Digital Curvature Estimation

This paper sets out to study the effect of digitization on curvature. It is put forward that digital curvature is an estimate with accuracy and precision. A theoretical analysis of the curvature estimation problem identifies the possible sources of errors in digital curvature estimation. In the literature, five essentially different classes of methods are found. From theoretical analysis of the methods, as well as by random experiments on generated arcs, we establish that almost all existing methods suffer from a severe directional inaccuracy and/or poor precision. Errors depend on the method, orientation, and scale, ranging from 1% to over 1000%. We present a practical solution with a residual error between 1% and 60%, also giving recommendations for the required resolution of the image.