A novel approach for quantification of retinal vessel tortuosity using quadratic polynomial decomposition

Abstract

Abstract-This paper describes a novel tortuosity measure, based on the premise that tortuosity is a measure of deviation from an ideal non-tortuous vessel. Hence, we propose to model the overall shape of an ideal vessel as a quadratic polynomial at a larger scale while the deviations are modeled as quadratic polynomials at smaller scales. Thus, a given vessel center-line is decomposed as a sum of quadratic polynomials of decreasing scale. This Quadratic Polynomial Decomposition is used as a framework for defining a quantitative measure of tortuosity. As opposed to the existing proposed measures, our method can distinguish between the relative size, shapes and orientations of the vessel bends. The measure is position and scale invariant and satisfies two key desired properties: it varies directly with frequency of twists at fixed amplitude and it varies directly with amplitude of twists when their frequency is fixed. The proposed method has been tested on a standard data set containing 30 artery and 30 vein vessel segments, and shown to be among the best measures as compared to the results of existing methods.

Recent Techniques and Trends for Retinal Blood Vessel Extraction and Tortuosity Evaluation: A Comprehensive Review

“…The authors used different sizes of datasets with several to dozens, but also hundreds of images. This depended on the choice of sample and on the size of the source database used, although some authors did not mention the size of the dataset in the article [72,136,139]. The images in databases differ in terms of the number of images, image quality, resolution, contrast, brightness, and artefacts (see Table III, Table IV).…”

Modified Curvature-based Trigonometric Identities for Retinal Blood Vessel Tortuosity Measurement in Diabetic Retinopathy Fundus Images

“…However, it does not consider the shape of the vessel curves, and the vessel segments with no variation in direction will not contribute to tortuosity measure. Other domain-based methods for evaluating blood vessel tortuosity have been introduced by other studies [48][49][50]. However, these proposed methods are difficult to apply and highly sensitive to noise during vessel extraction to obtain vessel midline [48].…”

“…However, these proposed methods are difficult to apply and highly sensitive to noise during vessel extraction to obtain vessel midline [48]. Furthermore, lower accuracy was achieved when compare to arc-to-chord ratio in terms of Spearman correlation [50]. Hence, we proposed a quantitative measurement that makes use of modified curvature-based trigonometric identities.…”

Automatic Retinal Vessel Detection and Tortuosity Measurement

“…Retinal vessel network tortuosity is the measure of twists and curvature of a vessel Onkaew et al;Chakravarty and Sivaswamy;. Several clinical studies have described the relation between vessel tortuosity and retinopathies such as DR, ROP (Scheie;1953;Capowski et al;.…”

“…1. One of the first changes in vessels morphology to occur in DR patients is the increase in vessel tortuosity (Scheie;1953;Kristinsson et al;Owen et al;Taarnhøj et al;Onkaew et al;Chakravarty and Sivaswamy;. Tortuosity has been shown to be a more reliable vascular parameter in differentiating ROP severity than vessel width (Capowski et al;.…”