A measure of tortuosity based on chain coding

A measure of tortuosity for 2D curves is presented. Tortuosity is a very important property of curves and has many applications, such as: how to measure the tortuosity of retinal blood vessels, intracerebral vasculature, aluminum foams, etc. The measure of tortuosity proposed here is based on a chain code called Slope Chain Code (SCC). The SCC uses some ideas which were described in [A geometric structure for 2D shapes and 3D surfaces, Pattern Recognition 25 (1992) 483-496]. The SCC of a curve is obtained by placing straight-line segments of constant length around the curve (the endpoints of the straight-line segments always touching the curve), and calculating the slope changes between contiguous straight-line segments scaled to a continuous range from −1 to 1. The SCC of a curve is independent of translation, rotation, and optionally, of scaling, which is an important advantage for computing tortuosity. Also, the minimum and maximum values of tortuosity for curves and a measure of normalized tortuosity are described. Finally, an application of the proposed measure of tortuosity is presented which corresponds to the computation of retinal blood vessel tortuosity.

► A novel measure of tortuosity is presented.
► The proposed measure of tortuosity is based on the slope chain code.
► A conjecture about plane-filling curves is described.