Measuring linearity of open planar curve segments

Abstract

In this paper we define a new linearity measure for open planar curve segments. We start with the integral of the squared distances between all the pairs of points belonging to the measured curve segment, and show that, for curves of a fixed length, such an integral reaches its maximum for straight line segments. We exploit this nice property to define a new linearity measure for open curve segments. The new measure ranges over the interval (0, 1], and produces the value 1 if and only if the measured open line is a straight line segment. The new linearity measure is invariant with respect to translations, rotations and scaling transformations. Furthermore, it can be efficiently and simply computed using line moments. Several experimental results are provided in order to illustrate the behaviour of the new measure.

Measuring linearity of curves in 2D and 3D

“…Since the identity of the signature is already known, the nearest neighbour matching is only applied to the set of genuine and forged examples of the subject's signature. Our previous results using the linearity measure defined in [36] achieved 93.1% accuracy, which is now improved. Computing linearity of the 2D signatures using L(C) produces 97.2% accuracy.…”

“…To compare objects considered we use linearity plots (the approach is taken from [36] and more details can be found therein) to provide more information than a single linearity measurement. The idea is to compute linearity incrementally, i.e.…”

“…Several linearity measures for curve segments are already considered in the literature [12,13,29,32,36]. All of these measures have their strengths and their weakness.…”

“…For example: the new linearity measure assigns the same value to all curves whose sum of the distances of the end points to the curve centroid is the same, the measure from [36] assigns the same value for all the curves having the same value of the boundary-based first Hu moment invariant analogue, etc. This cannot be avoided.…”

Measuring Linearity of Curves

“…Several linearity measures for curve segments are already considered in the literature (Gautama et al, 2004;Gautama et al, 2003;Stojmenović et al, 2008;Zunić and Rosin, 2011).…”