Copy igh
co
IF AC In elligen Componen s and Ins umen s
o Con ol Applica ions, Annecy, F ance, 1997
VISUAL
TRACKING
BASED
ON
ACCUMULATED
DIFFERENCES
1
Manuel
Va gas
and
F ancisco
R.
Rubio
Dp o. Ingenie ia
de
Sis emas y Au oma ica
Escuela Supe io
de
Ingenie os
A da. Reina Me cedes
sin,
41012-Se illa (Spain)
Tel:
34-5-4556855,
Fax:
34-5-4556849, E-mail: [email p o ec ed]
Abs ac .
This
a icle p esen s
an
algo i hm o acking
an
objec using a obo
p o ided wi h a came a in
he
inal e ec o . Simple me hods a e s udied o es ima -
ing
he
op ical
low
based on accumula ed di e ences which pe mi acking in eal
ime.
The
s udy
is i s ealized by simula ion
and
hen
he
bes
esul s a e ied
expe imen ally.
Keywo ds.
Robo ics, Image p ocessing, ViSual mo ion, Op ical low, T acking.
1. INTRODUCTION
This a icle is cen e ed on
he
analysis o
he
acking
p oblem linking a ision sys em
and
an
a icula ed
a m
by he
adap a ion
o a
came a
in
he
inal e ec o o
he
a m
( his
is
e med eye-in-hand con igu a ion).
The
ollowing p oblem
is
posed: "Obse ing
an
objec on
he
isible scene, compensa e i s displacemen s in such a
way
ha
i
always occupies
he
same posi ion in
he
image" (p e e ably
a
he
cen e ).
The
in o ma ion
abou
he
mo emen achie ed om a
sequence o images can be cha ac e ized by
he
so
called
op ical low (Balla d D.H., 1982).
The
op ical
low
is a
consequence o
he
ela i e mo emen be ween
he
cam-
e a
and
he
objec s on
he
scene. Se e al echniques o
es ima ing he op ical
low
ha e been de eloped (Ma -
in
W.N., 1988), (Fu K.S., 1986), (PapanikolopoulosN.P .. ,
1993), no able amongs
hem
being he echniques based
on he in ensi y unc ion g adien . Such echniques a e
based on
he
so called g adien cons ain equa ion, which
ela es
a
e e y pixel,
he
space- ime g adien o
he
eloci y ec o associa ed
o
ha
pixel. The e a e also
1
The
au ho s
would like
o
hank
o
CICYT o
suppo ing
his
wo k
unde
g an
TAP
95-0370.
259
SOme
s udies combining s e eoscopy wi h
he
op ical
low
de ec ion (AlIen P.K., 1993).
In
hei o iginal o m, all
hese algo i hms a e e y es ic ed. On one hand, hey
assume
ha
any change o he in ensi y unc ion
a
each
pixel
is
only due
o
he
mo emen . On
he
o he hand,
hey equi e images wi hou discon inui ies in space and
ime.
Many mono-came a isual acking algo i hms
y
o
de ec
and
ollow
well-known objec s, which ha e some
isual ea u es, he posi ion o each is accu a ely known
ela i e
o
an objec coo dina e sys em (Hashimo o, 1993).
The
acking p ocess es ablishes s ong imposi ions in
eal ime because
an
immedia e esponse
o
he
displace-
men s o he objec is needed. This a icle p esen s a
me hod based on
he
accumula ed di e ence echnique,
which allows o a apid esponse using
no
oo powe -
ul ha dwa e.
In
his me hod
he
in e es is cen e ed in
de ec ing and acking an objec wi hou a p e iously
de ined shape o s uc u e.
We
a e
jus
ocused o ob-
jec s which a e dis inguible om
he
backg ound and
which a e mo ing (since
he
pu pose is
o
ack mo ing
objec s,
he
mo ion i sel will be used as a di e encia ing
p ope y).
Hence, ou pu pose
is
o ack a bi a y shaped mo ing
spo s
in wo dimensions.
2.
OPTICAL
FLOW
The
i s
app oxima ion
o c ea ing a di e ence image
(Fu K.S.: 1986) is based on
he
c i e ion exp essed in
he
equa ion,
ADJ
j(x,
) = { 1
i
IJ(x ,y , j) -I(x , y,
j
)1 > 6; ( j > j)
}l
)
J Y 0
o he wise
;
The
new image, called ADI (Absolu e Di e ence
Im-
age)
is
he
esul o a compa ison be ween wo
ames
(g abbed images) successi e in ime,
he
i s one aken
a
i
and
he
second one
a
j.
This di e ence be ween
he
in ensi y
o
he
pixel be o e
and
a e wa ds
is
consid-
e ed signi ican
o
negligible, depending on
he
h eshold
alue used (8).
Thus
in
he
ADI image hose pixels o
he
di e ences
esul ing om
he
mo emen will
appea
as ones, and
also hose
due
o
noises which cause a change o in en-
si y supe io
o
he
e h eshold.
The
small a eas o 1 's
which
appea
can
be
due
o
noise o
o
eal
bu
insigni i-
can
di e ences,
a e
elimina ed by echniques o e osion
and
pos e io
dila ion
o
he
image objec s; his will also
egula ize
he
shape
o said objec s (as said be o e,
he
exa
c
objec 's
shape
is
no
o in e es ).
Th
e se o pixels o
he
mobile objec which ake
up
new posi ions in
he
image which p e iously belonged
o
he
backg ound, will
be
called
he
leading edge o
he
objec .
The
se
o
pixels o
he
mobile which lea e
posi ions which p e iously we e occupied by
he
objec
will be called
he
lea ing edge o
he
objec .
The
ADI image will show
bo h
he objec 's leading edge
and
lea ing edge as 1 '
so
Howe e
i
is
o en mo e in e -
es ing o o
b ain
in a di e ence image only one o hese
edges. This leads us
o
wo new ypes o di e ence im-
ages.
Th
e
wa
y
o
calcula ing
bo h
is
gi en by
he
equa-
ions,
PD1
i (
x.
'
={l
i I
(x ,y, ;)
-I
(x ,y,
j»
6; ( J > ;) }
J ' y ) 0
o
he wise;
(2)
,
VDJ
, I X . ) =
{l
i
-
(I
(x , y,
;J
-
I(x
,y,
j))
>
6:
( j > i ) }
J ' Y 0 o he Wlse;
This o mula ion does no ensu e
ha
one edge o
he
o he
is
ob ained
independen ly. This is only
ue
when
he
ange o in ensi ies o
he
mobile
is
highe
han
he
one o
h
e
backg ound
(in his case
PDI
p o ides
he
lea ing edge
and
NDI
he
leading edge), o when
he
in ensi y ange
o
he
mobile
is
lowe
han
he
one o
he
ba
ckg ound
(PDI
gi es
he
leading edge
and
NDI
he
lea 'ing one
).
Howe e his si ua ion de e io a es i
he
an
ge
o
he
objec
's in ensi ies
is
highe
han
he
backg ound's in some a eas
and
lowe in o he s.
260
2.1
Al e na i e
Fo mula ion
o
he
Di e ence
Me hod
Le 's suppose he in ensi y ange o
he
mobile
is
known:
=
[i
m in ' . .
ima",
l (e en i his ange is
no
known om
he
beginning, i can be es ima ed aking
ad an a
ge o
he
mo ion o he objec o in e es , see (Va gas, 1997)),
In o de
o
ob ain an image wi h
he
leading ed
ge
and
sepa a ely ano he wi h
he
lea ing edge
he
oll
owing
o mula ion can be used:
PDI
(x ) = {l i I (x ,y, j)
ET
and
I
(x
,y
,
j)
! .
T; ( j >
d
}
'J
' y 0 o he Wise;
N
DI
(x )
={l
i I
(x,y,
;J
! .TandI
(x , y,
j)
ET
; ( j
> ;)
}
'J ,y 0 o he Wise;
ADI.
" (x, ) = { 1
i
P
Dl
jj (x , y) = 1
o
N
DJjj
(x , y) =
1:
( ;
>
;)
J Y 0
o
he Wise;
wha e e
he
ela ionship be ween
he
in ensi ies o
he
backg ound and hose o
he
mobile migh b
e.
In his case
i
is
unimpo an
ha
in some egions
he
in ensi ies o he mobile a e abo e
and
in
o he
egions
below hose o
he
backg ound.
The
only p oblem which
may a ise
is
i he e a e in ensi ies o
he
backg ound
wi hin
he
ange, because in his case
i
is
no
possible
o
dis inguish wha
is
backg ound
and
wha
is
objec ;
hese egions
will
be
called
in e e ence
egions. Ac u-
all
y,
hese egions ha e no e ec du ing acking so long
as
he
mobile does no pass o e any o
hem
.
up
o now,
he
di e ence images ha e been
ob ain
ed u
s-
ing only wo consecu i e images. Howe e ,
wha
is usu-
ally used
is
he
so called accumula ed di e ence me hod.
In his me hod a i s image
(l
o)
is
aken as a e e en
ce:
R; and
he
ollowing n ames a e all compa ed
o
R
and a e accumula ed on op o
he
same
esul an
image.
~ex
,
he
new e e ence o be used o
he
ollo
,'
ing n
ames is aken: and so on.
Thus
,
he
equa ions
will
now
be
like:
N
DI
(x
)
={
1
i R
(x ,y)
! . andI(x
, y,
j)
ET
:}
(4
)
J ' Y 0 o he Wise;
The ac
ha
h
e
se
simple di e ences a e accumula ed
can be exp essed
by
h
e equa ion,
N
ADln
(x, y) = L
.l
VDI
J(x ,y) (5)
J
=I
Thus
he
PADI (Posi i e
Accumula ed
Di
e en
ce
Im-
age), NADI (Nega i e
Accumula ed
Di e ence
Imag
e)
and AADI (Absolu e
Accumula ed
Di e ence
Image
):
images a ise. The PADI indica es: o each pixel on which
he
objec was in he e e ence ame,
he
numbe o
ames ( om he e e ence) in which
he
objec has been
abse
n
om his pixel.
Th
e l' ADI indica es
he
numbe
R)
o ames
( om
he
e e ence) in which his pixel, which
ini ially was
no
occupied by
he
objec , has been occu-
pied by said objec .
Figu e 1 illus a es hese concep s wi h
an
example.
I
shows a mobile being displaced
a
he
a e
o 1 pixel/ ame
o
he
igh .
(R
) (R)
(I)
(2) m (4)
~
I)
l (2)
0>
(4)
(I)
.
~~
Cl>
P)
4 3 2 I
~~.
Lm n
: :
::
4 ) 2 I 4 3 2 I 4 3 2 I
(a)
.....
__
....
..
_-
(b)
(R): objec posi
i
on in
che
e e ence ame
(n): objec posi
i
on in he n·ch ame
(c)
Fig.
1.
(a)
PADI
di e
ence
s.
(b )
NADI
di
e ence
s.
(c)
AADI
di e ences
.
This
in o ma ion
abou
he
numbe o ames in which
he e
was no
objec
( o
he
PADI) o he e was
i
( o
he
NADI) is
ansla ed
in o
he
numbe o ames
elapsed since
he
objec le ( o
he
PAD!) o eached
( o
he
NADI) said pixel, ( his second in e p e a ion o
he
accumula ed di e ences allow, as will be seen,
he
eloci y in o ma ion
o
be ob ained). Howe e , his in-
e p e a ion
is
no
alid, o example, i
he
mobile is
e y small in ela ion
o
he
numbe o ames which
a e
accumula ed.
Le
's suppose, o ins ance,
he
objec in Figu e 2, pay-
ing
a en ion
o
he
pixel (x,
y)
showed,
and
calcula e
he
NADI which would
be
gene a ed o e his pixe!.
In
case (a), in which
he
objec
mo es
o
he
igh
a
he
a e
o
one pixel
pe
ame,
he
objec begins
o
be o e
(x
, y) when ame 3 is
aken
,
and
in all
he
ollowing
ames
he
poin
will con inue
o
be occupied by
he
objec
;
he e o e,
s a ing
om ame 3
he
alue accu-
mula
ed o e
he
pixel is inc eased by 1 o each ame
aken.
A
he
end
N
ADI
(x, y) = 5
is
ob ained;
and
his
coincides w
i h
he
numbe
o
ames
g abbed
since
he
pixel was occupied.
(R)
(I)
(2) (3) (4) (
S)
(
6)
(7) (R)
(I
) (2) (3) (4) (5) (
6)
(7)
l,,
ji "
'n,,
jiY
~
;;~
"
"
,
y
;
;
;",
(x.
y)
(R
):
Objec posi
i
on on he e e ence ame
(n):
Ob
jec po'; ion on he n
·
h ame
Fig
. 2.
Objec
mo i
ng
a 1
pixel
/
ame
owa ds
he
igh .
(a ) W
ide
obje
c .
(b) T
hin
o
bjec
.
Le
's now look
a
case (b) o Figu e 2 in which
he
ob-
jec
is specially na ow.
The
pixel is only occupied by
261
he
mobile du ing ames 3
and
4, he e o e
he
alue
i-
nally accumula ed in N
ADI
(x, y) is 2. Howe e ,
a
he
end,
he
numbe o ames elapsed since
he
pixel was
occupied is 5 (
he
same as in case (a)).
This incon enien is almos o e come
in
he
eloci
y
ex-
ac ion
p ocess, gi en
ha
he
di e ence be ween
he
alues accumula ed in a pixel
and
i s neighbo s
and
no
he
absolu e alues
a e
conside ed, as will
be
shown in
he
nex
sec ion.
I
is
con enien
o
poin
ou
a signi ican di e ence be-
ween
PADI
and
NADI;
I
is ob ious
ha
bo h
s op
g owing when
he
objec s ops,
bu
he
PADI
also
s ops
g owing when
he
objec comple ely
qui s
he
a ea
i
was occupying on
he
e e ence image.
This
poin
c
an
be
used, o example,
o
ex ac
s a ic
images om images
on which, om
he
beginning,
he e
a e
mobile objec s.
2.2 Op ical Flow S a ing om Accumula ed Di e ences
The op ical
low
ield
( he
ield o eloci ies
a
each pixel)
can
be
ob ained
om
an
image
o
accumula ed di e -
ences. We
a e
going
o
p esen his deduc ion
s a ing
om
he
N AD
1.
The
image con aining
he
NAD! will
be
called D o
sho
h oughou
his deduc ion.
I ,
as
said be o e,
i
can
be assumed
ha
he
di e ences accumula ed
a
e e y
pixel
can
be
aken
as
he
numbe o ames elapsed since
he
objec occupied
he
pixel
hen
,
D(x+
1,
y)
-D(x, y
),
ep esen s
he
numbe
o di e ence ames om when
he
objec occupied
he
posi ion (x, y) un il
i
occupied
(x + 1, y). Gi en
ha
a disc e e app oxima ion
o
he
de i a i e
is
a di e ence quo ien ,
he
ollowing
equa ion
can
be
w i en
,
D -
aD
~
D(x
+1
,y)
-D
(x,
y)
-D
( 1 )
-D
( )
"'_-~
_ x
+,
y x,y
ox
(x +
1)
-x (6)
D -aD
~
D
(x,y+
1)
-D
(x,y)
-D
(
l)
-D
()
y _ -
~
_ x , y +
x,
y
ay
(y + 1) - y
The
ho izon al componen o
he
eloci y
'"
is
he
num-
be
o
pixels passed o e ho izon ally
pe
ame elapsed
(
he
ime
uni
is
he
ame).
We
can
de ine
he
Vy
com-
ponen in
he
same
wa
y.
I
Dx
is
he
numbe o ames elapsed o
he
ob
j
ec
o
ad ance one pixel (assuming
ha
i
mo es
a
a con-
s an
speed),
and
Vy
is
he
numbe
o pixels passed o e
pe ame elapsed, one is
he
in e se
o
he
o he
. How-
e e ,
he e
is
one mo e de ail, i
he
objec
mo es o
he
igh
he
NADI dec eases in his di ec ion, he e o e Dx
is
nega i e; howe e ,
he
eloci y is posi i e in
ha
di-
ec ion. Acco ding o his,
he
ela ionship be ween
he
componen s o
he
eloci y
and
o
he
di e ence image
g adien is,
1
Vx: = -
-;
Vy
=
--
Dx
Dy (7)
In o de
o
make his g adien calcula ion mo e obus ,
he
pixel's 8-neighbou s will be aken in o accoun , using
he
Sobel masks. In his way,
an
app oxima ion o he
g adien
is
shown in
he
ollowing equa ion,
D
__
Sobelx .
x -8 '
Dy
= _ Sobely
8
2.3
Es ima ion
o
he Cen oid
o
he Mobile
(8)
Ano he me hod making use o accumula ed di e ence
images will be shown.
I
does
no
y
o
es ima e
he
op ical
low
a
each pixel,
bu
he cen oid o
he
mobile
a
each ins an .
I
implemen s a e y in ui i e idea
o
sol e he acking p oblem.
The
cen oid o
he
NADI egion p oduced by
he
mo-
bile will be calcula ed, and his cen oid
is
assumed as
an
es ima ion o
he
eal objec 's cen oid
a
each in-
s an . This
me hod
uses accumula ed di e ence images
al hough
he
accumula ed alues
a
each pixel hem-
sel es a e
no
o in e es ,
bu
he
ex ension
and
loca ion
o
he
accumula ed di e ence egion.
This
is
an app oxima ion which can be inaccu a e unde
some condi ions. In Figu e 3 h ee cases a e p esen ed.
(0)
,·
·w
···
·
' . .
, '
, .
'.
. I
(I)
(Z)
(b)
(2)
(I
):
Objec cen iod
(2
):
NADI
",si
Dn cen oid
(I)
(c)
,
~
."
..
:
...
.
'1
(»
)(
Z)
Fig.
3.
Cen oi
d
o
he
N
ADI
egion
p oduced
by
he
mob
ile.
(a)
In his case
he
a ea
o he NADI egion p oduced
by
he
mobile objec is small ela i e o
he
objec
a ea
; his causes
he
cen oid o he NADI egion
o
be a om
he
eal cen oid o he mobile.
The
g ea e
he
di e ence be ween
he
men ioned a eas
he
g ea e
he
e o .
(b)
This
is
ano he ex eme case in which
he
NADI
egion is much wide
han
he
mobile i sel . This case
is wo se
han
he
p e ious one, he e
he
disc epancy
be ween
he
posi ion o he NADI egion cen oid and
he
eal objec cen oid can be e y la ge.
(c) This
is
he
bes
case, he e
he
es ima ion is e y
p ecise.
The
a ea
o
he
mobile
and
he
a ea
o
he
NADI egion a e qui e simila .
In
his case he mobile
occupies almos exac ly he NADI egion
and
because
o his
bo h
cen oids p ac ically coincide.
262
As
can be seen
he
p ecision o
he
es ima e
is
s ongly
dependen on
he
quo ien
NADI
a ea / mobile a ea.
The
mos a o able case is when
his
quo ien is close o
one. Ac ually,
he
si ua ion in case (a)
is
no
inco ec
om
he
acking poin o iew, because
he
obo
is
di ec ed in on o
he
objec .
2.4
Res ic ions
o
Di e ence
Based
Me hods
The
me hods based on di e ences ha e se e al es ic-
ions such as:
•
The
ange o in ensi ies o
he
mobile mus no
change
oo
much h oughou
he
p ocess. This means
ha
he e canno be signi ican illumina ion di e -
ences along
he
pa h
ollowed by
he
mobile.
•
I
he e is a signi ican
a ea
o in e e ence
he
al-
go i hms con inue wo king well, p o ided
ha
he
mobile does
no
pass o e hose egions which in-
e e e.
•
The
eloci y o
he
mobile should be as li le a i-
able as
pOSSible,
a
leas du ing each accumula ion
cycle, o
he
op ical
low
es ima ion me hod (Sec-
ion
2.2). '
•
The
me hod o es ima ing op ical
low
is a ec ed by
i egula i y in he objec s' shape, while
he
cen oid
es ima ion me hod (Sec ion 2.3) is indi e en o
his aspec .
3.
PROPOSED
METHOD
OF
ACCUMULATED
DIFFERENCES
The
p oposed me hod consis s o es ima ing he cen oid
o he mobile using accumula ed di e ences (NADI).
S a ing om his,
he
absolu e posi ion o
he
mobile in
he
image (mo e p eCisely,
he
posi ion o i s cen oid)
can be es ima ed. P o ided
ha
he
aim is
o
keep
he
objec cen e ed,
he
displacemen which should be ap-
plied
o
he
came a
is
gi en by
he
di e ence be ween
he posi ion o
he
cen oid and
he
coo dina es o he
image cen e .
The displacemen ec o hus ob ained is ans o med
in o
he
uni e sal e e ence sys em,
and
he
obo
is
o -
de ed
o
displace he came a acco ding
o
he
esul ing
ec o .
The
gene al
s uc u e
is shown in Figu e 4.
~lO'"
p
O""
='li(
::::
'"
...:..+
*
_---'
un
un
Olge
L-
__
..:::
","
:::ima:::'::;::
c<l
=
SlI
::.:;
iu
::...
n
--,
I
Q l icoll
nuw
~
______
~
un
in
la.:,.'" .
c.
...
ima iu
n
Fig. 4. B
loc
k
diag
am
o
he
ac
k
ing
p o
c
ess
.
In
h
e acking p ocess
an
adjus men o
he
a io be-
ween pixels
and
dis ance in
he
eal wo ld (le 's call his
a io he scale
ac o
) is p e iously equi ed.
I
his ac-
o
is
no
accu a ely known, o i
he
dep h o
he
objec
ayec o y is
no
cons an , ela i e o
he
came a plane
o mo ion,
i
can
be
es ima ed
and
adap ed
on line.
I
is simple
o
use he look-and-mo e app oxima ion.
Tha
is, he
obo
emains mo ionless while
he
secuence
o n consecu i e images ( he i s o which
is
he
e -
e ence ame in equa ion 4) is being g abbed. O he -
wise, mo ion in o ma ion is gene a ed due
o
he came a
mo emen , in addi ion
o
he
objec mo ion. This unde-
si ed in o ma ion a ec s
o
he
in e e ence egions
oo
,
and
mus be emo ed making neccesa y a e y p ecise
calib a ion o
he
scale ac o .
The
main
ad an age
o his me hod in ela ion
o
he
use o simple bina iza ion is
ha
i
can cope wi h ion-
pe ec ly
s uc u ed
scenes.
Tha
is, he e can be some
backg ound a eas which ha e
he
same in ensi y ange
as
he
objec
o
in e es .
4. SIMULATIONS AND EXPERlMENTAL TESTS
In
o de
o
es
he
p oposed me hod, in
he
i s place
simula ions using simple syn he ic images ha e been ca -
ied
ou
.
The
poin
(0
,
0)
,
he
o igin o
he
g aphs which
a e
p esen ed, is
he
poin which occupies
he
cen e o
he
came a
a
he
momen when acking begins.
Fi s ly
he
beha io in
he
ideal case is analysed.
The
ideal condi ions a e gi en by:
• Mobile
objec
o egula shape ( ec angula ).
• Cons an eloci y o
he
mobile.
(a
exac ly 1 pixel
pe ame owa ds
he
igh and down:
(1
,
-1)).
•
The
scale ac o used by
he
algo i hm has i s eal
alue. In ollowing examples
he
e ec o using
an
inexac scale ac o is shown (so, a de icien cali-
b a ion
o
his
pa ame e
will be simula ed).
In all he simula ed examples,
he
s a ing
poin s o
he
ajec o ies a e
he
same:
he
objec cen oid
a
(
-16
,
10
),
and
he
came a cen e
a
(0,0).
The
ajec-
o
y o he mobile is ep esen ed by a con inuous line
and
he
cen e
o
he
came a by a dashed one.
Figu e 5 shows
he
ajec o ies om a simula ion o
he
gi en condi ions. Figu e 6 shows he y-coo dina es
o
he
mobile
and
came a cen e , co esponding
o
hose
ajec o ies.
Figu e 7 shows
he
esponse when a sudden change in
he mobile
ajec o
y
a
ame numbe 30 is gi en.
The
mobile changes om a displacemen in a sou h-eas di-
ec ion
o
a
no h
di ec ion.
The
same
ajec o
y
is
shown
in Figu e 8
bu
using scale- ac o au oma ic adjus men .
263
o ·
-10
Fig.
5.
T
aje
c
o
i
es
using
h
e p op
osed
m
e hod
unde
idea
l c
ond
i ions.
~
-~--------------------~
Fig.
6.
Y
-co
o dina. es
usin
g
he
p
op
osed
me
h
od
unde
ideal
cond
i ions.
I
can be seen how
h
e changes in
he
ajec o y
a ec
his me hod.
-10
Fig. 7.
T a
jec
o ie
s unde
ide
al
condi i
on
s,
in
he
p esence
o
a
su
dd
en
ch
an
ge in
h
e
a
j
ec
o y.
-10
~
-20
_10
i
I
!
10
20
30
Fig. 8.
T aje
c
o
i
es
usi
ng
h
e s
cale-
a.c
o
ad
ju
s
men
me hod
.
Figu e 9 p esen s
he
. ajec o ies when using
he
algo-
i hm wi hou scale- ac o co ec ion mechanism,
and
using a scale ac o wice
i
s eal alue.

"'
.
Fig. 9.
T ajec o ies
in
he
case
o
a
sys em
ill-calib a ed
,
wi hou
scale-
a
c
o
co ec ion
mechanism
.
Figu e
10
shows a compa ison o
he
ho izon al coo di-
na es, when au oma ic co ec ion o
he
scale ac o is
made
and
when
i
is
no
made.
I
can be seen
ha
co -
ec ing
he
scale ac o imp o es
he
acking when he
sys em
is
no
well-calib a ed.
--
,
-~
i
~~
]
~
..
:
-------
I
-"O
;-:-~-;20--;":---:";---:'SO;;---=----'7::-0
----="
Fig.
10
.
Compa ison
o
he
X-coo dina es
wi h
and
wi
h
ou
adjus men
o
he
scale
ac o
.
In iew o
he
simula ion esul s, a eal es has been
made using
he
p oposed me hod wi h cons an scale
ac o and calib a ing
he
sys em be o e he es .
The
componen s used we e:
• A PUMA 560 obo .
• A CCD came a a ached
o
he
end-e ec o o he
obo .
• A pe sonal 486 compu e wi h:
• A Ma ox
boa d
model Image-1280, o image p o-
cessing.
In
he
nex igu es, con inuous lines ep esen
he
cam-
e a
mo ion, and
do ed
lines
he
objec mo ion.
Fig-
u e
11
shows
he
ajec o ies
and
Figu e 12 shows he
espec i e y-coo dina es.
I
can be seen how
he
ob ained esul
is
qui e good,
aken in o accoun
ha
he
objec was mo ing
a
abou
80 pixels/second (mos o he ime
he
eloci y was con-
s an
).
264
'"
1
·so
·,
so
.>00
.""
·'00
...
."
Fig.
11.
T ajec o ies
o
a .
·cal
l's
o
he
ack
ing
algo i hm
.
...
'
so
so
...
-
.00
.150
0 " " 2S
Fig.
12.
V
-c
oo dina es
co
esponding
o
he
abo e
ajec o ies
.
5.
CONCLUSIONS
In his a icle a me hod
o
es ima e
he
op ical
low
based on
he
accumula ed di e ence echnique has been
p esen ed.
The
p oposed me hod has been
es ed
by sim-
ula ion
and
expe imen a ion
o
ack
an
objec in eal
ime, using a PUMA 560 obo wi h a
came a
in i s inal
e ec o .
6.
REFERENCES
AlIen P.
K.
,
A.
Timcenk
o,
B. Yoshimi (1993). Au oma ed
acking
and
g asping o a mo ing objec wi h a
obo ic hand-eye sys em.
IEEE
T ans. on Robo ics
and Au oma ion Vo1.9, pp.152-165.
Balla d D.H
.,
C.M. B own (1982). Compu e Vision.
P en ice-Hall.
En
glewood Cli s, N.J.
Fu
K.S., R.
C.
Gonzci1
ez, C.S.G. Lee (1986). Robo ics:
Con ol, Sensing,
Vi.sion
and In elligence. McG aw-
Hill.
Hashimo o (1993). Vi.mal Se oing. Wo ld Scien i ic.
Ma in W.N.,
J.K
. Agga wal (1988). Mo ion Unde -
s anding.
KAP
(Kluwe Academic Publishe s
).
Papanikolopoulos N.P.. P.K. Khosla
(1
993
).
Adap-
i e obo ic isual acking: Theo y
and
expe i-
men s.
IEEE
T a
nsac ions on Au oma ic Con ol
Vo1.38, pp.429-445.
Va gas,
M.
(1997
).
Bina izacion op-
ima
de imagenes
basada
en his og ama. In e nal
Repo ,
GAR
199
7/02
.