Hexagonality as a New Shape-Based Descriptor of Object

In this paper, we define a new shape-based measure which evaluates how much a given shape is hexagonal. Such an introduced measure ranges through the interval (0, 1] and reaches the maximal possible value 1 if and only if the shape considered is a hexagon. The new measure is also invariant with respect to rotation, translation and scaling transformations. A number of experiments, performed on both synthetic and real image data, are shown in order to confirm theoretical observations and illustrate the behavior of the new measure. The new hexagonality measure also provides several useful side results whose theoretical properties are discussed and experimentally evaluated. As side results, we obtain a new method that computes the shape orientation as the direction which optimizes the new hexagonality measure and a new shape elongation measure which computes the elongation of a given shape as the ratio of the lengths of the longer and shorter semi-axis of the appropriate associated hexagon. Several experiments relating to three well-known image datasets, such as MPEG-7 CE-1, Swedish Leaf, and Galaxy Zoo datasets, are also provided to illustrate effectiveness and benefits of the new introduced shape measures.