This work addresses two main contributions for shape measurement: First, a new circularity measure for planar shapes is introduced based on their geometrical properties in the projection space of Radon transform. Second, a general-purpose evaluation criterion, power of discrimination, for assessing the efficiency of a shape measure is proposed. The new measure ranges over the interval [0, 1] and produces the value 1 if and only if the measured shape is a perfect circle. The proposed measure is invariant with respect to translation, rotation and scaling transformations. Moreover, it is also robust against border distortion of shapes. It is theoretically well founded and can be extended to other problems of shape measurement. Our approach can deal with complex shapes composed of connected components that cannot be handled by classical contour-based methods. Several experiments show its good behavior and demonstrate the efficiency and applicability of our proposed measure. Finally, we also consider our proposed evaluation criterion for assessing different circularity measures.

中文翻译：

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基于投影的形状测量方法

这项工作解决了形状测量的两个主要问题：首先，根据Radon变换在投影空间中的几何特性，针对平面形状引入了一种新的圆度测量方法。其次，提出了一种通用的评估标准，即判别力，用于评估形状度量的效率。当且仅当被测形状为正圆时，新度量的范围为[0，1]，并产生值1。拟议的措施相对于平移，旋转和缩放变换是不变的。而且，它对于抵抗形状的边界变形也是鲁棒的。从理论上讲，它是有根据的，可以扩展到形状测量的其他问题。我们的方法可以处理由连接的组件组成的复杂形状，而这些形状无法通过经典的基于轮廓的方法来处理。几个实验表明它的良好行为，并证明了我们提出的措施的效率和适用性。最后，我们还考虑了我们建议的评估标准，用于评估不同的圆形度度量。