Slope Chain Code-based scale-independent tortuosity measurement on retinal vessels

Retinal vascular tortuosity presents valuable potential as a clinical biomarker for many relevant vascular and systemic diseases. Our work exhibits twofold: first, the definition of a novel scale-invariant metric to measure retinal blood vessel tortuosity; and second, the generation of a local database, called SCALE-TORT, with the intention of providing a means to test the scale invariance property on real retinal vessels rather than on synthetic data. The proposed scale invariant tortuosity metric is based on the Extended Slope Chain Code which uses variable straight-line segments for describing curves. It is focused on the representation of high-definition curves, the length of the segments is a function of the slope changes of the curve. Scale invariance is an important property when several different retinal image settings or different acquisition sources are used during a particular study or in clinical practice. The database SCALE-TORT, introduced herein, was built semi-automatically from digital images containing the coordinates of blood vessel central lines (curves) taken from images of the same eye obtained by two different imaging methodologies: retinal fundus camera and scanning laser ophthalmoscope. The vessel curves extracted from the same eye are paired for images acquired by the fundus camera and those acquired by the scanning laser ophthalmoscope to evaluate the scale invariance of the metric. Ten different tortuosity metrics were implemented and compared including our proposed metric. Three experiments were conducted to test the metrics and their properties. The first aimed to determine which tortuosity metrics possess the following properties: scale invariance, sensitivity to sudden tortuosity changes when the curve remains constant in size, and how they behave when curves are concatenated. In the second experiment, all reviewed metrics were tested on the publicly available RET-TORT database, to compare the results of the specific metric with the tortuosity classification provided by their experts and in comparison with other authors. Finally, in the third experiment, the behavior of different metrics, including those which are scale-invariant, were tested by utilizing the paired retinal vessel curves from our new SCALE-TORT database. In comparison with other tortuosity metrics, we show that the metric Extended Slope Chain Code proposed in this work optimally complies with scale invariance, in addition to having sufficient sensitivity to detect abrupt changes in tortuosity. Easy implementation being a further plus. Furthermore, we present a new and valuable database for scale property evaluation on images of retinal blood vessels called SCALE-TORT. As far as we are aware, there is no public database with these characteristics.