New Resolution Independent Measures of Circularity
In this paper we demonstrate that the most commonly used mathematical measure of circularity-the Form Factor-is highly resolution dependent. Furthermore we show that despite the abundance of papers proposing measures of roundness, most of the new measures are mathematically equivalent to the Form Factor. Only four measures were found that were different. We then present two new measures, the first based on the theory of Mean Deviations and the second based on the mathematical definition of a circle. When compared in terms of resolution dependence, order of complexity, ease of calculation, and how well they match human perception, the two new measures are shown to be better overall than the previous measures. The two new measures are resolution independent in the sense that changing the resolution makes no change to the order of circularity of different shapes. That is, changing the resolution does not change whether one object would be considered more round than another on the basis of the measure. None of the other measures has this property.
resolution circularity roundness human perception shape