Quantum Inf Process (2016) 15:2303–2323
A quantum mechanics-based algorithm for vessel
segmentation in retinal images
· Ahmed El-Rafei
Received: 17 November 2015 / Accepted: 26 February 2016 / Published online: 15 March 2016
© Springer Science+Business Media New York 2016
Abstract Blood vessel segmentation is an important step in retinal image analysis.
It is one of the steps required for computer-aided detection of ophthalmic diseases.
In this paper, a novel quantum mechanics-based algorithm for retinal vessel segmen-
tation is presented. The algorithm consists of three major steps. The ﬁrst step is the
preprocessing of the images to prepare the images for further processing. The second
step is feature extraction where a set of four features is generated at each image pixel.
These features are then combined using a nonlinear transformation for dimensionality
reduction. The ﬁnal step is applying a recently proposed quantum mechanics-based
framework for image processing. In this step, pixels are mapped to quantum systems
that are allowed to evolve from an initial state to a ﬁnal state governed by Schrödinger’s
equation. The evolution is controlled by the Hamiltonian operator which is a function
of the extracted features at each pixel. A measurement step is consequently performed
to determine whether the pixel belongs to vessel or non-vessel classes. Many functional
forms of the Hamiltonian are proposed, and the best performing form was selected.
The algorithm is tested on the publicly available DRIVE database. The average results
for sensitivity, speciﬁcity, and accuracy are 80.29, 97.34, and 95.83 %, respectively.
These results are compared to some recently published techniques showing the supe-
Electronics and Communication Engineering Department, Faculty of Engineering, Ain Shams
University, Cairo, Egypt
Engineering Physics and Mathematics Department, Faculty of Engineering, Ain Shams University,