Ant Colony-based System for Retinal Blood Vessels Segmentation

Abstract

The segmentation of retinal blood vessels in the eye funds images is crucial stage in diagnosing infection of diabetic retinopathy. Traditionally, the vascular network is mapped by hand in a time-consuming process that requires both training and skill. Automating the process allows consistency, and most importantly, frees up the time that a skilled technician or doctor would normally use for manual screening. Several studies were carried out on the segmentation of blood vessels in general, however only a small number of them were associated to retinal blood vessels. In this paper, an approach for segmenting retinal blood vessels is presented using only ant colony system. It uses eight features; four are based on gray-level and four are based on Hu moment-invariants. The features are directly computed from values of image pixels, so they take about 90 s in computation. The performance evaluation of this system is estimated by using classification accuracy. The presented approach accuracy is 90.28 % and its sensitivity is 74 %.

Appendix A: Equations of the eight Hu moment-invariants used in the study

$\varphi_{1} \; = \;\;\bar{\mu }_{20} \; + \;\bar{\mu }_{02}$	A.1
$\varphi_{2} = \;\left( {\bar{\mu }_{20} \; - \;\bar{\mu }_{02} } \right)^{2} \; + \;4\bar{\mu }_{11}^{2}$	A.2
$\varphi_{3} \; = \;\left( {\bar{\mu }_{30} \; - \;3\bar{\mu }_{12} } \right)^{2} \; + \;\left( {3\bar{\mu }_{21} \; - \;\bar{\mu }_{03} } \right)^{2}$	A.3
$\varphi_{4} \; = \;\;\left( {\bar{\mu }_{30} \; + \;\bar{\mu }_{12} } \right)^{2} \; + \;\left( {\bar{\mu }_{21} \; + \;\bar{\mu }_{03} } \right)^{2}$	A.4
$\begin{gathered} \varphi_{5} = \,\;\left( {\bar{\mu }_{30} + 3\bar{\mu }_{12} } \right)\left( {\bar{\mu }_{30} + \bar{\mu }_{12} } \right)\left[ {\left( {\bar{\mu }_{30} + \bar{\mu }_{12} } \right)^{2} - 3\left( {\bar{\mu }_{21} + \bar{\mu }_{03} } \right)^{2} } \right] + \hfill \\ \;\;\;\,\,\,\,\,\;\left( {3\bar{\mu }_{21} \; - \;\bar{\mu }_{03} } \right)\left( {\bar{\mu }_{21} + \bar{\mu }_{03} } \right)\left[ {3\left( {\bar{\mu }_{30} + \bar{\mu }_{12} } \right)^{2} - \left( {\bar{\mu }_{21} + \bar{\mu }_{03} } \right)^{2} } \right] \hfill \\ \end{gathered}$	A.5
$\begin{gathered} \varphi_{6} = \;\;\left( {\bar{\mu }_{20} \; - \;\bar{\mu }_{02} } \right)\;\left[ {\;\left( {\bar{\mu }_{30} \; + \;\bar{\mu }_{12} } \right)^{2} \; - \;\left( {\bar{\mu }_{21} \; + \;\bar{\mu }_{03} } \right)^{2} } \right] \hfill \\ \, + 4\bar{\mu }_{11} \;\left( {\bar{\mu }_{30} \; + \;\bar{\mu }_{12} } \right)\;\left( {\bar{\mu }_{21} \; + \;\bar{\mu }_{03} } \right) \hfill \\ \end{gathered}$	A.6
$\begin{gathered} \varphi_{7} = \left( {3\bar{\mu }_{21} \; - \;\bar{\mu }_{03} } \right)\left( {\bar{\mu }_{30} + \bar{\mu }_{12} } \right)\left[ {\left( {\bar{\mu }_{30} + \bar{\mu }_{12} } \right)^{2} - 3\left( {\bar{\mu }_{21} + \bar{\mu }_{03} } \right)^{2} } \right] - \hfill \\ \quad \;\,\,\,\left( {\bar{\mu }_{30} \; - \;3\bar{\mu }_{12} } \right)\left( {\bar{\mu }_{21} + \bar{\mu }_{03} } \right)\left[ {3\left( {\bar{\mu }_{30} + \bar{\mu }_{12} } \right)^{2} - \left( {\bar{\mu }_{21} + \bar{\mu }_{03} } \right)^{2} } \right] \hfill \\ \end{gathered}$	A.7
$\begin{gathered} \varphi_{8} \; = \;\bar{\mu }_{11} \;\left[ {\;\left( {\bar{\mu }_{30} \; + \;\bar{\mu }_{12} } \right)^{2} \; - \;\left( {\bar{\mu }_{03} \; + \;\bar{\mu }_{21} } \right)^{2} \;} \right] \hfill \\ \, - \left( {\bar{\mu }_{20} \; - \;\bar{\mu }_{02} } \right)\;\left( {\bar{\mu }_{30} \; + \;\bar{\mu }_{12} } \right)\;\left( {\bar{\mu }_{03} \; + \;\bar{\mu }_{21} } \right)\; \hfill \\ \end{gathered}$	A.8