Segmen ación del disco óp ico median e le el-se s con
in o mación de colo
A. Sáez1, I. Fondón1, C. Se ano1, S. Jiménez2, P. Alemany3, B. Acha1
1 Dp o. Teo ía de la Señal y Comunicaciones, Uni e sidad de Se illa, Se illa, España,
[email p o ec ed],{i ene ,cse ano,bacha}@us.es
2 Se icio de O almología, Hospi al Pue a del Ma , Cádiz, España, [email p o ec ed]
3 Facul ad de Medicina, Uni e sidad de Cádiz, Cádiz, España
Resumen
La segmen ación del Disco Óp ico (DO) es un paso esencial
pa a la ex acción au omá ica de es uc u as ana ómicas y
lesiones e inianas. La mayo ía de los algo i mos de
segmen ación de la li e a u a p ocesan exclusi amen e un solo
plano de la e inog a ía, desca ando la in o mación de colo .
En es e a ículo se p esen a un nue o algo i mo de
segmen ación del DO. En p ime luga se ealiza un
p ep ocesamien o pa a elimina los asos sanguíneos. A
con inuación se aplica un algo i mo de le el-se s basado en
bo des. La mayo con ibución del a ículo es la u ilización de
la in o mación de colo pa a el p oceso de segmen ación. Se
calculan g adien es ec o iales en el espacio de colo L*a*b*
que son u ilizados po el algo i mo de le el-se s. En luga de
u iliza la no ma Euclídea, se aplica la ó mula de di e encia de
colo CIE94 en los g adien es ec o iales. Se ha p obado con 22
e inog a ías donde los médicos han de ec ado manualmen e los
bo des del DO. El algo i mo ha de ec ado au omá icamen e el
DO en odos los casos, con un 92.35% de in e sección en e el
á ea ma cada po los expe os y la de ec ada. La Dis ancia
Media al Pun o más Ce cano es á po debajo de 5 píxeles en el
100% de las imágenes.
1. Mo i ación
El núme o de a ec ados de cegue a debido a
en e medades como la e inopa ía diabé ica o el
glaucoma ha aumen ado en los úl imos iempos.
T es cua as pa es de esas cegue as pueden
a a se y p e eni se cuando se ealiza un
con ol emp ano de la población. Los
p og amas de sc eening consis en
p incipalmen e en ob ene imágenes
o og á icas de ondo de ojo. Según el esul ado
del análisis de dichas imágenes los pacien es
son e e idos al o almólogo pa a su a amien o.
Po an o, es deseable una au oma ización del
p oceso inicial de analiza la g an can idad de
imágenes e inog á icas pa a agiliza y mejo a
el p oceso de sc eening.
La de ección del DO es un paso de
p ep ocesamien o muy impo an e en muchos
algo i mos diseñados pa a la ex acción de o as
es uc u as ana ómicas e inianas y lesiones
[1,2]. El cambio en la o ma, colo o
p o undidad del DO es un indicado de a ias
pa ologías, p incipalmen e del glaucoma [3].
Aunque el DO posee ca ac e ís icas bien
de inidas, la localización au omá ica del mismo
no es un p oceso sencillo, ya que la apa iencia
del mismo a ía signi ica i amen e con las
dis in as pa ologías. Así que, los mé odos
desa ollados deben ene en cuen a es a
a iación en e las di e en es imágenes. Exis en
muchos mé odos pa a la de ección del disco
óp ico, pe o la mayo ía u ilizan pa e de la
in o mación de colo de la imagen, como el uso
de un solo plano [1, 4-6].
En es e a ículo se p opone p ocesa cada píxel
de colo u ilizando un g adien e ec o ial pa a la
de ección de bo des u ilizada en la
segmen ación po le el-se s. Además se u iliza
un espacio de colo uni o me, L*a*b*, y se
co igen las no uni o midades de dicho espacio
de colo sus i uyendo la dis ancia Euclídea po
la CIE94 en el cálculo del g adien e [7].
2. Me odología
El diag ama de lujo mos ado en la Fig. 1
mues a los pasos del algo i mo p opues o.
2.1. Eliminación del á bol ascula
Pa a la eliminación del á bol ascula se ha
u ilizado el algo i mo diseñado pa a la
eliminación del ello en imágenes de lesiones
pigmen adas de la piel [8]. Cons a de es
e apas: de ección de asos con el uso de la
de i ada de la gaussiana (DOG) [9],
e inamien o del esul ado con écnicas
mo ológicas y sus i ución de asos po “ as
ma ching image inpain ing” [10].
Fig. 1 Sis ema p opues o
2.2. Localización del disco
El DO puede se iden i icado como una egión
b illan e en la imagen de ondo de ojo [11]. Po
ello se ha u ilizado la in o mación de
luminosidad pa a de ec a lo. El canal L* del
espacio de colo L*a*b* se sua iza con un il o
de p omediado. Los píxeles de la imagen
esul ado con in ensidades supe io es al 97% del
alo máximo de in ensidad son seleccionados.
Se calcula el cen o de masas de es e conjun o
de píxeles. Pa a de e mina la egión de in e és
(ROI: Region O In e es ) se escoge un
cuad ado de adio 90 píxeles y cen ado en el
cen o de masas. Es e cuad ado de ine el
con o no inicial
2.3. G adien e de colo
Los mé odos de le el-se son aplicados a un
g adien e de la imagen. En la li e a u a se u iliza
el g adien e de un solo plano, po ejemplo, en
[12] se u iliza el plano R. En el p esen e abajo
se iene en cuen a oda la in o mación de colo
u ilizando un g adien e ec o ial [13].
De inimos un píxel de la imagen en colo de la
o ma:
donde ep esen a el alo del píxel en el
plano i (i= 1, 2, 3).
El ope ado Sobel basado en la p ime a
de i ada, comúnmen e aplicado a imágenes en
escala de g ises, puede gene aliza se al caso
mul idimensional [14]. En es e a ículo se ha
aplicado la másca a de Sobel a la imagen en el
espacio de colo L*a*b* cons uyendo los
ec o es: , ,
, siguiendo la
no ación de la Fig. 2.
Fig. 2 Ven ana
Los g adien es a lo la go de la di ección x e y
son:
donde deno a la di e encia de colo CIE94
en e dos ec o es de inidos en el espacio CIE
L*a*b*. No malmen e se u iliza en es os casos
la dis ancia Euclídea, pe o en es e a ículo se ha
escogido la dis ancia CIE94 ya que se ha
demos ado que CIE94 es supe io [13].
La magni ud del g adien e se calcula:
.
2.4. Segmen ación basada en le el-se s
Una ez que los asos han sido eliminados, el
DO es segmen ado u ilizando la écnica de
le el-se s [15]. La idea de es e ipo de algo i mo
es ep esen a los con o nos como el conjun o
de ni el ce o de una unción implíci a de inida
en una dimensión mayo ( unción de le el-se
). La unción e oluciona á de o ma que el
ni el ce o con e ja a los bo des eales de la
imagen. La ecuación gene al es:
donde F ep esen a la unción de elocidad.
U ilizando el abajo de Li e al. [16] la
exp esión pa a el g adien e queda:
donde
µ
de e mina la des iación de
φ
de una
unción de dis ancia con signo,
λ
y
υ
son
coe icien es de la longi ud ponde ada de la
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
cu a de ni el ce o y del á ea ponde ada den o
de dicha cu a espec i amen e y es el paso de
iempo del expe imen o.
g es la unción indicado a de bo des y es á
de inida como:
donde es un núcleo gaussiano con
des iación es ánda
σ
e I es la imagen de es .
En es e a ículo, el g adien e u ilizado pa a es a
ó mula ha sido el g adien e ec o ial explicado
en la sección an e io . Po an o, la unción g
queda modi icada como:
donde VD es el g adien e ec o ial
implemen ado en el espacio de colo CIE
L*a*b* y con la dis ancia de colo CIE94.
2.5. Pos -p ocesamien o
La salida del paso an e io es el con o no del
DO. Sin emba go, di e sos au o es [12,17]
u ilizan la o ma de una elipse como úl imo
paso pa a sua iza el con o no de ec ado, ya que
así se asemeja más a la delineación manual que
hacen los expe os. En es e a ículo se es udian
los esul ados con y sin adap ación a una elipse.
3. Resul ados y e aluación
Algunos de los esul ados del mé odo p opues o
se mues an en las Figs. 3 y 4. Ambos
esul ados, salida del algo i mo de le el-se s y
salida de la adap ación a una elipse, son
e aluados.
El mé odo ha sido e aluado con 22 imágenes
segmen adas manualmen e po expe os. Se han
analizado dos medidas de p es aciones. La
p ime a compa a las á eas delimi adas
manualmen e y au omá icamen e. La segunda
da una idea de la des iación del con o no.
Fig. 3 a) Imagen o iginal, b) eliminación del á bol ascula , c)
segmen ación manual del DO ( e de) y segmen ación po le el-
se s (azul), d) adap ación a una elipse del con o no manual
( e de) y del con o no de ec ado (azul).
Fig. 4 a) Imagen o iginal, b) eliminación del á bol ascula , c)
segmen ación manual del DO ( e de) y segmen ación po le el-
se s (azul), d) adap ación a una elipse del con o no manual
( e de) y del con o no de ec ado (azul).
Pa a la in e sección de las á eas, las á eas
con enidas po los con o nos manuales y
au omá icos se han compa ado píxel a píxel.
Como á ea e e encia se ha escogido la
Figu e 1. P oposed sys em
Disc Localiza ion
The op ic disc can be iden i ied as a b igh egion on a e i-
nal undus image [12]. The e o e, ligh ness in o ma ion was used
o de ec he disc localiza ion. The channel L o L∗a∗b∗colou
space was smoo hed by an a e aging il e . The pixels o he e-
sul image wi h in ensi y alue highe han 97% o he maximum
in ensi y alue we e selec ed. The mass cen e o his se o pix-
els was calcula ed. A squa e wi h adius o 90 pixels and cen ed
a ha mass cen e was used o de e mine he ROI. This squa e
de ined he ini ial con ou equi ed o he le el-se segmen a ion,
explained in a ollowing sec ion.
Colou g adien
The edge-based le el se me hods a e applied o a g adien
image. In he li e a u e, all o he au ho s use he g adien o a
single channel in he p oblem a hand, example o ha is he wo k
o Wong e al. [13] whe e he le el-se algo i hm was applied o
ed channel. Howe e , in his pape he colou in o ma ion was
aken in o accoun , and a colou g adien was used [14].
In colou g adien s, he ec o na u e o colou is p ese ed
h oughou he compu a ion. Colou images can be iewed as a
wo-dimensional h ee channel ec o ield. Each pixel in his
ec o ield is cha ac e ized by a disc e e in ege unc ion a(x,y).
The alue o his unc ion a each poin is de ined by a h ee di-
mensional ec o in a gi en colou space. The e o e, a pixel is
de ined as:
a(x,y)=

C1(x,y)
C2(x,y)
C3(x,y)

(1)
whe e Ci(x,y) ep esen s he alue o he pixel in he i- h
colou plane (i=1,2,3), and (x,y) e e s o he spa ial dimensions
in he 2-D plane.
a1a2a3
a4a5a6
a7a8a9
Figu e 2. Sliding window
The ope a o Sobel based on he i s de i a i e, commonly
applied in g ayscale imaging, can be gene alized in o he mul i-
dimensional [15]. In his pape , Sobel mask was applied o CIE
L∗a∗b∗image by cons uc ing he ec o s (acco ding o he no a-
ion used in Fig. 2): V+
1=a3+2a6+a9,V−
1=a1+2a4+a7,
H+
1=a7+2a8+a9,H−
1=a1+2a2+a3. The g adien along x
and ydi ec ion espec i ely, is shown in equa ion 2 and 3.
Gx=#E%V+
1,V−
1&(2)
Gy=#E%H+
2,H−
2&(3)
whe e #Edeno es he CIE94 colou di e ence be ween he
wo ec o s de ined in he CIE L∗a∗b∗colou space. Usually, he
Euclidian dis ance (CIELAB) is used in his pu pose, howe e he
CIE94 colou dis ance was used in his pape because i has been
shown ha CIE94 ou pe o ms CIELAB [14].
The g adien magni ude is compu ed as shown in equa ion 4.
G='G2
x+G2
y(4)
Va ia ional le el-se
Once blood essels a e emo ed, op ic disc segmen a ion is
ca ied ou by using a a ia ional le el se o mula ion.
Le el se me hods, which we e i s in oduced by Oshe and
Se hian [16], ha e been widely used as global app oaches op i-
mizing ac i e con ou s o he segmen a ion o objec s o in e es
om he backg ound [17] [18] [19]. The basic idea is o ep esen
con ou s as he ze o le el se o an implici unc ion de ined in a
highe dimension, usually e e ed as he le el se unc ion (
φ
( )).
The challenge o a le el-se algo i hm is o make (
φ
) e ol e so
ha i s ze o le el con e ges a he eal bounda ies in he image.
The gene al le el se equa ion is p esen ed in 5,
∂φ
∂
+F|∇
φ
|=0 (5)
whe e F ep esen s he speed unc ion and
φ
he le el se
unc ion. One o he main challenges in he employmen o le el
se echniques has been he gene a ion o shocks which can esul
in less han accu a e con ou s. To o e come his, he me hod de-
eloped by Li e al [20] is employed. In he epo ed wo k, an
ene gy unc ion
ε
is in oduced in o 5 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
|*+
ν
g
δ
(
φ
)(6)
whe e
µ
de e mines he de ia ion o
φ
om a signed dis ance
unc ion,
λ
and
ν
a e he coe icien s o he weigh ed leng h o
he ze o le el cu e and o he 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 6
a e esponsible o d i ing he ze o le el cu e owa ds he objec
bounda ies. gis he edge indica o unc ion de ined by:
g=1
1+|∇G
σ
∗I|2(7)
(a) (b)
(c) (d)
Figu e 3. a) o iginal image, b) bool essels emo al, c) op ic disc man-
ual segmen a ion (g een) and segmen a ion by he le el se (blue) d) ellipse
i ing o con ou manually segmen ed (g een) and o he de ec ed con ou
(blue).
whe e G
σ
is he Gaussian ke nel wi h s anda d de ia ion
σ
and Iis he es image.
In his pape , he g adien used in his de ini ion i was he
ec o g adien explained in he p e ious sec ion. The e o e, he
gde ini ion is modi ied:
g=1
1+|VD(G
σ
∗I)|2(8)
whe e VDis he ec o g adien implemen ed in CIE L∗a∗b∗
using CIE94 colou di e ence equa ion, explained in he p e ious
sec ion.
Ellipse i ing
The ou pu o he abo e s ep is con ou o op ic disc. How-
e e , se e al au ho s [13], [22] used a ellipse i as pos -p ocessing
s ep in o de o smoo h his de ec ed con ou . In his pape , he e-
sul s ob ained wi h o wi hou ellipse i ing we e s udied.
Resul s and E alua ion
Some esul s o he p oposed me hod can be seen in Fig. 3
and Fig. 4, whe e a) shows he o iginal image, b) image wi hou
he bool essels, c) manually segmen ed op ic disc in g een and
segmen ed by he p oposed me hod in blue d) ellipse i ing o
con ou manually segmen ed (g een) and o he con ou de ec ed
(blue). Bo h esul s, ou pu o he le el se and ou pu o he el-
lipse i ing, we e e alua ed.
(a) (b)
(c) (d)
Figu e 4. a) o iginal image, b) bool essels emo al, c) op ic disc segmen-
a ion manually (g een) and segmen a ion by he le el se (blue) d) ellipse
i ing o con ou manually segmen ed (g een) and o he con ou de ec ed
(blue).
(a) (b)
(c) (d)
Figu e 3. a) o iginal image, b) bool essels emo al, c) op ic disc man-
ual segmen a ion (g een) and segmen a ion by he le el se (blue) d) ellipse
i ing o con ou manually segmen ed (g een) and o he de ec ed con ou
(blue).
whe e G
σ
is he Gaussian ke nel wi h s anda d de ia ion
σ
and Iis he es image.
In his pape , he g adien used in his de ini ion i was he
ec o g adien explained in he p e ious sec ion. The e o e, he
gde ini ion is modi ied:
g=1
1+|VD(G
σ
∗I)|2(8)
whe e VDis he ec o g adien implemen ed in CIE L∗a∗b∗
using CIE94 colou di e ence equa ion, explained in he p e ious
sec ion.
Ellipse i ing
The ou pu o he abo e s ep is con ou o op ic disc. How-
e e , se e al au ho s [13], [22] used a ellipse i as pos -p ocessing
s ep in o de o smoo h his de ec ed con ou . In his pape , he e-
sul s ob ained wi h o wi hou ellipse i ing we e s udied.
Resul s and E alua ion
Some esul s o he p oposed me hod can be seen in Fig. 3
and Fig. 4, whe e a) shows he o iginal image, b) image wi hou
he bool essels, c) manually segmen ed op ic disc in g een and
segmen ed by he p oposed me hod in blue d) ellipse i ing o
con ou manually segmen ed (g een) and o he con ou de ec ed
(blue). Bo h esul s, ou pu o he le el se and ou pu o he el-
lipse i ing, we e e alua ed.
(a) (b)
(c) (d)
Figu e 4. a) o iginal image, b) bool essels emo al, c) op ic disc segmen-
a ion manually (g een) and segmen a ion by he le el se (blue) d) ellipse
i ing o con ou manually segmen ed (g een) and o he con ou de ec ed
(blue).
(a) (b)
(c) (d)
Figu e 3. a) o iginal image, b) bool essels emo al, c) op ic disc man-
ual segmen a ion (g een) and segmen a ion by he le el se (blue) d) ellipse
i ing o con ou manually segmen ed (g een) and o he de ec ed con ou
(blue).
whe e G
σ
is he Gaussian ke nel wi h s anda d de ia ion
σ
and Iis he es image.
In his pape , he g adien used in his de ini ion i was he
ec o g adien explained in he p e ious sec ion. The e o e, he
gde ini ion is modi ied:
g=1
1+|VD(G
σ
∗I)|2(8)
whe e VDis he ec o g adien implemen ed in CIE L∗a∗b∗
using CIE94 colou di e ence equa ion, explained in he p e ious
sec ion.
Ellipse i ing
The ou pu o he abo e s ep is con ou o op ic disc. How-
e e , se e al au ho s [13], [22] used a ellipse i as pos -p ocessing
s ep in o de o smoo h his de ec ed con ou . In his pape , he e-
sul s ob ained wi h o wi hou ellipse i ing we e s udied.
Resul s and E alua ion
Some esul s o he p oposed me hod can be seen in Fig. 3
and Fig. 4, whe e a) shows he o iginal image, b) image wi hou
he bool essels, c) manually segmen ed op ic disc in g een and
segmen ed by he p oposed me hod in blue d) ellipse i ing o
con ou manually segmen ed (g een) and o he con ou de ec ed
(blue). Bo h esul s, ou pu o he le el se and ou pu o he el-
lipse i ing, we e e alua ed.
(a) (b)
(c) (d)
Figu e 4. a) o iginal image, b) bool essels emo al, c) op ic disc segmen-
a ion manually (g een) and segmen a ion by he le el se (blue) d) ellipse
i ing o con ou manually segmen ed (g een) and o he con ou de ec ed
(blue).
(a) (b)
(c) (d)
Figu e 3. a) o iginal image, b) bool essels emo al, c) op ic disc man-
ual segmen a ion (g een) and segmen a ion by he le el se (blue) d) ellipse
i ing o con ou manually segmen ed (g een) and o he de ec ed con ou
(blue).
whe e G
σ
is he Gaussian ke nel wi h s anda d de ia ion
σ
and Iis he es image.
In his pape , he g adien used in his de ini ion i was he
ec o g adien explained in he p e ious sec ion. The e o e, he
gde ini ion is modi ied:
g=1
1+|VD(G
σ
∗I)|2(8)
whe e VDis he ec o g adien implemen ed in CIE L∗a∗b∗
using CIE94 colou di e ence equa ion, explained in he p e ious
sec ion.
Ellipse i ing
The ou pu o he abo e s ep is con ou o op ic disc. How-
e e , se e al au ho s [13], [22] used a ellipse i as pos -p ocessing
s ep in o de o smoo h his de ec ed con ou . In his pape , he e-
sul s ob ained wi h o wi hou ellipse i ing we e s udied.
Resul s and E alua ion
Some esul s o he p oposed me hod can be seen in Fig. 3
and Fig. 4, whe e a) shows he o iginal image, b) image wi hou
he bool essels, c) manually segmen ed op ic disc in g een and
segmen ed by he p oposed me hod in blue d) ellipse i ing o
con ou manually segmen ed (g een) and o he con ou de ec ed
(blue). Bo h esul s, ou pu o he le el se and ou pu o he el-
lipse i ing, we e e alua ed.
(a) (b)
(c) (d)
Figu e 4. a) o iginal image, b) bool essels emo al, c) op ic disc segmen-
a ion manually (g een) and segmen a ion by he le el se (blue) d) ellipse
i ing o con ou manually segmen ed (g een) and o he con ou de ec ed
(blue).
segmen ación manual. En la Tabla 1 se
mues an los esul ados con y sin adap ación a
una elipse. El po cen aje de acie o se de ine
como el po cen aje del amaño de la
in e sección de ambas á eas. La asa de alsos
posi i os (FP) se de ine como el á ea
segmen ada e óneamen e como DO po el
mé odo. Y la asa de alsos nega i os (FN)
como el á ea pe enecien e al DO que no ha sido
segmen ada po el mé odo p opues o.
Tabla 1. Resul ado de la in e sección de las á eas
La segunda medida, denominada dis ancia
media al pun o más ce cano (MDCP, de las
siglas en inglés) [18], e alúa la dis ancia media
desde el con o no de ec ado al segmen ado
manualmen e (con o no de e e encia). El
con o no de e e encia, R, consis e en píxeles
indi iduales i, i = 1,2, …, M, donde M es la
can idad de píxeles del con o no de e e encia.
Sea S el con o no inal de ec ado po el mé odo
p opues o. Pa a cada pun o del con o no S(n),
n= 1, 2, …, N, la dis ancia al pun o más ce cano
(DCP) del con o no de e e encia se de ine
como:
La exac i ud del con o no de ec ado se e alúa
po la media de DCP (MDCP):
Los esul ados ob enidos con es a medida es án
esumidos en la Tabla 2. Las MDCP son 2.72 y
3.07 pa a píxeles pa a el mé odo p opues o con
adap ación a elipse y sin dicha adap ación,
espec i amen e.
Tabla 2. Resul ados de la MDCP
4. Discusión y conclusiones
La de ección del DO es un paso muy impo an e
en sis emas CAD que u ilizan e inog a ías, po
ejemplo, en la de ección del glaucoma. La
mayo ía de abajos publicados sólo u ilizan un
plano de colo pa a la de ección. En es e abajo
se pe esen a un mé odo que u iliza oda la
in o mación de colo pa a la eliminación del
á bol ascula y la de ección de bo des usada en
el algo i mo de le el-se s de segmen ación. Se
ob iene una sensibilidad del 92.35%.
Ag adecimien os
Es e abajo se ha ealizado g acias al p oyec o
TEC2010-21619-C04-02.
Re e encias
[1] Han X., Xu C., P ince J., A opology p ese ing le el se me hod o
geome ic de o mable models, IEEE T ans. Pa . Anal. Mach. In ell.,
ol. 25, pp. 755-768, (2003).
[2] Caselles V., Ca e F., Coll T., Dibos F., A geome ic model o ac i e
con ou s in image p ocessing, Nume . Ma h., ol. 66, pp. 1-31 (1993).
[3] Malladi R., Se hian J. A., Vemu i B. C., Shape modeling wi h on
p opaga ion: a le el se app oach, IEEE T ans. Pa . Anal. Mach. In ell.,
ol. 17, pp. 158-175, (1995).
[4] Fi zgibbon, A., Pilu, M., Fishe , R.B., Di ec leas squa e i ing o
ellipses, IEEE T ans. Pa . Anal. Mach. In ell,21 (5), pp. 476-480 (1999)
[5] Zhang, Z., Liu, J., Wong, W.K., Tan, N.M., Lim, J.H., Lu, S., Li, H.,
Wong, T.Y., Neu o- e inal op ic cup de ec ion in glaucoma diagnosis,
BMEI 2009 , a . no. 5305076 (2009).
[6] Xu, J., Chu a ape, O., Chew, P., Au oma ed op ic disk Bounda y
de ec ion by modi ied ac i e con ou model, IEEE T ansac ions on
Biomedical Enginee ing 54 (3), a . no. 16, pp. 473-482 (2007).
[7] Rangayyan R, Acha B, Se ano C, Colo Image P ocessing wi h
Biomedical Applica ions, SPIE P ess, Bellingham, EEUU (2011).
[8] S.Ka i ha, S.Ka hikeyan, K.Du aiswamy, Ea ly De ec ion o
Glaucoma in Re inal Images Using Cup o Disc Ra io, P oc. In . Con .
On Compu ing, Communica ion and Ne wo king Technologies(2010).
[9] Aliaa Abdel-Haleim Abdel-Razik Youssi , A e Zaki Ghalwash, and
Am Ahmed Sab y Abdel-Rahman Ghoneim, Op ic Disc De ec ion
F om No malized Digi al Fundus Images by Means o a Vessels
Di ec ion Ma ched Fil e , IEEE T ans. on Medical Imaging, 27, 1 (2008)
[10] L. Gagnon, M. Lalonde, M. Beaulieu, and M.-C. Bouche ,
P ocedu e o de ec ana omical s uc u es in op ical undus images, P oc.
Con . Med. Imag. 2001, pp. 12181225. (2001).
[11] R. A. Abdel-Gha a , T. Mo is, T. Ri chings, and I. Wood, De ec-
ion and cha ac e isa ion o he op ic disk in glaucoma and diabe ic
e inopa hy, P oc. Med. Image Unde s and. Anal. Con . (1998).
[12] Wong, D.W.K., Liu, J., Lim, J.H., Jia, X., Yin, F., Li, H., Wong,
T.Y. Le el-se based au oma ic cup- o-disc a io de e mina ion using
e inal undus images in ARGALI. EMBS 2008 pp. 2266-2269, (2008)
[13] Sez, A., Se ano, C., Acha, B., E alua ion pe cep ual colo edge
de ec ion algo i hms, 5 h Eu opean Con . on Colou in G aphics,
Imaging, and Vision, CGIV 2010/MCS’10 , pp. 222-22, (2010).
[14] K.N. Pla anio is, A.N. Vene sanopoulos, Colo Image P ocessing
and Applica ions, Sp inge -Ve lag, Be lin, 2000.
[15] Oshe S. , Se hian J. A., F on s p opaga ing wi h
cu a u edependen speed - algo i hms based on hamil on-jacobi
o mula ions, J Compu Phys, 79, 12-49 (1998).
[16] C. Li, C. Xu, C. Gui, M. D. Fox, Le el se e olu ion wi hou e-
ini ializa ion: a new a ia ional o mula ion, IEEE Compu e Socie y
Con e ence on Compu e Vision and Pa e n Recogni ion, (2005).
[17] Zhang, Z., Liu, J., Wong, W.K., Tan, N.M., Lim, J.H., Lu, S., Li,
H., Wong, T.Y., Neu o- e inal op ic cup de ec ion in glaucoma
diagnosis, 2nd In . Con . on Biomedical Enginee ing and In o ma ics,
BMEI 2009 , a . no. 5305076 (2009).
[18] Xu, J., Chu a ape, O., Chew, P., Au oma ed op ic disk Bounda y
de ec ion by modi ied ac i e con ou model, IEEE T ans. on Biomedical
Enginee ing 54 (3), a . no. 16, pp. 473-482 (2007).
Resul s o in e sec ion o he a eas
Me hod % success
pe cen age
% FN % FP
Wi h ellipse
i ing
92.35% 7.64% 4.7%
Wi hou el-
lipse i ing
92.32% 7.67% 5.67%
The me hod was es ed in 22 images manually segmen ed by
expe s om Hospi al o Cadiz o e alua e i s pe o mance. Two
measu emen s we e analysed. The i s one compa es in e sec ion
o a eas delimi ed by manual and au oma ed segmen a ion. The
second measu emen gi es an idea o he con ou s de ia ion.
Fo compa ing he in e sec ion o he a eas, he enclosed a -
eas o bo h con ou lines (manual and au oma ed segmen a ion)
we e compa ed pixel by pixel. As a e e ence a ea o each im-
age, he a ea delimi ed by he manually ou lined con ou was
used. In Table 1 he esul s wi h and wi hou ellipse i ing a e
shown. The success pe cen age was de ined as he pe cen age he
size o he e e ence a ea in e sec ion wi h he a ea segmen ed
by he me hod. False posi i e (FP) a e was de ined as he a ea
e oneously segmen ed as op ic disc by he me hod. And alse
nega i e (FN) a e as he a ea belonging o disc op ic ha i has
no been segmen ed by he me hod. These de ini ions a e clea ly
ep esen ed in Fig. 5.
Figu e 5. In e sec ion o he a eas
The second measu emen , called mean dis ance o he clos-
es poin (MDCP) [23], e alua es he a e age dis ance om he
de ec ed bounda y o he g ound u h. G ound u h is he con-
ou o he e e ence a ea (manually segmen ed a ea ). Re e -
ence con ou , deno ed by R, consis s o he indi idual pixels i,
i:1,2,...,M, whe e M is he amoun o he pixels on he e e ence
con ou . Sis he inal con ou de ec ed by he p oposed me hod.
Fo each con ou poin S(n)n:1,2,...,N, he dis ance o he clos-
es poin (DCP) o e e ence con ou is de ined as:
DCP(S(n),R)=min!S(n)− i!,i:1,2,..., M(9)
The accu acy o he de ec ed bounda y is e alua ed by he
mean o DCP (MDCP) as ollows:
MDCP(S,R)= 1
N
N
∑
n=1
DCP(S(n),R)(10)
Mean dis ance o closes poin (MDCP)
Me hod Wi h ellipse
i ing
Wi hou el-
lipse i ing
MDCP 2.72 pixels 3.07 pixels
MDCP <3pixels (%
images)
66.66% 59.09%
3≤MDCP ≤5pixels
(% images)
33.33% 36.36%
MDCP >5pixels (%
images)
0% 4.54%
The esul ob ained wi h MDCP a e summa ized in Table 2.
The measu ed MDCPs a e, espec i ely, 2.72 and 3.07 pixels o
he p oposed me hod wi h ellipse i ing and wi hou i . In he
able is also shown pe cen age o images ob ained wi h MDCP <
3 pixels, wi h 3 ≤MDCP ≤5 pixels and wi h MDCP >5 pixels
o bo h ou pu s.
Discussion and conclusions
OD de ec ion is an impo an p ep ocessing s ep in Compu e
Aided Diagnosis(CAD) sys ems o many e inopa hies. Speci i-
cally, in glaucoma diagnosis an impo an pa ame e is cup-op ic
disc a io (CDR). The e o e, a s ong e o has been di ec ed o-
wa d an accu a e OD segmen a ion. Ne e heless, no wi hs and-
ing ha e inog aphies a e colo images, mos o he imp o e-
men s in OD segmen a ion ha e been applied o one colo plane
[7, 2, 8, 6]. In [7, 2, 6], good OD loca ion a es a e epo ed bu
he p ecise OD edges a e no es ima ed. [8] p esen s a sensi i i y
o 0.86. In his pape , a new me hod ha loca es he OD edges
has been p esen ed. I ob ains a high sensi i i y in he edge es i-
ma ion, wi h a sensi i i y o 92.35%. P obably his imp o emen
in compa ison wi h [8] is due o he use o he colo in o ma ion
con ained in he image: essel emo al is pe o med wi h an im-
age modi ica ion in he L∗a∗b∗colo space and colo ec o s and
CIE94 di e ence equa ion a e employed o es ima e he g adien .
Ou u u e esea ch will be ocused on a be e alida ion, wi h an
ex ense da ase , on one hand, and, on he o he hand, on segmen -
ing he cup o es ima e he CDR.
Re e ences
[1] S.Ka i ha, S.Ka hikeyan, K.Du aiswamy, Ea ly De ec ion o Glau-
coma in Re inal Images Using Cup o Disc Ra io, P oc. In . Con . on
Compu ing, Communica ion and Ne wo king Technologies(2010).
[2] Aliaa Abdel-Haleim Abdel-Razik Youssi , A e Zaki Ghalwash, and
Am Ahmed Sab y Abdel-Rahman Ghoneim, Op ic Disc De ec ion
F om No malized Digi al Fundus Images by Means o a Vessels
Di ec ion Ma ched Fil e , IEEE T ans. on Medical Imaging, 27, 1
(2008).
[3] L. Gagnon, M. Lalonde, M. Beaulieu, and M.-C. Bouche , P ocedu e
o de ec ana omical s uc u es in op ical undus images, P oc. Con .
Med. Imag. 2001, pp. 12181225. (2001).
[4] R. A. Abdel-Gha a , T. Mo is, T. Ri chings, and I. Wood, De ec-
ion and cha ac e isa ion o he op ic disk in glaucoma and diabe ic
e inopa hy, P oc. Med. Image Unde s and. Anal. Con . (1998).
[5] A. Osa eh, M. Mi mehdi, B. Thomas, and R. Ma kham, Classi i-
ca ion and localisa ion o diabe ic- ela ed eye disease, P oc. ECCV,
Resul s o in e sec ion o he a eas
Me hod % success
pe cen age
% FN % FP
Wi h ellipse
i ing
92.35% 7.64% 4.7%
Wi hou el-
lipse i ing
92.32% 7.67% 5.67%
The me hod was es ed in 22 images manually segmen ed by
expe s om Hospi al o Cadiz o e alua e i s pe o mance. Two
measu emen s we e analysed. The i s one compa es in e sec ion
o a eas delimi ed by manual and au oma ed segmen a ion. The
second measu emen gi es an idea o he con ou s de ia ion.
Fo compa ing he in e sec ion o he a eas, he enclosed a -
eas o bo h con ou lines (manual and au oma ed segmen a ion)
we e compa ed pixel by pixel. As a e e ence a ea o each im-
age, he a ea delimi ed by he manually ou lined con ou was
used. In Table 1 he esul s wi h and wi hou ellipse i ing a e
shown. The success pe cen age was de ined as he pe cen age he
size o he e e ence a ea in e sec ion wi h he a ea segmen ed
by he me hod. False posi i e (FP) a e was de ined as he a ea
e oneously segmen ed as op ic disc by he me hod. And alse
nega i e (FN) a e as he a ea belonging o disc op ic ha i has
no been segmen ed by he me hod. These de ini ions a e clea ly
ep esen ed in Fig. 5.
Figu e 5. In e sec ion o he a eas
The second measu emen , called mean dis ance o he clos-
es poin (MDCP) [23], e alua es he a e age dis ance om he
de ec ed bounda y o he g ound u h. G ound u h is he con-
ou o he e e ence a ea (manually segmen ed a ea ). Re e -
ence con ou , deno ed by R, consis s o he indi idual pixels i,
i:1,2,..., M, whe e M is he amoun o he pixels on he e e ence
con ou . Sis he inal con ou de ec ed by he p oposed me hod.
Fo each con ou poin S(n)n:1,2,...,N, he dis ance o he clos-
es poin (DCP) o e e ence con ou is de ined as:
DCP(S(n),R)=min!S(n)− i!,i:1,2,..., M(9)
The accu acy o he de ec ed bounda y is e alua ed by he
mean o DCP (MDCP) as ollows:
MDCP(S,R)= 1
N
N
∑
n=1
DCP(S(n),R)(10)
Mean dis ance o closes poin (MDCP)
Me hod Wi h ellipse
i ing
Wi hou el-
lipse i ing
MDCP 2.72 pixels 3.07 pixels
MDCP <3pixels (%
images)
66.66% 59.09%
3≤MDCP ≤5pixels
(% images)
33.33% 36.36%
MDCP >5pixels (%
images)
0% 4.54%
The esul ob ained wi h MDCP a e summa ized in Table 2.
The measu ed MDCPs a e, espec i ely, 2.72 and 3.07 pixels o
he p oposed me hod wi h ellipse i ing and wi hou i . In he
able is also shown pe cen age o images ob ained wi h MDCP <
3 pixels, wi h 3 ≤MDCP ≤5 pixels and wi h MDCP >5 pixels
o bo h ou pu s.
Discussion and conclusions
OD de ec ion is an impo an p ep ocessing s ep in Compu e
Aided Diagnosis(CAD) sys ems o many e inopa hies. Speci i-
cally, in glaucoma diagnosis an impo an pa ame e is cup-op ic
disc a io (CDR). The e o e, a s ong e o has been di ec ed o-
wa d an accu a e OD segmen a ion. Ne e heless, no wi hs and-
ing ha e inog aphies a e colo images, mos o he imp o e-
men s in OD segmen a ion ha e been applied o one colo plane
[7, 2, 8, 6]. In [7, 2, 6], good OD loca ion a es a e epo ed bu
he p ecise OD edges a e no es ima ed. [8] p esen s a sensi i i y
o 0.86. In his pape , a new me hod ha loca es he OD edges
has been p esen ed. I ob ains a high sensi i i y in he edge es i-
ma ion, wi h a sensi i i y o 92.35%. P obably his imp o emen
in compa ison wi h [8] is due o he use o he colo in o ma ion
con ained in he image: essel emo al is pe o med wi h an im-
age modi ica ion in he L∗a∗b∗colo space and colo ec o s and
CIE94 di e ence equa ion a e employed o es ima e he g adien .
Ou u u e esea ch will be ocused on a be e alida ion, wi h an
ex ense da ase , on one hand, and, on he o he hand, on segmen -
ing he cup o es ima e he CDR.
Re e ences
[1] S.Ka i ha, S.Ka hikeyan, K.Du aiswamy, Ea ly De ec ion o Glau-
coma in Re inal Images Using Cup o Disc Ra io, P oc. In . Con . on
Compu ing, Communica ion and Ne wo king Technologies(2010).
[2] Aliaa Abdel-Haleim Abdel-Razik Youssi , A e Zaki Ghalwash, and
Am Ahmed Sab y Abdel-Rahman Ghoneim, Op ic Disc De ec ion
F om No malized Digi al Fundus Images by Means o a Vessels
Di ec ion Ma ched Fil e , IEEE T ans. on Medical Imaging, 27, 1
(2008).
[3] L. Gagnon, M. Lalonde, M. Beaulieu, and M.-C. Bouche , P ocedu e
o de ec ana omical s uc u es in op ical undus images, P oc. Con .
Med. Imag. 2001, pp. 12181225. (2001).
[4] R. A. Abdel-Gha a , T. Mo is, T. Ri chings, and I. Wood, De ec-
ion and cha ac e isa ion o he op ic disk in glaucoma and diabe ic
e inopa hy, P oc. Med. Image Unde s and. Anal. Con . (1998).
[5] A. Osa eh, M. Mi mehdi, B. Thomas, and R. Ma kham, Classi i-
ca ion and localisa ion o diabe ic- ela ed eye disease, P oc. ECCV,
Resul s o in e sec ion o he a eas
Me hod % success
pe cen age
% FN % FP
Wi h ellipse
i ing
92.35% 7.64% 4.7%
Wi hou el-
lipse i ing
92.32% 7.67% 5.67%
The me hod was es ed in 22 images manually segmen ed by
expe s om Hospi al o Cadiz o e alua e i s pe o mance. Two
measu emen s we e analysed. The i s one compa es in e sec ion
o a eas delimi ed by manual and au oma ed segmen a ion. The
second measu emen gi es an idea o he con ou s de ia ion.
Fo compa ing he in e sec ion o he a eas, he enclosed a -
eas o bo h con ou lines (manual and au oma ed segmen a ion)
we e compa ed pixel by pixel. As a e e ence a ea o each im-
age, he a ea delimi ed by he manually ou lined con ou was
used. In Table 1 he esul s wi h and wi hou ellipse i ing a e
shown. The success pe cen age was de ined as he pe cen age he
size o he e e ence a ea in e sec ion wi h he a ea segmen ed
by he me hod. False posi i e (FP) a e was de ined as he a ea
e oneously segmen ed as op ic disc by he me hod. And alse
nega i e (FN) a e as he a ea belonging o disc op ic ha i has
no been segmen ed by he me hod. These de ini ions a e clea ly
ep esen ed in Fig. 5.
Figu e 5. In e sec ion o he a eas
The second measu emen , called mean dis ance o he clos-
es poin (MDCP) [23], e alua es he a e age dis ance om he
de ec ed bounda y o he g ound u h. G ound u h is he con-
ou o he e e ence a ea (manually segmen ed a ea ). Re e -
ence con ou , deno ed by R, consis s o he indi idual pixels i,
i:1,2,...,M, whe e M is he amoun o he pixels on he e e ence
con ou . Sis he inal con ou de ec ed by he p oposed me hod.
Fo each con ou poin S(n)n:1,2,..., N, he dis ance o he clos-
es poin (DCP) o e e ence con ou is de ined as:
DCP(S(n),R)=min!S(n)− i!,i:1,2, ..., M(9)
The accu acy o he de ec ed bounda y is e alua ed by he
mean o DCP (MDCP) as ollows:
MDCP(S,R)= 1
N
N
∑
n=1
DCP(S(n),R)(10)
Mean dis ance o closes poin (MDCP)
Me hod Wi h ellipse
i ing
Wi hou el-
lipse i ing
MDCP 2.72 pixels 3.07 pixels
MDCP <3pixels (%
images)
66.66% 59.09%
3≤MDCP ≤5pixels
(% images)
33.33% 36.36%
MDCP >5pixels (%
images)
0% 4.54%
The esul ob ained wi h MDCP a e summa ized in Table 2.
The measu ed MDCPs a e, espec i ely, 2.72 and 3.07 pixels o
he p oposed me hod wi h ellipse i ing and wi hou i . In he
able is also shown pe cen age o images ob ained wi h MDCP <
3 pixels, wi h 3 ≤MDCP ≤5 pixels and wi h MDCP >5 pixels
o bo h ou pu s.
Discussion and conclusions
OD de ec ion is an impo an p ep ocessing s ep in Compu e
Aided Diagnosis(CAD) sys ems o many e inopa hies. Speci i-
cally, in glaucoma diagnosis an impo an pa ame e is cup-op ic
disc a io (CDR). The e o e, a s ong e o has been di ec ed o-
wa d an accu a e OD segmen a ion. Ne e heless, no wi hs and-
ing ha e inog aphies a e colo images, mos o he imp o e-
men s in OD segmen a ion ha e been applied o one colo plane
[7, 2, 8, 6]. In [7, 2, 6], good OD loca ion a es a e epo ed bu
he p ecise OD edges a e no es ima ed. [8] p esen s a sensi i i y
o 0.86. In his pape , a new me hod ha loca es he OD edges
has been p esen ed. I ob ains a high sensi i i y in he edge es i-
ma ion, wi h a sensi i i y o 92.35%. P obably his imp o emen
in compa ison wi h [8] is due o he use o he colo in o ma ion
con ained in he image: essel emo al is pe o med wi h an im-
age modi ica ion in he L∗a∗b∗colo space and colo ec o s and
CIE94 di e ence equa ion a e employed o es ima e he g adien .
Ou u u e esea ch will be ocused on a be e alida ion, wi h an
ex ense da ase , on one hand, and, on he o he hand, on segmen -
ing he cup o es ima e he CDR.
Re e ences
[1] S.Ka i ha, S.Ka hikeyan, K.Du aiswamy, Ea ly De ec ion o Glau-
coma in Re inal Images Using Cup o Disc Ra io, P oc. In . Con . on
Compu ing, Communica ion and Ne wo king Technologies(2010).
[2] Aliaa Abdel-Haleim Abdel-Razik Youssi , A e Zaki Ghalwash, and
Am Ahmed Sab y Abdel-Rahman Ghoneim, Op ic Disc De ec ion
F om No malized Digi al Fundus Images by Means o a Vessels
Di ec ion Ma ched Fil e , IEEE T ans. on Medical Imaging, 27, 1
(2008).
[3] L. Gagnon, M. Lalonde, M. Beaulieu, and M.-C. Bouche , P ocedu e
o de ec ana omical s uc u es in op ical undus images, P oc. Con .
Med. Imag. 2001, pp. 12181225. (2001).
[4] R. A. Abdel-Gha a , T. Mo is, T. Ri chings, and I. Wood, De ec-
ion and cha ac e isa ion o he op ic disk in glaucoma and diabe ic
e inopa hy, P oc. Med. Image Unde s and. Anal. Con . (1998).
[5] A. Osa eh, M. Mi mehdi, B. Thomas, and R. Ma kham, Classi i-
ca ion and localisa ion o diabe ic- ela ed eye disease, P oc. ECCV,
Resul s o in e sec ion o he a eas
Me hod % success
pe cen age
% FN % FP
Wi h ellipse
i ing
92.35% 7.64% 4.7%
Wi hou el-
lipse i ing
92.32% 7.67% 5.67%
The me hod was es ed in 22 images manually segmen ed by
expe s om Hospi al o Cadiz o e alua e i s pe o mance. Two
measu emen s we e analysed. The i s one compa es in e sec ion
o a eas delimi ed by manual and au oma ed segmen a ion. The
second measu emen gi es an idea o he con ou s de ia ion.
Fo compa ing he in e sec ion o he a eas, he enclosed a -
eas o bo h con ou lines (manual and au oma ed segmen a ion)
we e compa ed pixel by pixel. As a e e ence a ea o each im-
age, he a ea delimi ed by he manually ou lined con ou was
used. In Table 1 he esul s wi h and wi hou ellipse i ing a e
shown. The success pe cen age was de ined as he pe cen age he
size o he e e ence a ea in e sec ion wi h he a ea segmen ed
by he me hod. False posi i e (FP) a e was de ined as he a ea
e oneously segmen ed as op ic disc by he me hod. And alse
nega i e (FN) a e as he a ea belonging o disc op ic ha i has
no been segmen ed by he me hod. These de ini ions a e clea ly
ep esen ed in Fig. 5.
Figu e 5. In e sec ion o he a eas
The second measu emen , called mean dis ance o he clos-
es poin (MDCP) [23], e alua es he a e age dis ance om he
de ec ed bounda y o he g ound u h. G ound u h is he con-
ou o he e e ence a ea (manually segmen ed a ea ). Re e -
ence con ou , deno ed by R, consis s o he indi idual pixels i,
i:1,2, ..., M, whe e M is he amoun o he pixels on he e e ence
con ou . Sis he inal con ou de ec ed by he p oposed me hod.
Fo each con ou poin S(n)n:1,2, ..., N, he dis ance o he clos-
es poin (DCP) o e e ence con ou is de ined as:
DCP(S(n),R)=min!S(n)− i!,i:1,2,..., M(9)
The accu acy o he de ec ed bounda y is e alua ed by he
mean o DCP (MDCP) as ollows:
MDCP(S,R)= 1
N
N
∑
n=1
DCP(S(n),R)(10)
Mean dis ance o closes poin (MDCP)
Me hod Wi h ellipse
i ing
Wi hou el-
lipse i ing
MDCP 2.72 pixels 3.07 pixels
MDCP <3pixels (%
images)
66.66% 59.09%
3≤MDCP ≤5pixels
(% images)
33.33% 36.36%
MDCP >5pixels (%
images)
0% 4.54%
The esul ob ained wi h MDCP a e summa ized in Table 2.
The measu ed MDCPs a e, espec i ely, 2.72 and 3.07 pixels o
he p oposed me hod wi h ellipse i ing and wi hou i . In he
able is also shown pe cen age o images ob ained wi h MDCP <
3 pixels, wi h 3 ≤MDCP ≤5 pixels and wi h MDCP >5 pixels
o bo h ou pu s.
Discussion and conclusions
OD de ec ion is an impo an p ep ocessing s ep in Compu e
Aided Diagnosis(CAD) sys ems o many e inopa hies. Speci i-
cally, in glaucoma diagnosis an impo an pa ame e is cup-op ic
disc a io (CDR). The e o e, a s ong e o has been di ec ed o-
wa d an accu a e OD segmen a ion. Ne e heless, no wi hs and-
ing ha e inog aphies a e colo images, mos o he imp o e-
men s in OD segmen a ion ha e been applied o one colo plane
[7, 2, 8, 6]. In [7, 2, 6], good OD loca ion a es a e epo ed bu
he p ecise OD edges a e no es ima ed. [8] p esen s a sensi i i y
o 0.86. In his pape , a new me hod ha loca es he OD edges
has been p esen ed. I ob ains a high sensi i i y in he edge es i-
ma ion, wi h a sensi i i y o 92.35%. P obably his imp o emen
in compa ison wi h [8] is due o he use o he colo in o ma ion
con ained in he image: essel emo al is pe o med wi h an im-
age modi ica ion in he L∗a∗b∗colo space and colo ec o s and
CIE94 di e ence equa ion a e employed o es ima e he g adien .
Ou u u e esea ch will be ocused on a be e alida ion, wi h an
ex ense da ase , on one hand, and, on he o he hand, on segmen -
ing he cup o es ima e he CDR.
Re e ences
[1] S.Ka i ha, S.Ka hikeyan, K.Du aiswamy, Ea ly De ec ion o Glau-
coma in Re inal Images Using Cup o Disc Ra io, P oc. In . Con . on
Compu ing, Communica ion and Ne wo king Technologies(2010).
[2] Aliaa Abdel-Haleim Abdel-Razik Youssi , A e Zaki Ghalwash, and
Am Ahmed Sab y Abdel-Rahman Ghoneim, Op ic Disc De ec ion
F om No malized Digi al Fundus Images by Means o a Vessels
Di ec ion Ma ched Fil e , IEEE T ans. on Medical Imaging, 27, 1
(2008).
[3] L. Gagnon, M. Lalonde, M. Beaulieu, and M.-C. Bouche , P ocedu e
o de ec ana omical s uc u es in op ical undus images, P oc. Con .
Med. Imag. 2001, pp. 12181225. (2001).
[4] R. A. Abdel-Gha a , T. Mo is, T. Ri chings, and I. Wood, De ec-
ion and cha ac e isa ion o he op ic disk in glaucoma and diabe ic
e inopa hy, P oc. Med. Image Unde s and. Anal. Con . (1998).
[5] A. Osa eh, M. Mi mehdi, B. Thomas, and R. Ma kham, Classi i-
ca ion and localisa ion o diabe ic- ela ed eye disease, P oc. ECCV,