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De elopmen and E alua ion o Pe cep ually Adap ed Colo G adien s
A icleinImage P ocessing, IET · June 2013
DOI: 10.1049/ie -ip .2012.0085
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De elopmen and e alua ion o pe cep ually adap ed
colo g adien s o colo edge de ec ion
Au o a S´aez, Ca los S. Mendoza, Bego˜na Acha, Ca men Se ano
Abs ac
Al hough se e al colo edge de ec o s ha e been p oposed, mos o hem
u ilized Euclidean colo dis ances in di e en colo spaces o measu e colo
di e ences. In his pape a se o colo g adien s based on colo isual pe -
cep ion is p oposed. These colo g adien s a e designed in uni o m colo
spaces and use pe cep ual colo di e ence equa ions. In o de o be able
o s udy he g adien s pe o mance, hey ha e been applied in a a ia ional
le el se o mula ion. A compa a i e s udy has been pe o med. A se o
syn he ic images, gene a ed o his pu pose, has allowed ca ying ou an ex-
ensi e e alua ion. Bo h quan i a i e and quali a i e measu es a e used. I
can be conclude ha de ec o s based on CIE94 colo di e ence equa ion a e
he bes ega ding o he co ela ion wi h colo isual pe cep ion. Ou main
con ibu ions a e: he de i a ion o pe cep ual colo g adien s, he design o
a pe cep ual e alua ion wi h a speci ic syn he ic da ase and he compa ison
be ween de ec o s based on di e en colo di e ences.
Keywo ds: pe cep ual colo g adien s, pe cep ual e alua ion, colo
di e ence equa ions
1. In oduc ion
Edge de ec ion is one o he undamen al ope a ions in compu e ision.
Edges co espond o ab up discon inui ies in physical quan i ies such as
g ay-le el, colo , ex u e o mo ion. In o de o analyze an image, he hu-
man isual sys em de ec s changes in i , ha is, discon inui ies. Nowadays,
he majo i y o he image p ocessing asks a e de eloped o colo images.
The ad an age o colo edge de ec ion schemes o e g ayscale app oaches is
easily demons a ed by conside ing he ac ha hose edges ha exis a he
bounda y be ween egions o di e en colo s canno be de ec ed in g ayscale
P ep in submi ed o Else ie July 1, 2011
images i he e is no change in in ensi y [1]. The colo edge de ec o s can
be classi ied in o wo g oups: hose echniques ex ended om g ayscale edge
de ec o s which apply he de ec ion me hod in each colo plane and combin-
ing he esul s, and hose echniques ha ake in o accoun he ec o na u e
o he colo images [2]. Se e al colo edge de ec o s p ese ing his ec o
na u e ha e been p oposed [2] bu none o hem ake in o accoun ecen
ad ances in measu ing pe cep ual colo di e ences.
Di e en algo i hms ha ex end he concep o de i a i e ope a o o
h ee-colo -componen pixels ha e been de eloped in he li e a u e. One o
simples app oxima ions consis s in gene alizing he ope a o s based on he
i s de i a i e, e.g. Sobel, commonly applied in he g ayscale images in o
he mul idimensional case. Wesolkowski compa ed se e al edge de ec o s in
mul iple colo spaces, and he d ew he conclusion ha he pe o mance o
Sobel ope a o is supe io o o he s [3]. This is he eason why Sobel op-
e a o is chosen in his pape . As esul s co ela ed wi h pe cep ual colo
di e ences a e in ended, RGB space is a oided because i is no a pe cep-
ually uni o m colo space. Ins ead, we make use o a pe cep ual uni o m
colo space (CIE L∗a∗b∗) and he CIELAB, CIE94 and CIEDE2000 colo
di e ence equa ions [4],[5]. A compa a i e s udy be ween hese g adien s is
ca ied ou . To e alua e he pe o mance o hem, a a ia ional Le el Se
echnique whe e hese colo g adien s con ol ex e nal ene gies is de eloped.
As he aim is o measu e how he de ec o s a e co ela ed wi h he human
isual pe cep ion, an ex ensi e e alua ion is pe o med. A da abase o med
by 96 images has been gene a ed and bo h quan i a i e and quali a i e mea-
su es a e used o es he co ela ion be ween he de ec o ou pu and he
isually pe cei ed colo di e ence. O he au ho s ha e app oached o he
ield o pe cep ual colo edge de ec o s. Howe e , in hei wo k, he e is lack
o a hou ogh e alua ion[6], [7], [8].
The es o he pape is o ganized as ollows: Sec ion 2 summa izes he
colo g adien s p oposed. The a ia ional Le el Se echnique implemen ed
o e alua e he colo g adien s is in oduced b ie ly in Sec ion 3. In Sec ion
4 he comple e de eloped me hod is exposed. The expe imen al esul s a e
explained in Sec ion 5. Some conclusions a e p esen ed in Sec ion 6.
2
2. Colo g adien s
In his pape se e al pe cep ual colo g adien s a e p oposed and com-
pa ed. These colo g adien s a e de eloped in a uni o m colo space and
p ese e he ec o na u e o he colo images in ha space.
2.1. Pe cep ual Uni o m Colo Space and Colo Di e ence Equa ions
In 1976, In e na ional Commission on Illumina ion (CIE) s anda dized
L∗a∗b∗space as pe cep ually uni o m [9]. A colo space is pe cep ually uni-
o m i pe cep ual colo di e ences can be measu ed wi h Euclidean dis ances
in his space. The h ee coo dina es o L∗a∗b∗ ep esen he ligh ness o he
colo (L∗), i s posi ion be ween ed/magen a and g een (a∗) and i s posi ion
be ween yellow and blue (b∗). I can also be exp essed in e ms o cylind ical
coo dina es wi h he pe cei ed ligh ness L∗, he ch oma C∗
ab and he hue h∗
ab,
de ined in (1) and (2) espec i ely.
Cab
∗=pa∗2+b∗2(1)
hab =a c an b∗2
a∗2(2)
CIELAB colo di e ence, also known as ∆E∗
ab, is calcula ed using (3).
∆E∗
ab =p∆L∗2+ ∆a∗2+ ∆b∗2(3)
whe e ∆L∗=L∗
1−L∗
2(∆a∗and ∆b∗a e de ined in he same manne o
coo dina es a∗and b∗).
Howe e , subsequen expe imen s demons a ed ha Euclidean dis ance
∆E∗
ab is no an accu a e measu e o pe cei ed colo di e ence be ween wo
s imuli. To co ec he p oblem a new di e ence o mula was ecommended
by CIE [4] in 1994.
∆E94
∗=s∆L∗
kLSL2
+∆C∗
ab
kCSC2
+∆H∗
ab
kHSH2
(4)
SL= 1,(5)
SC= 1 + 0.045 C∗
ab ,(6)
3
SH= 1 + 0.015 C∗
ab .(7)
The ac o s kL,kCand kH, a e included o ma ch he pe cep ion o he
backg ound condi ions.
La e , CIEDE2000 was de eloped o co ec de iciencies o p e ious colo
di e ence equa ions [10]. I s accu acy o p edic small pe cei ed colo di e -
ences ha e been demons a ed [11]
∆E00 =s∆L0
KLSL2
+∆C0
KCSC2
+∆H0
KHSH2
+RT∆C0
KCRC ∆H0
KHSH
(8)
whe e ∆C0and ∆H0a e de ined in [5].
2.2. P oposed colo g adien s
In colo g adien s, he ec o na u e o colo is p ese ed h oughou he
compu a ion. Colo images a e iewed as a wo-dimensional h ee channel
ec o ield. Each channel in his ec o is cha ac e ized by a disc e e in ege
unc ion (x, y). The alue o his unc ion a each poin is de ined by a h ee
dimensional ec o in a gi en colo space [2]. The e o e, a pixel is de ined as
in (9).
(x, y) = 

C1(x, y)
C2(x, y)
C3(x, y)
(9)
whe e Ci(x, y) ep esen s he alue o he pixel in he i- h colo plane (i=
1,2,3), and (x, y) e e s o he spa ial dimensions in he 2-D plane.
The ope a o based on he i s de i a i e, commonly applied in he g ayscale
imaging, is gene alized in o mul idimensional case in [2]. Pla anio is ex-
ends he Sobel ope a o , wi h he ho izon al and e ical masks shown in
(10), by cons uc ing he ec o s: H+= 7+ 2 3+ 8,H−= 9+ 2 2+ 6,
V+= 6+ 2 4+ 8,V−= 9+ 2 5+ 7, acco ding o he no a ion used
in Figu e 1. They calcula e he colo ec o g adien as H+−H−and
V+−V−, espec i ely. In o de o es ima e he colo a ia ion in he e i-
cal and ho izon al di ec ions, he ollowing scala s a e calcula ed: kH+−H−k
,kV+−V−k. The magni ude Bo he maximun a ia ion is es ima ed as:
4

B=pkH+−H−k2+kV+−V−k2.
9 5 7
2 1 3
6 4 8
Figu e 1: Sliding window
X1=

−1 0 1
−2 0 2
−1 0 1 
, X2=

−1−2−1
000
121
(10)
In his pape , we p opose calcula ing he g adien along xand ydi ec ion
as shown (11) and (12).
Gx= ∆EH+,H−(11)
Gy= ∆EV+,V−(12)
whe e ∆Edeno es he colo di e ence be ween wo ec o s. Then, he g a-
dien magni ude can be compu ed as shown in (13).
G=qG2
x+G2
y(13)
In his pape h ee colo g adien s a e s udied, each one o hem is ob-
ained by applying:
• (x, y) = [L∗(x, y), a∗(x, y), b∗(x, y)] and ∆Ede e mined by Euclidean
dis ance (CIELAB).
• (x, y) = [L∗(x, y), a∗(x, y), b∗(x, y)] and ∆Ede e mined by CIE94
colo di e ence equa ion.
• (x, y) = [L∗(x, y), a∗(x, y), b∗(x, y)] and ∆Ede e mined by CIEDE2000
colo di e ence equa ion.
5
3. Va ia ional le el se
Once a colo g adien is es ima ed, he simples edge de ec o is ob ained
by h esholding his g adien . In he h ee p oposed colo g adien es ima-
o s, he dynamic ange o he colo g adien di e s be ween he h ee colo
di e ence measu es. This implies ha a di e en h eshold should be chosen
o de ec edges wi h he di e en g adien es ima o s and he quali y o edges
de ec ed om each g adien es ima o depends s ongly on he choice o his
h eshold. The e o e, in o de o make he compa ison be ween he h ee
g adien es ima o s independen om his choice, a le el se o mula ion has
been applied.
Le el se me hods [12] ha e been widely used as global app oaches owa ds
he op imiza ion o ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound. In hese me hods, in each ime edges a e conside ed
o be in he ze o-le el o a scala unc ion φ( ), called le el-se unc ion. The
challenge o a le el-se algo i hm is o make φe ol e along so ha i s ze o
le el con e ge a he eal bounda ies in he image. The gene al le el se
equa ion is p esen ed in (14),
∂φ
∂ +F|∇φ|= 0 (14)
whe e F ep esen s he speed unc ion. One o he main challenges in he
employmen o le el se echniques is o o e come he gene a ion o shocks
in φ, e y sha p o la shape du ing he e olu ion, which can esul in less
han accu a e con ou s. Many au ho s a oid his p oblem by e-ini ializing
he unc ion φ o a signed unc ion pe iodically. In his pape , his p oblem
is o e come wi h he me hod de eloped by Li e al [13]. In he epo ed
wo k, a new e m is in oduced in o (14) o main ain he le el se unc ion
nea he signed dis ance unc ion, hus a oiding he need o e-ini ializa ion
o he le el se unc ion. I has been shown ha he esul ing exp ession is
he ollowing g adien low:
∂φ
∂ =µ∆φ−di ∇φ
|∇φ|+λδ(φ)di g∇φ
|∇φ|+νgδ(φ) (15)
whe e µde e mines he de ia ion o φ om a signed dis ance unc ion, λand
νa e he coe icien s o he weigh ed leng h o he ze o le el cu e and o he
6
weigh ed a ea inside he ze o le el cu e espec i ely, and is he ime s ep
o he expe imen .
The second and he hi d e m in he igh hand side o (15) a e espon-
sible o d i ing he ze o le el cu e owa ds he objec bounda ies. gis he
edge indica o unc ion, usually de ined as:
g=1
1 + |∇Gσ∗I|2(16)
whe e Gσis he Gaussian ke nel wi h s anda d de ia ion σand Iis he es
image.
In he p oposed me hod, he edge indica ion unc ion ghas been modi ied
o:
g=1
1 + |V D(di {I})|2(17)
whe e di is an aniso opic di usion il e and V D a e he p oposed colo
g adien s ha a e applied o he di used image. The e o e, modi ying he
edge indica o unc ion includes wo aspec s:
•The Gaussian il e smo hing is subs i u ed by an colo aniso opic di -
usion il e [15]. Bo h smoo hing we e es ed bu he colo aniso opic
di usion il e ob ained be e esul s acco ding expe imen s.
•G adien s he di used image a e compu ed wi h he h ee p oposed
colo g adien s app oaches explained in Sec ion 2.
4. Me hodology
The da a low diag am in Figu e 2 gi es an o e iew o he main s eps o
he pe cep ual colo de ec o s based on p oposed colo g adien s.
a. Uni o m colo space ans o m. The RGB image is ans o m in o he
uni o m colo space CIE L∗a∗b∗, p e iously desc ibed.
b. Aniso opic di usion il e ing. In he aniso opic di usion [14] a wi hin-
egion smoo hing is la gely pe o med wi hou blu ing be ween- egion
bounda ies. In his pape an ex ension o he me hod o colo image is
implemen ed [15], whe e a sepa a e aniso opic di usion o ch oma ic
7
Figu e 2: P oposed sys em
and ach oma ic channels is pe o med. This way inds i s a ionale in
he models o colo ision: he human isual sys em senses colo in o -
ma ion h ough pho o ecep o s which can be ega ded as h ee se s o
il e s uned o he wa eleng hs o ed, g een and blue; his in o ma ion
is hen spli in o ch oma ic (2-D) and ach oma ic (1 -D) channels be-
o e being u he and independen ly p ocessed. Neu ophysiological e -
idence shows ha he e exis s a pe ec ag eemen be ween he second
Human Visual Sys em p ocessing s age and he opponen -colo s heo y
based on he h ee an agonis ic mechanisms ed-g een, blue-yellow and
black-whi e. These s imuli can also be con enien ly exp essed in e ms
o hue, sa u a ion and ligh ness. Hue and sa u a ion a e p ocessed o-
ge he using he o malism o phaso s: hue is he phase and sa u a ion
is he magni ude o a complex unc ion de ined as he complex ch o-
ma ici y. The scala ach oma ic in o ma ion ep esen ed by ligh ness is
sepa a ely di used.
c. Pe cep ual colo g adien s compu a ion. The p oposed colo g adien s
explained in Sec ion 2 a e compu ed om di used image.
d. Le el se echnique. The le el se o mula ion explained in Sec ion 3 is
applied wi h he edge indica o unc ion as:
g=1
1 + |V D(di {I})|2(18)
8
(a)
(b) (c) (d)
Figu e 7: a) Tes image. b) Ou pu o de ec o based on CIELAB. c) Ou pu o de ec o
based on CIE94. d) Ou pu o de ec o based on CIEDE2000.
6. Conclusions
In his pape h ee di e en pe cep ually adap ed colo g adien s ha e
been p oposed. These g adien s ha e been in eg a ed in a le el-se ame-
wo k o colo edge de ec ion. This colo edge de ec ion algo i hm is used o
e alua e he h ee colo g adien s wi h wo e alua ion es s: a subjec i e es
and a quan i a i e e alua ion measu e. To his pu pose, a syn he ic image
da abase ollowing CIE guidelines o coo dina ed esea ch on colo di e ence
e alua ion [17] has been de eloped. The edge de ec o using he colo g adi-
en based on CIE94 esul ed he bes bo h acco ding o he subjec i e es
and he pe cei ed quan i a i e measu e (pe cei ed FP a ). An addi ional
ad an age o CIE94 colo di e ence equa ion is i s low compu a ional cos
when compa ed o CIEDE2000 di e ence equa ion.
15

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17
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