A measure of tortuosity based on chain coding

A measure of tortuosity for 20 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. (C) 2012 Elsevier Ltd. All rights reserved.