Shape rectangularity measures

Abstract

This paper introduces a family of rectangularity measures. The measures depend on two parameters which enable their flexibility, i.e. the possibility to adapt with respect to a concrete application. Several rectangularity measures exist in the literature, and they are designed to evaluate numerically how much the shape considered differs from a perfect rectangle. None of these measures distinguishes rectangles whose edge ratios differ, i.e. they assume that all rectangles (including squares) have the same shape. Such property can be a disadvantage in applications. In this paper, we consider differently elongated rectangles to have different shapes, and propose a family of new rectangularity measures which assigns different values to rectangles whose edge ratios differ. The new rectangularity measures are invariant with respect to translation, rotation and scaling transformations. They range over the interval[0, 1] and attain the value 1 only for perfect rectangles with a desired edge ratio.