Purpose: The study of retinal blood vessel morphology is of great importance in retinal image analysis. The retinal blood vessels have a number of distinct features such as width, diameter, tortuosity, etc. In this paper, a method is proposed to measure the tortuosity of retinal blood vessels obtained from retinal fundus images. Tortuosity is a situation in which blood vessels become tortuous, that is, curved or non-smooth. It is one of the earliest changes that occur in blood vessels in some retinal diseases. Hence, its detection at an early stage can prevent the progression of retinal diseases such as diabetic retinopathy, hypertensive retinopathy, retinopathy of prematurity, etc. The present study focuses on the measurement of retinal blood vessel tortuosity for the analysis of hypertensive retinopathy. Hypertensive retinopathy is a condition in which the retinal vessels undergo changes and become tortuous due to long term high blood pressure. Early recognition of hypertensive retinopathy signs remains an important step in determining the target-organ damage and risk assessment of hypertensive patients. Hence, this paper attempts to estimate tortuosity using image-processing techniques that have been tested on artery and vein segments of retinal images.
 Design: Image processing-based model designed to measure blood vessel tortuosity.
 Methods: In this paper, a novel image processing-based model is proposed for tortuosity measurement. This parameter will be helpful for analyzing hypertensive retinopathy. To test the eff ectiveness of the system in determining tortuosity, the method is first applied on a set of synthetically generated blood vessels. Then, the method is repeated on blood vessel (both artery and vein) segments extracted from retinal images collected from publicly available databases and on images collected from a local eye hospital. The blood vessel segment images that are used in the method are binary images where blood vessels are represented by white pixels (foreground), while black pixels represent the background. Vessels are then classified into normal, moderately tortuous, and severely tortuous by following the analysis performed on the images in the Retinal Vessel Tortuosity Data Set (RET-TORT) obtained from BioIm Lab, Laboratory of Biomedical Imaging (Padova, Italy). This database consists of 30 artery segments and 30 vein segments, which were manually ordered on the basis of increasing tortuosity by Dr. S. Piermarocchi, a retinal specialist belonging to the Department of Ophthalmology of the University of Padova (Italy). The artery and vein segments with the fewest number of turns are given a low tortuosity ranking, while those with the greatest number of turns are given a high tortuosity ranking by the expert. Based on this concept, our proposed method defines retinal image segments as normal when they present the fewest number of twists/turns, moderately tortuous when they present more twists/turns than normal but fewer than severely tortuous vessels, and severely tortuous when they present a greater number of twists/turns than moderately tortuous vessels. On implementing our image processing-based method on binary blood vessel segment images that are represented by white pixels, it is found that the vessel pixel (white pixels) count increases with increasing vessel tortuosity. That is, for normal blood vessels, the white pixel count is less compared to moderately tortuous and severely tortuous vessels. It should be noted that the images obtained from the different databases and from the local hospital for this experiment are not hypertensive retinopathy images. Instead, they are mostly normal eye images and very few of them show tortuous blood vessels.
 Results: The results of the synthetically generated vessel segment images from the baseline for the evaluation of retinal blood vessel tortuosity. The proposed method is then applied on the retinal vessel segments that are obtained from the DRIVE and HRF databases, respectively. Finally, to evaluate the capability of the proposed method in determining the tortuosity level of the blood vessels, the method is tested with a standard tortuous database, namely, the RET-TORT database. The results are then compared with the tortuosity level mentioned in the database. It was found that our method is able to classify blood vessel images as normal, moderately tortuous, and severely tortuous, with results closely matching the clinical ordering provided by the expert in the RET-TORT database. Subjective evaluation was also performed by research scholars and postgraduate students to cross-validate the results.
 Conclusion: The close correlation between the tortuosity evaluation using the proposed method and the clinical ordering of retinal vessels as provided by the retinal specialist in the RET-TORT database shows that, although simple, this method can evaluate the tortuosity of vessel segments effectively.
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