SHAPE RECTANGULARITY MEASURES

This paper introduces a family of rectangularity measures. The measures depend on two parameters which enable their flexibility, allowing adaptation to a specific application. Several rectangularity measures exist in the literature, designed to evaluate numerically how much a given shape differs from a perfect rectangle, but none of them distinguishes rectangles whose edge ratios differ; they assume that all rectangles (including squares) have the same shape. This property can be a disadvantage in applications. In this paper we consider differently elongated rectangles to have different shapes, and we propose a family of new rectangularity measures which assign 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.