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

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.