Measuring linearity of planar curves

Abstract

In this paper we define a new linearity measure which can be applied to open planar curve segments. We have considered the sum of the distances between the curve end points and the curve centroid. We have shown that this sum is bounded from above by the length of the curve segment considered. In addition, we have proven that this sum equals the length of the curve segment only in the case of straight line segments. Exploiting such a nice characterization of straight line segments, we define a new linearity measure for planar curves. The new measure ranges over the interval (0, 1], and produces the value 1 if and only if the measured line is a perfect straight line segment. Also, the new linearity measure is invariant with respect to translations, rotations and scaling transformations.