Measuring linearity of curves in 2D and 3D

Abstract

In this paper we define a new linearity measure for open curve segments in 2D and 3D. The measure considers the distance of the curve end points to the curve centroid. It is simple to compute and has the basic properties that should be satisfied by any linearity measure. The new measure ranges over the interval (0, 1], and produces the value 1 if and only if the measured curve is a perfect straight line segment. Also, the new linearity measure is invariant with respect to translations, rotations and scaling transformations. The new measure is theoretically well founded and, because of this, its behaviour can be well understood and predicted to some extent. This is always beneficial because it indicates the suitability of the new measure to the desired application.Several experiments are provided to illustrate the behaviour and to demonstrate the efficiency and applicability of the new linearity measure.

A Projection-Based Method for Shape Measurement

“…Different methods have been introduced using Fourier transform [41], phase congruency calculated from Gabor wavelets [42] or image moments [43]. Linearity, which measures the similarity between an open curve and a straight segment, has also been studied in different works [44,45].…”

Co-occurrence Features for Writer Identification

“…Unlike the traditional methods which measure the curvature on a point of the curves using the first and secondregularized derivatives [26] or the integral invariants [24], the C(F c ) measures the curvature of a contour fragment instead of the curvature on a point. The C(F c ) is also known as the straightness index [5], which is the simplest one of the linearity measures of an open curve segment [33]. This method has also been used for shape classification in [20].…”

Measuring how much an object has a ring-like shape

“…There exist already a number of computing procedures (so called shape measures) for the evaluation of different shape properties. Examples of these measures include are circularity (often called compactness) [1,2], ellipticity [3,4], linearity [5], tortuosity [6], etc. Some of the measures were established a long time ago (e.g.…”