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.

中文翻译：

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六边形作为对象的基于形状的新描述符

在本文中，我们定义了一种新的基于形状的度量，该度量可评估给定形状为六边形的程度。这种引入的量度范围为（0，1]，并且当且仅当所考虑的形状为六边形时才达到最大可能值1，新量度在旋转，平移和缩放变换方面也不变。为了证实理论上的观察结果并说明了该新措施的行为，对合成和真实图像数据进行了实验，新的六边形措施还提供了一些有用的副结果，并对其理论性质进行了讨论和实验评估。 ，我们获得了一种新的方法，该方法将形状方向计算为优化新六角形量度的方向，并获得了新形状伸长量度，该形状伸长量度计算了给定形状的伸长率，该伸长率是相应的长半轴和短半轴的长度之比相关的六角形。还提供了与三个众所周知的图像数据集（例如MPEG-7 CE-1，Swedish Leaf和Galaxy Zoo数据集）有关的实验，以说明新引入的形状度量的有效性和好处。