Measuring shape rectangularities

This paper introduces a family of rectangularity measures. Several rectangularity measures already exist in literature, and all of them evaluate how much the shape considered differs from a perfect rectangle. But all existing measures assume that all rectangles have the same shape, and a consequence is that these measures do not distinguish among the rectangles whose edge-ration differs. In this paper we consider that differently elongated rectangles have different shape and propose a family of new rectangularity measures which distinguish among such rectangles. New rectangularity measures are invariant with respect to translation, rotation and scaling transformations. In addition, we introduce a tuning parameter which enables an additional flexibility of the new measures with respect to performing applications.