Linearity measure for curve segments

In this paper, we consider linearity measure for a bounded length curves. First, we define a new linearity measure for open curve segments, and then extend method to closed curves (contours). The derived measures (for both, open curve segments and closed curves) are invariant with respect to similarity transformations. The linearity measure for open curve segments picks the value 1 if and only if the measured open line segment is a perfect straight line segment while the established linearity measures for closed curves never reach 1, as preferred.