Segmentación del disco óptico mediante level-sets con información de color

Segmentación del disco óptico mediante level-sets con información de color A. Sáez1, I. Fondón1, C. Serrano1, S. Jiménez2, P. Alemany3, B. Acha1 1 Dpto. Teoría de la Señal y Comunicaciones, Universidad de Sevilla, Sevilla, España, [email protected],{irenef,cserrano,bacha}@us.es 2 Servicio de Oftalmología, Hospital Puerta del Mar, Cádiz, España, [email protected] 3 Facultad de Medicina, Universidad de Cádiz, Cádiz, España Resumen La segmentación del Disco Óptico (DO) es un paso esencial para la extracción automática de estructuras anatómicas y lesiones retinianas. La mayoría de los algoritmos de segmentación de la literatura procesan exclusivamente un solo plano de la retinografía, descartando la información de color. En este artículo se presenta un nuevo algoritmo de segmentación del DO. En primer lugar se realiza un preprocesamiento para eliminar los vasos sanguíneos. A continuación se aplica un algoritmo de level-sets basado en bordes. La mayor contribución del artículo es la utilización de la información de color para el proceso de segmentación. Se calculan gradientes vectoriales en el espacio de color L*a*b* que son utilizados por el algoritmo de level-sets. En lugar de utilizar la norma Euclídea, se aplica la fórmula de diferencia de color CIE94 en los gradientes vectoriales. Se ha probado con 22 retinografías donde los médicos han detectado manualmente los bordes del DO. El algoritmo ha detectado automáticamente el DO en todos los casos, con un 92.35% de intersección entre el área marcada por los expertos y la detectada. La Distancia Media al Punto más Cercano está por debajo de 5 píxeles en el 100% de las imágenes. 1. Motivación El número de afectados de ceguera debido a enfermedades como la retinopatía diabética o el glaucoma ha aumentado en los últimos tiempos. Tres cuartas partes de esas cegueras pueden tratarse y prevenirse cuando se realiza un control temprano de la población. Los programas de screening consisten principalmente en obtener imágenes fotográficas de fondo de ojo. Según el resultado del análisis de dichas imágenes los pacientes son referidos al oftalmólogo para su tratamiento. Por tanto, es deseable una automatización del proceso inicial de analizar la gran cantidad de imágenes retinográficas para agilizar y mejorar el proceso de screening. La detección del DO es un paso de preprocesamiento muy importante en muchos algoritmos diseñados para la extracción de otras estructuras anatómicas retinianas y lesiones [1,2]. El cambio en la forma, color o profundidad del DO es un indicador de varias patologías, principalmente del glaucoma [3]. Aunque el DO posee características bien definidas, la localización automática del mismo no es un proceso sencillo, ya que la apariencia del mismo varía significativamente con las distintas patologías. Así que, los métodos desarrollados deben tener en cuenta esta variación entre las diferentes imágenes. Existen muchos métodos para la detección del disco óptico, pero la mayoría utilizan parte de la información de color de la imagen, como el uso de un solo plano [1, 4-6]. En este artículo se propone procesar cada píxel de color utilizando un gradiente vectorial para la detección de bordes utilizada en la segmentación por level-sets. Además se utiliza un espacio de color uniforme, L*a*b*, y se corrigen las no uniformidades de dicho espacio de color sustituyendo la distancia Euclídea por la CIE94 en el cálculo del gradiente [7]. 2. Metodología El diagrama de flujo mostrado en la Fig. 1 muestra los pasos del algoritmo propuesto. 2.1. Eliminación del árbol vascular Para la eliminación del árbol vascular se ha utilizado el algoritmo diseñado para la eliminación del vello en imágenes de lesiones pigmentadas de la piel [8]. Consta de tres etapas: detección de vasos con el uso de la derivada de la gaussiana (DOG) [9], refinamiento del resultado con técnicas morfológicas y sustitución de vasos por “fast marching image inpainting” [10]. Fig. 1 Sistema propuesto 2.2. Localización del disco El DO puede ser identificado como una región brillante en la imagen de fondo de ojo [11]. Por ello se ha utilizado la información de luminosidad para detectarlo. El canal L* del espacio de color L*a*b* se suaviza con un filtro de promediado. Los píxeles de la imagen resultado con intensidades superiores al 97% del valor máximo de intensidad son seleccionados. Se calcula el centro de masas de este conjunto de píxeles. Para determinar la región de interés (ROI: Region Of Interest) se escoge un cuadrado de radio 90 píxeles y centrado en el centro de masas. Este cuadrado define el contorno inicial 2.3. Gradiente de color Los métodos de level-set son aplicados a un gradiente de la imagen. En la literatura se utiliza el gradiente de un solo plano, por ejemplo, en [12] se utiliza el plano R. En el presente trabajo se tiene en cuenta toda la información de color utilizando un gradiente vectorial [13]. Definimos un píxel de la imagen en color de la forma: donde representa el valor del píxel en el plano i (i= 1, 2, 3). El operador Sobel basado en la primera derivada, comúnmente aplicado a imágenes en escala de grises, puede generalizarse al caso multidimensional [14]. En este artículo se ha aplicado la máscara de Sobel a la imagen en el espacio de color L*a*b* construyendo los vectores: , , , siguiendo la notación de la Fig. 2. Fig. 2 Ventana Los gradientes a lo largo de la dirección x e y son: donde denota la diferencia de color CIE94 entre dos vectores definidos en el espacio CIE L*a*b*. Normalmente se utiliza en estos casos la distancia Euclídea, pero en este artículo se ha escogido la distancia CIE94 ya que se ha demostrado que CIE94 es superior [13]. La magnitud del gradiente se calcula: . 2.4. Segmentación basada en level-sets Una vez que los vasos han sido eliminados, el DO es segmentado utilizando la técnica de level-sets [15]. La idea de este tipo de algoritmo es representar los contornos como el conjunto de nivel cero de una función implícita definida en una dimensión mayor (función de level-set ). La función evolucionará de forma que el nivel cero converja a los bordes reales de la imagen. La ecuación general es: donde F representa la función de velocidad. Utilizando el trabajo de Li et al. [16] la expresión para el gradiente queda: donde µ determina la desviación de φ de una función de distancia con signo, λ y υ son coeficientes de la longitud ponderada de la Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) curva de nivel cero y del área ponderada dentro de dicha curva respectivamente y t es el paso de tiempo del experimento. g es la función indicadora de bordes y está definida como: donde es un núcleo gaussiano con desviación estándar σ e I es la imagen de test. En este artículo, el gradiente utilizado para esta fórmula ha sido el gradiente vectorial explicado en la sección anterior. Por tanto, la función g queda modificada como: donde VD es el gradiente vectorial implementado en el espacio de color CIE L*a*b* y con la distancia de color CIE94. 2.5. Post-procesamiento La salida del paso anterior es el contorno del DO. Sin embargo, diversos autores [12,17] utilizan la forma de una elipse como último paso para suavizar el contorno detectado, ya que así se asemeja más a la delineación manual que hacen los expertos. En este artículo se estudian los resultados con y sin adaptación a una elipse. 3. Resultados y evaluación Algunos de los resultados del método propuesto se muestran en las Figs. 3 y 4. Ambos resultados, salida del algoritmo de level-sets y salida de la adaptación a una elipse, son evaluados. El método ha sido evaluado con 22 imágenes segmentadas manualmente por expertos. Se han analizado dos medidas de prestaciones. La primera compara las áreas delimitadas manualmente y automáticamente. La segunda da una idea de la desviación del contorno. Fig. 3 a) Imagen original, b) eliminación del árbol vascular, c) segmentación manual del DO (verde) y segmentación por levelsets (azul), d) adaptación a una elipse del contorno manual (verde) y del contorno detectado (azul). Fig. 4 a) Imagen original, b) eliminación del árbol vascular, c) segmentación manual del DO (verde) y segmentación por levelsets (azul), d) adaptación a una elipse del contorno manual (verde) y del contorno detectado (azul). Para la intersección de las áreas, las áreas contenidas por los contornos manuales y automáticos se han comparado píxel a píxel. Como área referencia se ha escogido la Figure 1. Proposed system Disc Localization The optic disc can be identified as a bright region on a retinal fundus image [12]. Therefore, lightness information was used to detect the disc localization. The channel L of L∗a∗b∗colour space was smoothed by an averaging filter. The pixels of the result image with intensity value higher than 97% of the maximum intensity value were selected. The mass centre of this set of pixels was calculated. A square with radius of 90 pixels and centred at that mass center was used to determine the ROI. This square defined the initial contour required for the level-set segmentation, explained in a following section. Colour gradient The edge-based level set methods are applied to a gradient image. In the literature, all of the authors use the gradient of a single channel in the problem at hand, example of that is the work of Wong et al. [13] where the level-set algorithm was applied to red channel. However, in this paper the colour information was taken into account, and a colour gradient was used [14]. In colour gradients, the vector nature of colour is preserved throughout the computation. Colour images can be viewed as a two-dimensional three channel vector field. Each pixel in this vector field is characterized by a discrete integer function a(x,y). The value of this function at each point is defined by a three dimensional vector in a given colour space. Therefore, a pixel is defined as: a(x,y)=  C1(x,y) C2(x,y) C3(x,y)  (1) where Ci(x,y)represents the value of the pixel in the i-th colour plane (i=1,2,3), and (x,y)refers to the spatial dimensions in the 2-D plane. a1a2a3 a4a5a6 a7a8a9 Figure 2. Sliding window The operator Sobel based on the first derivative, commonly applied in grayscale imaging, can be generalized into the multidimensional [15]. In this paper, Sobel mask was applied to CIE L∗a∗b∗image by constructing the vectors (according to the notation 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 gradient along x and ydirection respectively, is shown in equation 2 and 3. Gx=#E%V+ 1,V− 1&(2) Gy=#E%H+ 2,H− 2&(3) where #Edenotes the CIE94 colour difference between the two vectors defined in the CIE L∗a∗b∗colour space. Usually, the Euclidian distance (CIELAB) is used in this purpose, however the CIE94 colour distance was used in this paper because it has been shown that CIE94 outperforms CIELAB [14]. The gradient magnitude is computed as shown in equation 4. G='G2 x+G2 y(4) Variational level-set Once blood vessels are removed, optic disc segmentation is carried out by using a variational level set formulation. Level set methods, which were first introduced by Osher and Sethian [16], have been widely used as global approaches optimizing active contours for the segmentation of objects of interest from the background [17] [18] [19]. The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function ( φ (t)). The challenge of a level-set algorithm is to make ( φ ) evolve so that its zero level converges at the real boundaries in the image. The general level set equation is presented in 5, ∂φ ∂ t+F|∇ φ |=0 (5) where Frepresents the speed function and φ the level set function. One of the main challenges in the employment of level set techniques has been the generation of shocks which can result in less than accurate contours. To overcome this, the method developed by Li et al [20] is employed. In the reported work, an energy function ε is introduced into 5 to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂ t= µ (# φ −div)∇ φ |∇ φ |*++ λδ ( φ )div)g∇ φ |∇ φ |*+ ν g δ ( φ )(6) where µ determines the deviation of φ from a signed distance function, λ and ν are the coefficients of the weighted length of the zero level curve and of the weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of 6 are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function defined by: g=1 1+|∇G σ ∗I|2(7) (a) (b) (c) (d) Figure 3. a) original image, b) bool vessels removal, c) optic disc manual segmentation (green) and segmentation by the level set (blue) d) ellipse fitting to contour manually segmented (green) and to the detected contour (blue). where G σ is the Gaussian kernel with standard deviation σ and Iis the test image. In this paper, the gradient used in this definition it was the vector gradient explained in the previous section. Therefore, the gdefinition is modified: g=1 1+|VD(G σ ∗I)|2(8) where VDis the vector gradient implemented in CIE L∗a∗b∗ using CIE94 colour difference equation, explained in the previous section. Ellipse fitting The output of the above step is contour of optic disc. However, several authors [13], [22] used a ellipse fit as post-processing step in order to smooth this detected contour. In this paper, the results obtained with or without ellipse fitting were studied. Results and Evaluation Some results of the proposed method can be seen in Fig. 3 and Fig. 4, where a) shows the original image, b) image without the bool vessels, c) manually segmented optic disc in green and segmented by the proposed method in blue d) ellipse fitting to contour manually segmented (green) and to the contour detected (blue). Both results, output of the level set and output of the ellipse fitting, were evaluated. (a) (b) (c) (d) Figure 4. a) original image, b) bool vessels removal, c) optic disc segmentation manually (green) and segmentation by the level set (blue) d) ellipse fitting to contour manually segmented (green) and to the contour detected (blue). (a) (b) (c) (d) Figure 3. a) original image, b) bool vessels removal, c) optic disc manual segmentation (green) and segmentation by the level set (blue) d) ellipse fitting to contour manually segmented (green) and to the detected contour (blue). where G σ is the Gaussian kernel with standard deviation σ and Iis the test image. In this paper, the gradient used in this definition it was the vector gradient explained in the previous section. Therefore, the gdefinition is modified: g=1 1+|VD(G σ ∗I)|2(8) where VDis the vector gradient implemented in CIE L∗a∗b∗ using CIE94 colour difference equation, explained in the previous section. Ellipse fitting The output of the above step is contour of optic disc. However, several authors [13], [22] used a ellipse fit as post-processing step in order to smooth this detected contour. In this paper, the results obtained with or without ellipse fitting were studied. Results and Evaluation Some results of the proposed method can be seen in Fig. 3 and Fig. 4, where a) shows the original image, b) image without the bool vessels, c) manually segmented optic disc in green and segmented by the proposed method in blue d) ellipse fitting to contour manually segmented (green) and to the contour detected (blue). Both results, output of the level set and output of the ellipse fitting, were evaluated. (a) (b) (c) (d) Figure 4. a) original image, b) bool vessels removal, c) optic disc segmentation manually (green) and segmentation by the level set (blue) d) ellipse fitting to contour manually segmented (green) and to the contour detected (blue). (a) (b) (c) (d) Figure 3. a) original image, b) bool vessels removal, c) optic disc manual segmentation (green) and segmentation by the level set (blue) d) ellipse fitting to contour manually segmented (green) and to the detected contour (blue). where G σ is the Gaussian kernel with standard deviation σ and Iis the test image. In this paper, the gradient used in this definition it was the vector gradient explained in the previous section. Therefore, the gdefinition is modified: g=1 1+|VD(G σ ∗I)|2(8) where VDis the vector gradient implemented in CIE L∗a∗b∗ using CIE94 colour difference equation, explained in the previous section. Ellipse fitting The output of the above step is contour of optic disc. However, several authors [13], [22] used a ellipse fit as post-processing step in order to smooth this detected contour. In this paper, the results obtained with or without ellipse fitting were studied. Results and Evaluation Some results of the proposed method can be seen in Fig. 3 and Fig. 4, where a) shows the original image, b) image without the bool vessels, c) manually segmented optic disc in green and segmented by the proposed method in blue d) ellipse fitting to contour manually segmented (green) and to the contour detected (blue). Both results, output of the level set and output of the ellipse fitting, were evaluated. (a) (b) (c) (d) Figure 4. a) original image, b) bool vessels removal, c) optic disc segmentation manually (green) and segmentation by the level set (blue) d) ellipse fitting to contour manually segmented (green) and to the contour detected (blue). (a) (b) (c) (d) Figure 3. a) original image, b) bool vessels removal, c) optic disc manual segmentation (green) and segmentation by the level set (blue) d) ellipse fitting to contour manually segmented (green) and to the detected contour (blue). where G σ is the Gaussian kernel with standard deviation σ and Iis the test image. In this paper, the gradient used in this definition it was the vector gradient explained in the previous section. Therefore, the gdefinition is modified: g=1 1+|VD(G σ ∗I)|2(8) where VDis the vector gradient implemented in CIE L∗a∗b∗ using CIE94 colour difference equation, explained in the previous section. Ellipse fitting The output of the above step is contour of optic disc. However, several authors [13], [22] used a ellipse fit as post-processing step in order to smooth this detected contour. In this paper, the results obtained with or without ellipse fitting were studied. Results and Evaluation Some results of the proposed method can be seen in Fig. 3 and Fig. 4, where a) shows the original image, b) image without the bool vessels, c) manually segmented optic disc in green and segmented by the proposed method in blue d) ellipse fitting to contour manually segmented (green) and to the contour detected (blue). Both results, output of the level set and output of the ellipse fitting, were evaluated. (a) (b) (c) (d) Figure 4. a) original image, b) bool vessels removal, c) optic disc segmentation manually (green) and segmentation by the level set (blue) d) ellipse fitting to contour manually segmented (green) and to the contour detected (blue). segmentación manual. En la Tabla 1 se muestran los resultados con y sin adaptación a una elipse. El porcentaje de acierto se define como el porcentaje del tamaño de la intersección de ambas áreas. La tasa de falsos positivos (FP) se define como el área segmentada erróneamente como DO por el método. Y la tasa de falsos negativos (FN) como el área perteneciente al DO que no ha sido segmentada por el método propuesto. Tabla 1. Resultado de la intersección de las áreas La segunda medida, denominada distancia media al punto más cercano (MDCP, de las siglas en inglés) [18], evalúa la distancia media desde el contorno detectado al segmentado manualmente (contorno de referencia). El contorno de referencia, R, consiste en píxeles individuales ri, i = 1,2, …, M, donde M es la cantidad de píxeles del contorno de referencia. Sea S el contorno final detectado por el método propuesto. Para cada punto del contorno S(n), n= 1, 2, …, N, la distancia al punto más cercano (DCP) del contorno de referencia se define como: La exactitud del contorno detectado se evalúa por la media de DCP (MDCP): Los resultados obtenidos con esta medida están resumidos en la Tabla 2. Las MDCP son 2.72 y 3.07 para píxeles para el método propuesto con adaptación a elipse y sin dicha adaptación, respectivamente. Tabla 2. Resultados de la MDCP 4. Discusión y conclusiones La detección del DO es un paso muy importante en sistemas CAD que utilizan retinografías, por ejemplo, en la detección del glaucoma. La mayoría de trabajos publicados sólo utilizan un plano de color para la detección. En este trabajo se peresenta un método que utiliza toda la información de color para la eliminación del árbol vascular y la detección de bordes usada en el algoritmo de level-sets de segmentación. Se obtiene una sensibilidad del 92.35%. Agradecimientos Este trabajo se ha realizado gracias al proyecto TEC2010-21619-C04-02. Referencias [1] Han X., Xu C., Prince J., A topology preserving level set method for geometric deformable models, IEEE Trans. Patt. Anal. Mach. Intell., vol. 25, pp. 755-768, (2003). [2] Caselles V., Catte F., Coll T., Dibos F., A geometric model for active contours in image processing, Numer. Math., vol. 66, pp. 1-31 (1993). [3] Malladi R., Sethian J. A., Vemuri B. C., Shape modeling with front propagation: a level set approach, IEEE Trans. Patt. Anal. Mach. Intell., vol. 17, pp. 158-175, (1995). [4] Fitzgibbon, A., Pilu, M., Fisher, R.B., Direct least square fitting of ellipses, IEEE Trans. Patt. Anal. Mach. Intell,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., Neuro-retinal optic cup detection in glaucoma diagnosis, BMEI 2009 , art. no. 5305076 (2009). [6] Xu, J., Chutatape, O., Chew, P., Automated optic disk Boundary detection by modified active contour model, IEEE Transactions on Biomedical Engineering 54 (3), art. no. 16, pp. 473-482 (2007). [7] Rangayyan R, Acha B, Serrano C, Color Image Processing with Biomedical Applications, SPIE Press, Bellingham, EEUU (2011). [8] S.Kavitha, S.Karthikeyan, K.Duraiswamy, Early Detection of Glaucoma in Retinal Images Using Cup to Disc Ratio, Proc. Int. Conf. On Computing, Communication and Networking Technologies(2010). [9] Aliaa Abdel-Haleim Abdel-Razik Youssif, Atef Zaki Ghalwash, and Amr Ahmed Sabry Abdel-Rahman Ghoneim, Optic Disc Detection From Normalized Digital Fundus Images by Means of a Vessels Direction Matched Filter, IEEE Trans. on Medical Imaging, 27, 1 (2008) [10] L. Gagnon, M. Lalonde, M. Beaulieu, and M.-C. Boucher, Procedure to detect anatomical structures in optical fundus images, Proc. Conf. Med. Imag. 2001, pp. 12181225. (2001). [11] R. A. Abdel-Ghafar, T. Morris, T. Ritchings, and I. Wood, Detection and characterisation of the optic disk in glaucoma and diabetic retinopathy, Proc. Med. Image Understand. Anal. Conf. (1998). [12] Wong, D.W.K., Liu, J., Lim, J.H., Jia, X., Yin, F., Li, H., Wong, T.Y. Level-set based automatic cup-to-disc ratio determination using retinal fundus images in ARGALI. EMBS 2008 pp. 2266-2269, (2008) [13] Sez, A., Serrano, C., Acha, B., Evaluation perceptual color edge detection algorithms, 5th European Conf. on Colour in Graphics, Imaging, and Vision, CGIV 2010/MCS’10 , pp. 222-22, (2010). [14] K.N. Plataniotis, A.N. Venetsanopoulos, Color Image Processing and Applications, Springer-Verlag, Berlin, 2000. [15] Osher S. , Sethian J. A., Fronts propagating with curvaturedependent speed - algorithms based on hamilton-jacobi formulations, J Comput Phys, 79, 12-49 (1998). [16] C. Li, C. Xu, C. Gui, M. D. Fox, Level set evolution without reinitialization: a new variational formulation, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, (2005). [17] Zhang, Z., Liu, J., Wong, W.K., Tan, N.M., Lim, J.H., Lu, S., Li, H., Wong, T.Y., Neuro-retinal optic cup detection in glaucoma diagnosis, 2nd Int. Conf. on Biomedical Engineering and Informatics, BMEI 2009 , art. no. 5305076 (2009). [18] Xu, J., Chutatape, O., Chew, P., Automated optic disk Boundary detection by modified active contour model, IEEE Trans. on Biomedical Engineering 54 (3), art. no. 16, pp. 473-482 (2007). Results of intersection of the areas Method % success percentage % FN % FP With ellipse fitting 92.35% 7.64% 4.7% Without ellipse fitting 92.32% 7.67% 5.67% The method was tested in 22 images manually segmented by experts from Hospital of Cadiz to evaluate its performance. Two measurements were analysed. The first one compares intersection of areas delimited by manual and automated segmentation. The second measurement gives an idea of the contours deviation. For comparing the intersection of the areas, the enclosed areas of both contour lines (manual and automated segmentation) were compared pixel by pixel. As a reference area for each image, the area delimited by the manually outlined contour was used. In Table 1 the results with and without ellipse fitting are shown. The success percentage was defined as the percentage the size of the reference area intersection with the area segmented by the method. False positive (FP) rate was defined as the area erroneously segmented as optic disc by the method. And false negative (FN) rate as the area belonging to disc optic that it has not been segmented by the method. These definitions are clearly represented in Fig. 5. Figure 5. Intersection of the areas The second measurement, called mean distance to the closest point (MDCP) [23], evaluates the average distance from the detected boundary to the ground truth. Ground truth is the contour of the reference area (manually segmented area ). Reference contour, denoted by R, consists of the individual pixels ri, i:1,2,...,M, where M is the amount of the pixels on the reference contour. Sis the final contour detected by the proposed method. For each contour point S(n)n:1,2,...,N, the distance to the closest point (DCP) of reference contour is defined as: DCP(S(n),R)=min!S(n)−ri!,i:1,2,..., M(9) The accuracy of the detected boundary is evaluated by the mean of DCP (MDCP) as follows: MDCP(S,R)= 1 N N ∑ n=1 DCP(S(n),R)(10) Mean distance to closest point (MDCP) Method With ellipse fitting Without ellipse fitting 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 result obtained with MDCP are summarized in Table 2. The measured MDCPs are, respectively, 2.72 and 3.07 pixels for the proposed method with ellipse fitting and without it. In the table is also shown percentage of images obtained with MDCP < 3 pixels, with 3 ≤MDCP ≤5 pixels and with MDCP >5 pixels for both outputs. Discussion and conclusions OD detection is an important preprocessing step in Computer Aided Diagnosis(CAD) systems for many retinopathies. Specifically, in glaucoma diagnosis an important parameter is cup-optic disc ratio (CDR). Therefore, a strong effort has been directed toward an accurate OD segmentation. Nevertheless, notwithstanding that retinographies are color images, most of the improvements in OD segmentation have been applied to one color plane [7, 2, 8, 6]. In [7, 2, 6], good OD location rates are reported but the precise OD edges are not estimated. [8] presents a sensitivity of 0.86. In this paper, a new method that locates the OD edges has been presented. It obtains a high sensitivity in the edge estimation, with a sensitivity of 92.35%. Probably this improvement in comparison with [8] is due to the use of the color information contained in the image: vessel removal is performed with an image modification in the L∗a∗b∗color space and color vectors and CIE94 difference equation are employed to estimate the gradient. Our future research will be focused on a better validation, with an extense dataset, on one hand, and, on the other hand, on segmenting the cup to estimate the CDR. References [1] S.Kavitha, S.Karthikeyan, K.Duraiswamy, Early Detection of Glaucoma in Retinal Images Using Cup to Disc Ratio, Proc. Int. Conf. on Computing, Communication and Networking Technologies(2010). [2] Aliaa Abdel-Haleim Abdel-Razik Youssif, Atef Zaki Ghalwash, and Amr Ahmed Sabry Abdel-Rahman Ghoneim, Optic Disc Detection From Normalized Digital Fundus Images by Means of a Vessels Direction Matched Filter, IEEE Trans. on Medical Imaging, 27, 1 (2008). [3] L. Gagnon, M. Lalonde, M. Beaulieu, and M.-C. Boucher, Procedure to detect anatomical structures in optical fundus images, Proc. Conf. Med. Imag. 2001, pp. 12181225. (2001). [4] R. A. Abdel-Ghafar, T. Morris, T. Ritchings, and I. Wood, Detection and characterisation of the optic disk in glaucoma and diabetic retinopathy, Proc. Med. Image Understand. Anal. Conf. (1998). [5] A. Osareh, M. Mirmehdi, B. Thomas, and R. Markham, Classification and localisation of diabetic-related eye disease, Proc. ECCV, Results of intersection of the areas Method % success percentage % FN % FP With ellipse fitting 92.35% 7.64% 4.7% Without ellipse fitting 92.32% 7.67% 5.67% The method was tested in 22 images manually segmented by experts from Hospital of Cadiz to evaluate its performance. Two measurements were analysed. The first one compares intersection of areas delimited by manual and automated segmentation. The second measurement gives an idea of the contours deviation. For comparing the intersection of the areas, the enclosed areas of both contour lines (manual and automated segmentation) were compared pixel by pixel. As a reference area for each image, the area delimited by the manually outlined contour was used. In Table 1 the results with and without ellipse fitting are shown. The success percentage was defined as the percentage the size of the reference area intersection with the area segmented by the method. False positive (FP) rate was defined as the area erroneously segmented as optic disc by the method. And false negative (FN) rate as the area belonging to disc optic that it has not been segmented by the method. These definitions are clearly represented in Fig. 5. Figure 5. Intersection of the areas The second measurement, called mean distance to the closest point (MDCP) [23], evaluates the average distance from the detected boundary to the ground truth. Ground truth is the contour of the reference area (manually segmented area ). Reference contour, denoted by R, consists of the individual pixels ri, i:1,2,..., M, where M is the amount of the pixels on the reference contour. Sis the final contour detected by the proposed method. For each contour point S(n)n:1,2,...,N, the distance to the closest point (DCP) of reference contour is defined as: DCP(S(n),R)=min!S(n)−ri!,i:1,2,..., M(9) The accuracy of the detected boundary is evaluated by the mean of DCP (MDCP) as follows: MDCP(S,R)= 1 N N ∑ n=1 DCP(S(n),R)(10) Mean distance to closest point (MDCP) Method With ellipse fitting Without ellipse fitting 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 result obtained with MDCP are summarized in Table 2. The measured MDCPs are, respectively, 2.72 and 3.07 pixels for the proposed method with ellipse fitting and without it. In the table is also shown percentage of images obtained with MDCP < 3 pixels, with 3 ≤MDCP ≤5 pixels and with MDCP >5 pixels for both outputs. Discussion and conclusions OD detection is an important preprocessing step in Computer Aided Diagnosis(CAD) systems for many retinopathies. Specifically, in glaucoma diagnosis an important parameter is cup-optic disc ratio (CDR). Therefore, a strong effort has been directed toward an accurate OD segmentation. Nevertheless, notwithstanding that retinographies are color images, most of the improvements in OD segmentation have been applied to one color plane [7, 2, 8, 6]. In [7, 2, 6], good OD location rates are reported but the precise OD edges are not estimated. [8] presents a sensitivity of 0.86. In this paper, a new method that locates the OD edges has been presented. It obtains a high sensitivity in the edge estimation, with a sensitivity of 92.35%. Probably this improvement in comparison with [8] is due to the use of the color information contained in the image: vessel removal is performed with an image modification in the L∗a∗b∗color space and color vectors and CIE94 difference equation are employed to estimate the gradient. Our future research will be focused on a better validation, with an extense dataset, on one hand, and, on the other hand, on segmenting the cup to estimate the CDR. References [1] S.Kavitha, S.Karthikeyan, K.Duraiswamy, Early Detection of Glaucoma in Retinal Images Using Cup to Disc Ratio, Proc. Int. Conf. on Computing, Communication and Networking Technologies(2010). [2] Aliaa Abdel-Haleim Abdel-Razik Youssif, Atef Zaki Ghalwash, and Amr Ahmed Sabry Abdel-Rahman Ghoneim, Optic Disc Detection From Normalized Digital Fundus Images by Means of a Vessels Direction Matched Filter, IEEE Trans. on Medical Imaging, 27, 1 (2008). [3] L. Gagnon, M. Lalonde, M. Beaulieu, and M.-C. Boucher, Procedure to detect anatomical structures in optical fundus images, Proc. Conf. Med. Imag. 2001, pp. 12181225. (2001). [4] R. A. Abdel-Ghafar, T. Morris, T. Ritchings, and I. Wood, Detection and characterisation of the optic disk in glaucoma and diabetic retinopathy, Proc. Med. Image Understand. Anal. Conf. (1998). [5] A. Osareh, M. Mirmehdi, B. Thomas, and R. Markham, Classification and localisation of diabetic-related eye disease, Proc. ECCV, Results of intersection of the areas Method % success percentage % FN % FP With ellipse fitting 92.35% 7.64% 4.7% Without ellipse fitting 92.32% 7.67% 5.67% The method was tested in 22 images manually segmented by experts from Hospital of Cadiz to evaluate its performance. Two measurements were analysed. The first one compares intersection of areas delimited by manual and automated segmentation. The second measurement gives an idea of the contours deviation. For comparing the intersection of the areas, the enclosed areas of both contour lines (manual and automated segmentation) were compared pixel by pixel. As a reference area for each image, the area delimited by the manually outlined contour was used. In Table 1 the results with and without ellipse fitting are shown. The success percentage was defined as the percentage the size of the reference area intersection with the area segmented by the method. False positive (FP) rate was defined as the area erroneously segmented as optic disc by the method. And false negative (FN) rate as the area belonging to disc optic that it has not been segmented by the method. These definitions are clearly represented in Fig. 5. Figure 5. Intersection of the areas The second measurement, called mean distance to the closest point (MDCP) [23], evaluates the average distance from the detected boundary to the ground truth. Ground truth is the contour of the reference area (manually segmented area ). Reference contour, denoted by R, consists of the individual pixels ri, i:1,2,...,M, where M is the amount of the pixels on the reference contour. Sis the final contour detected by the proposed method. For each contour point S(n)n:1,2,..., N, the distance to the closest point (DCP) of reference contour is defined as: DCP(S(n),R)=min!S(n)−ri!,i:1,2, ..., M(9) The accuracy of the detected boundary is evaluated by the mean of DCP (MDCP) as follows: MDCP(S,R)= 1 N N ∑ n=1 DCP(S(n),R)(10) Mean distance to closest point (MDCP) Method With ellipse fitting Without ellipse fitting 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 result obtained with MDCP are summarized in Table 2. The measured MDCPs are, respectively, 2.72 and 3.07 pixels for the proposed method with ellipse fitting and without it. In the table is also shown percentage of images obtained with MDCP < 3 pixels, with 3 ≤MDCP ≤5 pixels and with MDCP >5 pixels for both outputs. Discussion and conclusions OD detection is an important preprocessing step in Computer Aided Diagnosis(CAD) systems for many retinopathies. Specifically, in glaucoma diagnosis an important parameter is cup-optic disc ratio (CDR). Therefore, a strong effort has been directed toward an accurate OD segmentation. Nevertheless, notwithstanding that retinographies are color images, most of the improvements in OD segmentation have been applied to one color plane [7, 2, 8, 6]. In [7, 2, 6], good OD location rates are reported but the precise OD edges are not estimated. [8] presents a sensitivity of 0.86. In this paper, a new method that locates the OD edges has been presented. It obtains a high sensitivity in the edge estimation, with a sensitivity of 92.35%. Probably this improvement in comparison with [8] is due to the use of the color information contained in the image: vessel removal is performed with an image modification in the L∗a∗b∗color space and color vectors and CIE94 difference equation are employed to estimate the gradient. Our future research will be focused on a better validation, with an extense dataset, on one hand, and, on the other hand, on segmenting the cup to estimate the CDR. References [1] S.Kavitha, S.Karthikeyan, K.Duraiswamy, Early Detection of Glaucoma in Retinal Images Using Cup to Disc Ratio, Proc. Int. Conf. on Computing, Communication and Networking Technologies(2010). [2] Aliaa Abdel-Haleim Abdel-Razik Youssif, Atef Zaki Ghalwash, and Amr Ahmed Sabry Abdel-Rahman Ghoneim, Optic Disc Detection From Normalized Digital Fundus Images by Means of a Vessels Direction Matched Filter, IEEE Trans. on Medical Imaging, 27, 1 (2008). [3] L. Gagnon, M. Lalonde, M. Beaulieu, and M.-C. Boucher, Procedure to detect anatomical structures in optical fundus images, Proc. Conf. Med. Imag. 2001, pp. 12181225. (2001). [4] R. A. Abdel-Ghafar, T. Morris, T. Ritchings, and I. Wood, Detection and characterisation of the optic disk in glaucoma and diabetic retinopathy, Proc. Med. Image Understand. Anal. Conf. (1998). [5] A. Osareh, M. Mirmehdi, B. Thomas, and R. Markham, Classification and localisation of diabetic-related eye disease, Proc. ECCV, Results of intersection of the areas Method % success percentage % FN % FP With ellipse fitting 92.35% 7.64% 4.7% Without ellipse fitting 92.32% 7.67% 5.67% The method was tested in 22 images manually segmented by experts from Hospital of Cadiz to evaluate its performance. Two measurements were analysed. The first one compares intersection of areas delimited by manual and automated segmentation. The second measurement gives an idea of the contours deviation. For comparing the intersection of the areas, the enclosed areas of both contour lines (manual and automated segmentation) were compared pixel by pixel. As a reference area for each image, the area delimited by the manually outlined contour was used. In Table 1 the results with and without ellipse fitting are shown. The success percentage was defined as the percentage the size of the reference area intersection with the area segmented by the method. False positive (FP) rate was defined as the area erroneously segmented as optic disc by the method. And false negative (FN) rate as the area belonging to disc optic that it has not been segmented by the method. These definitions are clearly represented in Fig. 5. Figure 5. Intersection of the areas The second measurement, called mean distance to the closest point (MDCP) [23], evaluates the average distance from the detected boundary to the ground truth. Ground truth is the contour of the reference area (manually segmented area ). Reference contour, denoted by R, consists of the individual pixels ri, i:1,2, ..., M, where M is the amount of the pixels on the reference contour. Sis the final contour detected by the proposed method. For each contour point S(n)n:1,2, ..., N, the distance to the closest point (DCP) of reference contour is defined as: DCP(S(n),R)=min!S(n)−ri!,i:1,2,..., M(9) The accuracy of the detected boundary is evaluated by the mean of DCP (MDCP) as follows: MDCP(S,R)= 1 N N ∑ n=1 DCP(S(n),R)(10) Mean distance to closest point (MDCP) Method With ellipse fitting Without ellipse fitting 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 result obtained with MDCP are summarized in Table 2. The measured MDCPs are, respectively, 2.72 and 3.07 pixels for the proposed method with ellipse fitting and without it. In the table is also shown percentage of images obtained with MDCP < 3 pixels, with 3 ≤MDCP ≤5 pixels and with MDCP >5 pixels for both outputs. Discussion and conclusions OD detection is an important preprocessing step in Computer Aided Diagnosis(CAD) systems for many retinopathies. Specifically, in glaucoma diagnosis an important parameter is cup-optic disc ratio (CDR). Therefore, a strong effort has been directed toward an accurate OD segmentation. Nevertheless, notwithstanding that retinographies are color images, most of the improvements in OD segmentation have been applied to one color plane [7, 2, 8, 6]. In [7, 2, 6], good OD location rates are reported but the precise OD edges are not estimated. [8] presents a sensitivity of 0.86. In this paper, a new method that locates the OD edges has been presented. It obtains a high sensitivity in the edge estimation, with a sensitivity of 92.35%. Probably this improvement in comparison with [8] is due to the use of the color information contained in the image: vessel removal is performed with an image modification in the L∗a∗b∗color space and color vectors and CIE94 difference equation are employed to estimate the gradient. Our future research will be focused on a better validation, with an extense dataset, on one hand, and, on the other hand, on segmenting the cup to estimate the CDR. References [1] S.Kavitha, S.Karthikeyan, K.Duraiswamy, Early Detection of Glaucoma in Retinal Images Using Cup to Disc Ratio, Proc. Int. Conf. on Computing, Communication and Networking Technologies(2010). [2] Aliaa Abdel-Haleim Abdel-Razik Youssif, Atef Zaki Ghalwash, and Amr Ahmed Sabry Abdel-Rahman Ghoneim, Optic Disc Detection From Normalized Digital Fundus Images by Means of a Vessels Direction Matched Filter, IEEE Trans. on Medical Imaging, 27, 1 (2008). [3] L. Gagnon, M. Lalonde, M. Beaulieu, and M.-C. Boucher, Procedure to detect anatomical structures in optical fundus images, Proc. Conf. Med. Imag. 2001, pp. 12181225. (2001). [4] R. A. Abdel-Ghafar, T. Morris, T. Ritchings, and I. Wood, Detection and characterisation of the optic disk in glaucoma and diabetic retinopathy, Proc. Med. Image Understand. Anal. Conf. (1998). [5] A. Osareh, M. Mirmehdi, B. Thomas, and R. Markham, Classification and localisation of diabetic-related eye disease, Proc. ECCV,