UNSUPERVISED
IMAGE
SEGMENTATION
CONTROLLED
BY
MORPHOLOGICAL CONTRAST EXTRACTION
Fe an MARQUES, Jo di CUNILLERA, An oni GASULL
Dep . Teo ia de la Seiial
y
Comunicaciones
E.T.S.E.T.B.
-
U.P.C. Apdo.
30002
08071
Ba celona, SPAIN
e-mail: e an@ sc .upc.es
ABSTRACT
A
no el app oach o unsupe ised image segmen a ion
is desc ibed in his pape . This app oach makes
use
o
a
Gaussian py amid
as
mul i esolu ion decomposi ion o
analyse images. Compound andom ields a e used o
model images a each esolu ion. The hie a chical
image model is o med by a S auss p ocess in he
lowe le el and a se o whi e Gaussian andom ields in
he uppe le el. This basic image model is adap ed o
he da a p esen a each esolu ion. Segmen a ions a
coa se esolu ions a e used o guide segmen a ions a
ines esolu ions. Segmen a ion quali y is con olled,
a each le el, by means o mo phological ools. The
con ol p ocedu e is based on he esidue be ween he
o iginal image and a mo phological cen e ans o m.
This p ocedu e checks whe he he cu en segmen a ion
con ains all he ele an egions in he scene.
I
no , he
algo i hm in oduces seeds in o he segmen ed image in
o de
o
de ec he new egions.
I.- INTRODUCTION
Compound Random Fields (CRFs) [1,2] a e
nowadays widely used in image p ocessing. Wi hin he
amewo k o image segmen a ion, se e al me hods
ha e been p oposed elying on such a kind o image
models. These me hods a e ei he e y ime demanding
[3], i hey use s ochas ic maximisa ion echniques,
o
e y depending on he ini ial segmen a ion
[4],
i hey
use de e minis ic maximisa ion app oaches.
In
o de o
dec ease he dependency on he ini ial segmen a ion
o
de e minis ic app oaches, mul iple esolu ion analyses
ha e been in oduced in he segmen a ion p ocedu e
[5,6].
In
hese echniques, coa se esolu ion
segmen a ions guide he me hod o be e esul s when
segmen ing ines esolu ion images. Howe e ,
mul i esolu ion echniques s ill a ise some p oblems.
In
his pape , an unsupe ised mul i esolu ion
segmen a ion echnique based on compound
andom ields and con olled by ma hema ical
mo phology ools is p esen ed. The s uc u e o he
This
wo k
has been pa ially suppo ed by he p ojec
TIC-92-0800-COS-03
o
he Spanish Go e nmen
pape is as ollows. A e his b ie in oduc ion, in
Sec ion 11, he basic mul i esolu ion segmen a ion
scheme p esen ed in
[6]
and i s main d awbacks a e
p esen ed. Sec ion I11 deals wi h he unsupe ised
adap a ion
o
he model pa ame e s o he da a in he
image, in o de o imp o e he pe o mance
o
he
segmen a ion echnique. Sec ion IV p esen s a
mo phological s age in oduced o de ec in e io
egions. Once an in e io egion has been de ec ed, he
p e ious echnique decides whe he his new egion
dese es o be included in o he inal segmen a ion.
Finally, Sec ion
V
is de o ed o he p esen a ion o
some esul s and conclusions.
II.-
BASIC MULTJRESOLUTION SCHEME
In
his sec ion, he mul i esolu ion segmen a ion
echnique p esen ed in [6] is ou lined o comple eness
pu poses. This echnique makes use o a Gaussian
py amid as mul i esolu ion decomposi ion. Mo eo e ,
i elies on CRFs o model images a each esolu ion.
The CRF uppe le el
X
( ex u e model) is o med by a
se
o independen whi e Gaussian andom ields. On
i s
u n, he CRF lowe le el
Q
(con ou model) is
assumed o
be
a S auss p ocess
[7]
de ined on a second
o de neighbou hood. Pa ame e s cha ac e ising he
ex u e model a e es ima ed om he image
da a.
The
con ou model pa ame e s a e ixed o he whole
segmen a ion p ocedu e. These ixed alues a e ob ained
om an analysis o hei in luence on he inal
segmen a ions esul s [8].
The segmen a ion p ocedu e
s a s
by segmen ing
he coa ses esolu ion
in
he Gaussian py amid. Once
he image a a esolu ion
(k)
is segmen ed, his esul is
used as ini ial segmen a ion o he nex ine
esolu ion (k-1). This p ocedu e is i e a ed down o he
ines esolu ion ( he image i sel ) is segmen ed.
In
his
way, coa se esolu ion segmen a ions lead he p ocedu e
o good quali y inal segmen a ions. Mul iple
esolu ion decomposi ions allow o achie e good
quali y esul s when using de e minis ic maximisa ion
echniques a each esolu ion. Tha is, he dependency
o de e minis ic app oaches on he ini ial segmen a ions
is almos comple ely emo ed by mul i esolu ion
analyses.
V-17
0-7803-0946-4/93 $3.00
0
1993
IEEE
A
each esolu ion le el, he mono esolu ion
segmen a ion echnique p oposed
in
[4] is used. Tha is.
he segmen a ion a each le el is pe o med by seeking
he pa i ion Q(k) o he image
X(k)
which maximises
he p obabili y P(Q(k)/X(k)). This esul can be
achie ed by maximising P(X(k), Q(k)):
1
P(X(k),Q(k))
= Z
exp
(-
T
(nl(k)V1
+
n2(k)V2))
.
.nP(xn(k)
/
mn(k),
02
(1)
n
whe e Z is a no malising cons an , T s ands o he
empe a u e, nl(k) and n2(k) a e he numbe o cliques
in he pa i ion o he le el
(k)
wi h po en ial
V1
and
V2 espec i ely
[4],
and mn(k) and On(k) a e he
pa ame e s o he Gaussian andom ield cha ac e ising
he egion
n.
The maximisa ion p ocedu e is ca ied ou
by a p og essi e bounda y e inemen o he ini ial
segmen a ion.
This echnique yields good quali y segmen a ion
esul s
[6].
Howe e , inal segmen a ions may o e look
de ails in he o iginal image. The -on o his lack o
de ail is mainly wo old. Fi s , he use o he same
pa ame e s o cha ac e ise images h ough he whole
decomposi ion does no comple ely exploi he
possibili ies o he mul i esolu ion analysis.
In
addi ion, gi en ha he maximisa ion elies on a
bounda y e inemen p ocedu e, o ally in e io egions
( ha is, egions whose con ou s do no ouch o he
con ou egions) which a e no p esen in he ini ial
segmen a ion canno
be
de ec ed by his segmen a ion
echnique.
III.-
XMAGE
MODEL
ADAPTATXON
Image da a a di e en decomposi ion le els do no
sha e he same ea u es, due o he il e ing p ocedu e
in ol ed in he compu a ion o he Gaussian py amid.
Thus, di e en model pa ame e s should
be
used in
o de o cha ac e ise he da a a di e en decomposi ion
le els. Since uppe le el pa ame e s a e al eady
cons an ly upda ed in he basic mul i esolu ion scheme,
only lowe le el model pa ame e s ha e o
be
adap ed.
The h ee pa ame e s used in (1) o modelling he
lowe le el can
be
educed o only
wo:
Ac ually, only he
T*
pa ame e adap a ion esul s in an
imp o emen o he p ocedu e pe o mance
[SI.
This pa ame e con ols he ela ionship
be ween
he
lowe le el model and he uppe le el model in he
CRF. In o de o adap i s alue o he da a con ained a
each esolu ion, he in o ma ion o he Laplacian
py amid is in oduced in o he p ocedu e. Each le el o
he Laplacian py amid (k) con ains he di e ence
be ween wo consecu i e le els o he Gaussian
py amid. Assuming ha le el (k+l) has been co ec ly
segmen ed, he in o ma ion con ained in he le el
(k)
o
he Laplacian py amid gi es an es ima ion o how a
his segmen a ion is om ha o le el (k). Tha is, i
mos o he pixels a le el
(k)
o he Laplacian py amid
ha e ze o alue, segmen a ion a le el (k+l) o he
Gaussian py amid is e y close
o
ha a le el
(k).
On
he o he hand,
o
ha e se e al pixels wi h high alues
in he Laplacian le el ansla es in o he necessi y o
pe o ming se e al co ec ions in he segmen a ion o
le el (k+l)
so
ha he segmen a ion
o
le el
(k)
is
ob ained. Tha is, new egions ha e
o
be
de ec ed and
con ou s ha e o
be
e ined in o de o con o m o hose
o le el (k). The way o ca y ou such asks is by
gi ing p io i y o he ex u e in o ma ion wi h espec
o he con ou in o ma ion in he
CFW
[8].
The alue
o he T* pa ame e a each esolu ion is he e o e gi en
by he ollowing exp ession:
whe e Lij(k) is he g ay alue
o
he pixel (i.
j)
a le el
(k)
o he Laplacian py amid. This app oach leads o
good esul s, as illus a ed in Figu e 1. In his igu e,
he o iginal Came aman image (Figu e l.a), i s
Gaussian py amid as well as hei segmen a ions a e
shown. The inal segmen a ion
(264
egions) is
p esen ed as a con ou image (Figu e 1.c) and as a
mosaic image (Figu e 1.d). In mosaic images, each
egion is illed wi h i s mean g ay alue. I has o be
highligh ed ha hese segmen a ions p esen good
quali y and imp o e hose ob ained by he basic
mul i esolu ion echnique
[6].
In addi ion, he T*(k)
alues yielded by
(3)
a e e y close o hese ound
manually o be op imal. Ac ually, e en
he
di e en
beha iou ound o ex u ed and non- ex u ed images is
espec ed
by his es ima ion p ocedu e [8].
Howe e , i has o
be
no iced ha , in spi e o he
abo e commen ed imp o emen , some de ails a e s ill
o e looked in he inal segmen a ion (e. g.: he s icks
in he ipod, he ae ials o some pa s o he came a
and he ace)
.
This d awback is owing o he p esence
o in e io egions in he image, which canno be
ex ac ed by means o he p e ious algo i hms. To
sol e his p oblem, a s age con olling ha , a each
le el o he decomposi ion, he inal segmen a ion does
no o e look in e io egions has been in oduced in he
algo i hm.
-18
whe e
Y
and
CP
s and o he open and close il e s
espec i ely, and he cen e
is
de ined
as
cen e
(Y
CP,
CP
Y,
I)
=
Min
(Y
0,
Max
(9
Y,
I))
(5)
Figu e
1.-
Segmen a ion
o
he Came aman image
IV.-
SEED
EXTRACTION
BY
MORPHOLOGICAL
TOOLS
To analyse he p esence o non-de ec ed in e io
egions wi hin a segmen a ion, he e o image is buil .
This image con ains he di e ence be ween he o iginal
image and he mosaic ep esen a ion o i s
segmen a ion. Assuming ha segmen a ions ha e been
co ec ly pe o med, e o image in o ma ion is mainly
ela ed o ex u es in he o iginal image and
non-
de ec ed in e io egions. The e o e, he main ask is o
disc imina e be ween ex u e and non-de ec ed in e io
egion in o ma ion. In e io egions
appea
in
he e o
image
as
nea ly la , con as ed a eas; whe eas ex u ed
in o ma ion appea s
as
dense, con as ed luc ua ions.
Since ex u ed a eas may yield pixels wi h la ge
absolu e alues han hose p oduced by non-de ec ed
in e io egions, classical h esholding echniques
canno be used. Thus mo phological ools
[9]
ha e
been
applied, gi en ha hey a e known o e icien ly
pe o m in disc imina ing be ween hese kinds o
in o ma ion.
Mo phological il e s do no sol e he abo e
p oblem. Hence, he necessi y o using o he e kind o
ans o ms, such as mo phological esidues. F om he
se o di e en esidues ha can
be
de ined, he esidue
be ween he o iginal signal and a mo phological cen e
[lo]
(con as ex ac ion ans o m) u ns ou
o
be e y
e icien o de ec ing in e io egions. The cen e is
compu ed om he open-close, he close-open and he
iden i y ope a o s:
Con as ex ac o :
I
I
-
cen e
(Y
CP,
CP
Y,
I)
I
(4)
An
example using a monodimensional signal is shown
in Figu e
2
o illus a ing he pe o mance o he
mo phological con as ex ac o . This signal con ains
wo con as ed, almos la a eas which a e ela ed o
in e io egions as well
as
h ee con as ed zones wi h
apid luc ua ions, ela ed
o
ex u ed
a eas.
No e
ha
he con as ex ac o de ec s bo h in e io egions,
yielding only
a
single connec ed componen o each
one o hem (concep o
seed).
On he o he hand,
ex u ed in o ma ion is almos comple ely emo ed.
The small emaining componen s can be wi hd awn by
pe o ming
a
cleaning s ep elying on size and g ay
le el alue c i e ia
[8].
"1
I
."A
/
con--dm
Figu e
2.-
Monodimensional example
A e he cleaning s ep, he emaining componen s
a e used
as
seeds o de ec ing new egions in he
segmen a ion p ocedu e. Tha is,
seeds
a e added o he
p e ious segmen a ion and his new pa i ion is used
as
ini ial segmen a ion in he p ocedu e desc ibed in
Sec ion 111. In his way,
seeds
do no di ec ly con o m
new egions bu he mono esolu ion segmen a ion
echnique decides whe he hey dese e
o
o m a new
egion o no . I a
seed
is conside ed o be ela ed
o
ai
o e looked in e io egion, he segmen a ion me hod
inds i s ac ual shape.
V.-
RESULTS
AND
CONCLUSIONS
The use o mo phological ools allows emo ing
apid a ia ions o he signal while p o iding wi h
seeds
o in e io egions. The e o e, in ex u ed zones,
new egions do no appea and hei o e segmen a ion
is a oided. On he o he hand, in e io egions a e
clea ly de ec ed. This e ec can be
Seen
in Figu e 3,
whe e he segmen a ion o he Came aman image is
pe o med using he abo e echnique. Figu e 3.a shows,
-19
in i s le -hand side, he segmen a ion a each le el o
he py amid, while, in i s igh -hand side, he se o
seeds
ob ained a each le el. On i s u n, Figu e 3.b
shows he
seeds
ob ained
a
he bo om o he py amid.
Finally, Figu es 3.c and 3.d show he con ou s o he
inal segmen a ion (353 egions) and i s mosaic
ep esen a ion, espec i ely.
The high quali y o he inal segmen a ion can
be
obse ed. I deals co ec ly wi h la ge ex u ed a eas
wi hou wi hd awing any ele an small egion. I is
wo h no icing ha he mo phological s ep de ec s
ele an in e io egions wi hou in oducing new ones
in ex u ed a eas (e. g.: he
g ass).
This e ec
is
e en
mo e no iceable in he example o Figu e
4.
In i , he
image p esen s a la ge ex u ed
a ea
which has
been
ga he ed in o a ew egions. Fu he mo e, no main
de ail in he image has
been
o e looked and, hus, he
ep esen a ion o he hand and he acke is o e y high
quali y. The inal segmen a ion
o
his image con ains
75
egions.
I has o be highligh ed ha , in spi e o he quali y
o he esul s achie ed by his echnique, i is no ime
demanding. Ac ually, he a e age compu a ional load
equi ed o segmen ing 256x256 pixel images wi h a
Sun
Spa c I1 wo ks a ion is o 27 seconds.
The cu en wo k is mainly wo old. Fi s , i copes
wi h he ex ension o he whole segmen a ion echnique
o he case o segmen ing image sequences. In pa allel,
we a e applying his segmen a ion me hod o he
p oblem o image coding. Tha is, a egion-based image
coding scheme is being de eloped.
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Woods
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Figu e
3.-
Final segmen a ion o he Came aman image
Figu e
4.-
Segmen a ion
o
a ex u ed image
-20