A Projection-Based Method for Shape Measurement

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.