 17
].
The D-S fusi
on model fo
r video multiple feature
s
un
der the fram
ewo
r
k of the
particl
e
filter is sho
w
n in Figure 2
.
Read the kth fr
ame ima
ge from a video se
que
nce. Extract color
feature a
nd e
dge featu
r
e o
f
the tar
get. Map color fe
ature a
s
evid
ence
1
m
and ed
ge feature as
eviden
ce
2
m
.At the same time
, read the
(k-1)th fram
e pa
rticle
set an
d
get the kth frame pa
rticle
set
{
12
,
kk
k
N
s
X
XX
} by state tran
sition. Map the pa
rti
c
le set as th
e frame of di
scern
m
ent
.
Acco
rdi
ng to the colo
r featu
r
e of the targ
et, ma
tch feature by cal
c
ul
ating Bhattacharyya dista
n
c
e
betwe
en
current ch
ara
c
te
ristic and
ob
ject cha
r
acte
ristic.
Define
an ob
se
rva
t
ion pro
babili
ty
den
sity functi
on of th
e p
a
rt
icle to
mea
s
u
r
e the
si
milari
ty. At this poi
nt, we
have
establi
s
h
ed t
he
D-S fusio
n
model for video multi-fe
ature fusi
on.
In the mo
del, the basic mappi
ng
s are
summ
ari
z
ed as
follo
ws:
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ISSN: 2302-4
046
Multiple-fe
a
tu
re Tracking B
a
se
d on the Im
prov
e
d
De
m
p
ster-Sh
a
fe
r Theo
ry (Leil
e
i Guo)
730
12
{,
,
}
kk
k
Ns
X
X
X
frame
o
f
d
isc
e
rnment
1
color
h
is
to
g
ram
f
ea
t
u
r
e
ev
i
d
e
n
c
e
m
,
2
ed
g
e
f
ea
t
u
r
e
e
v
i
d
en
ce
m
12
1
1
,
2
{,
,
}
(
)
s
s
cc
c
k
Ni
i
N
ww
w
m
X
，
12
2
1
,
2
{,
,
}
(
)
s
s
tt
t
k
Ni
i
N
ww
w
m
X
Figure 2. The
process of e
s
tabli
s
hin
g
D-S model for video multi-fe
ature fusi
on
3.2. Numeric
a
l Example
Firstly, we ap
plied the ne
w algorithm, Sun [18],
Yager [19], Li [20] t
o
s
i
mulation for Ex1,
We get the fu
sion results which a
r
e sho
w
n in Tabl
e 4
Table 4. Fu
si
on re
sult of different situati
o
n
After simulati
on the evide
n
c
e
which p
r
ovided by
Ex
1,
we can clea
r observe
the result
in
Table
4. The
algorith
m
by
Yager is
pron
e to t
he
phe
n
o
meno
n of
o
ne ticket veto
. The al
gorith
m
of Sun ove
r
comes the
ph
enome
non
of
one
ticket
v
e
to, ho
wever, this m
e
tho
d
exist
s
ma
ny
unkno
wn pa
rts, so combin
ation re
sults
are not
cond
uctive to making. The fusi
on re
sults
wh
ich
cal
c
ulate
d
fro
m
the algorith
m
of Li and our pr
opo
se
d are content p
eople’
s no
rm
al cog
n
ition.
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ISSN: 2302-4
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TELKOM
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Vol. 12, No
. 1, Janua
ry 2014: 724 – 7
3
3
731
Secon
d
ly, this stu
d
y will compa
r
e
with some
cla
s
sic D-S evide
n
ce theory al
go
rithms.
We
will
dem
o
n
strate
the
superi
o
rity the
ne
w al
go
ri
thm. Assume
that the ta
rg
et ha
s th
ree
m
o
st
likely states
at each mom
ent. The frame of disce
rnment is:
= {
1
1
XS
t
a
t
e
,
2
2
XS
t
a
t
e
,
3
3
X
S
ta
te
}.Data is
colle
cted by five cameras. The
dates a
r
e sho
w
n in Tabl
e 5
.
Table 5. The
BPA of evide
n
c
e
s
Evidence
BPA
State output
m
1
m
1
(X
1
)=0
.
5
，
m
1
(X
2
)=0.2
，
m
1
(X
3
)
=
0.3 State1
m
2
m
2
(X
1
)=0
，
m
2
(X
2
)=0.9
，
m
2
(X
3
)
=
0.1 State2
m
3
m
3
(X
1
)=0
.
6
，
m
3
(X
2
)=0.1
，
m
3
(X
3
)
=
0.3
State1
m
4
m
4
(X
1
)=0
.
8
，
m
4
(X
2
)=0.1
，
m
4
(X
3
)
=
0.1 State1
From Ta
ble 5
.
We can o
b
serve that thre
e
eviden
ce
s suppo
rt state
X1. But the e
v
idence
m
2
gives the state X2. So the fusio
n
re
sults sh
ould gi
ve state X1.
Table 6. Fu
si
on re
sult of different algo
rithms
Algorithm m
1
,m
2
m
1
,m
2
,m
3
m
1
,m
2
,m
3
,m
4
Dempster
m(X
1
)=0.00
00,
m(X
2
)=0.85
71,
m(X
3
)=0.14
29,
m(X
1
)=0.00
00,
m(X
2
)=0.66
67,
m(X
3
)=0.33
33 ,
m(X
1
)=0.00
00,
m(X
2
)=0.66
67,
m(X
3
)=0.33
33,
State output
State 2(Er
ror
)
State 2 (Er
r
or
)
State 2(Er
ror
)
Y
age
r
m(X
1
)=0.00
00,
m(X
2
)=0.18
00,
m(X
3
)=0.03
00,
m(X
1
)=0.00
00,
m(X
2
)=0.01
80,
m(X
3
)=0.00
90 ,
m(X
1
)=0.00
00,
m(X
2
)=0.00
18,
m(X
3
)=0.00
09,
State output
State 2(Er
ror
)
State 2 (Er
r
or
)
State 2(Er
ror
)
Sun
m(X
1
)=0.13
31,
m(X
2
)=0.47
27,
m(X
3
) =0.1
364,
m(X
1
)=0.24
48,
m(X
2
)=0.28
51,
m(X
3
)=0.16
48,
m(X
1
)=0.33
41,
m(X
2
)=0.23
04,
m(X
3
)=0.14
16,
State output
State 2(Er
ror
)
State 2 (Er
r
or
)
State 1(Co
rrect)
Murph
y
m(X
1
)=0.15
43,
m(X
2
)=0.74
69,
m(X
3
)=0.09
88 ,
m(X
1
)=0.39
15,
m(X
2
)=0.50
78,
m(X
3
)=0.10
01,
m(X
1
)=0.79
95,
m(X
2
)=0.17
54,
m(X
3
)=0.02
51,
State output
State 2(Er
ror
)
State 2 (Er
r
or
)
State 1(Co
rrect)
Thi
s
s
t
ud
y
m(X
1
)=0.42
06,
m(X
2
)=0.39
44,
m(X
3
)=0.18
50,
m(X
1
)=0.67
09,
m(X
2
)=0.12
92,
m(X
3
)=0.19
98,
m(X
1
)=0.85
53,
m(X
2
)=0.08
14,
m(X
3
)=0.06
32,
State output
State 1(Co
rrect)
State 1 (Co
rrect)
State 1 (Co
rrect)
After sim
u
lati
on the
evide
n
ce
which p
r
ovi
ded
by Ta
ble 5,
we
ca
n cl
ea
r o
b
se
rve the
result in T
abl
e 6. Th
e alg
o
r
ithms by D-S and Ya
ge
r are pro
ne
to
exist
the
p
h
e
nomen
on of one
ticket veto, we always
can
not get corre
c
t state.
The algorith
m
s of Sun has di
sa
dvantage of slo
w
conve
r
ge
nce, so
fusi
on
re
sults i
s
n
o
t con
ductive to
ma
king. After ge
tting the fou
r
t
h
evide
n
ce, we
can ma
ke
correctly de
cision. The al
gorithm
by Murp
hy exce
ssive
exag
g
e
rated the
si
ngle
eviden
ce, this algo
rithm h
a
s di
sadva
n
tage of sl
o
w
converg
e
n
c
e. Simultaneo
usly, the algorithm
by Murphy [21] identifies the
correct
target’s stat
e when g
e
tting the fourth evidence. As
illustrate
d in
Table
6, the
perfo
rma
n
ce
of co
nverg
e
n
ce
of p
r
opo
sed
algo
rith
m is
better t
han
above al
go
rithms. T
he
re
aso
n
is that
our propo
se
d algo
rithm
can
strength
en the
effect
of
cre
d
ible
evid
ence fu
rther
and
at the
sa
me time
w
e
a
k
en
the
effect
of in
credible
eviden
ce fu
rther.
So whe
n
fusi
ng two evid
e
n
ce
s
we can
get co
rre
ct
state.
Furth
e
rmore,
the ta
rget’s
state X1
obtains 0.8553 degree of
suppor
t
when fusi
ng the fourth evidenc
e, so the reliability of
our
algorith
m
is b
e
st. Overall,
our p
r
op
osed
algorithm i
s
rational an
d effective.
3.3 Video Multi-Fea
t
ure F
u
sion Trac
king
The belo
w
ex
perim
ent is that we u
s
ed
D-S
theo
ry and pro
p
o
s
ed
algorith
m
to fuse the
target’s two f
eature
s
incl
u
d
ing
col
o
r fe
a
t
ure
and
edg
e featu
r
e. Th
e len
g
th of thi
s
vide
o
seq
u
ence
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 2302-4
046
Multiple-fe
a
tu
re Tracking B
a
se
d on the Im
prov
e
d
De
m
p
ster-Sh
a
fe
r Theo
ry (Leil
e
i Guo)
732
is 83 fra
m
e
s
, this video
se
quen
ce h
a
s t
he followi
ng chara
c
te
risti
c
s: the backgro
und inte
rfere
n
ce
is bigg
er, the target is ob
scured by othe
r similar g
oal
s.
Figure 3. Tra
cki
ng re
sult
s by:D-S evide
n
ce (th
e
first row), p
r
op
ose
d
algorith
m
(the se
co
nd ro
w)
(Frame
s:48,6
1
,62,66,70,8
0
)
We
ca
n
clea
r ob
serve
the
tracking
resul
t
s in
Figu
re
3
.
From
Figu
re 3,
we
ca
n f
i
nd that
D-S
eviden
ce
don’t
stably
track ta
rget i
n
complex
e
n
vironm
ent.
Before
occlu
s
ion
as fram
e 48,
becau
se tra
d
i
t
ional eviden
ce theo
ry do
n’t have pr
e
p
r
ocessin
g
ste
p
, the particl
es di
strib
u
tio
n
is
diverge
n
t. Our alg
o
rithm
has th
e p
r
ep
ro
ce
ssi
ng
step, so the pa
rticle
s distrib
u
tion
is
con
c
e
n
trated.
Namely, ou
r algo
rithm i
m
prove
s
the
tracking
accuracy
com
p
ared t
r
aditio
nal
eviden
ce the
o
ry. Wh
en
occlu
s
ion
occu
rs a
s
frame
s
(61, 62, 6
6
). T
he tra
d
it
ional eviden
ce can
not
accurately tra
ck th
e target, on the
cont
rary, our
algorithm c
a
n ac
curately track
the target. After
occlu
s
ion as frame
s
(70, 80),
tradition
al
evi
den
ce
theory
ca
n re
cover the t
r
a
cki
ng. Thi
s
vi
deo
seq
uen
ce illu
strate
s that
prop
osed al
g
o
rithm i
s
bett
e
r than
D-S eviden
ce in t
e
rm
s of overall
perfo
rman
ce.
4. Conclusio
n
Demp
ste
r
’s rule of
co
mbin
ation
can
out
-come
counte
r
-intuitive resu
lts when
the
different
eviden
ce to
b
e
combin
ed
a
r
e hi
ghly
conf
licting.The
p
r
opo
sed
algo
ri
thm by jointly
usi
ng the
K-L
distan
ce of e
v
idence and
the un
certai
n
t
y meas
u
r
e can efficiently
handle
co
nflicting evide
n
c
e
with b
e
tter
pe
rforma
nce of
conve
r
ge
nce.Furthe
rm
o
r
e
,use
d o
u
r
alg
o
rithm
achiev
ed the
tra
c
kin
g
of
target.This achi
evement has
a certai
n
pra
c
tical signi
fican
c
e.
Ackn
o
w
l
e
dg
ement
This work was supp
orte
d by the National Natu
ral Scien
c
e
Found
ation
of China
(612
630
31)
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