A Probabilistic Measure of Circularity

The circle is a useful morphological structure: in many situations, the importance is focused on the measuring of the similarity of a perfect circle against the object of interest. Traditionally, the well-known geometrical structures are employed as useful geometrical descriptors, but an adequate characterization and recognition are deeply affected by scenarios and physical limitations (such as resolution and noise acquisition, among others). Hence, this work proposes a new circularity measure which offers several advantages: it is not affected by the overlapping, incompleteness of borders, invariance of the resolution, or accuracy of the border detection. The propounded approach deals with the problem as a stochastic non-parametric task; the maximization of the likelihood of the evidence is used to discover the true border of the data that represent the circle. In order to validate the effectiveness of our proposal, we compared it with two recently effective measures: the mean roundness and the radius ratio.