Framework for characterizing circularity based on a probability distribution

• A new circularity measure based on probabilistic approach.
• It is based on the distribution of distance of center to the border.
• The framework is invariant to the norm and resolution.
• The framework supports partial and non-connected borders.
• Framework works for n-dimensional circles.

Traditionally, the well-known geometrical structures are used as useful geometrical descriptors, but, an adequate characterization and recognition are deeply affected by scenarios (which include occlusions, low contrast of background and foreground, unsharpened borders, etc.) and physical limitations (such as resolution and noise acquisition, among others). Hence, this work proposes a framework for measuring the circularity which offers several advantages: it is not affected by the overlapping, incompleteness of borders (in this work only for two dimensional case is dealt with), invariance of the resolution, and 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; and in a real application, the circularity of nodules of graphite in compound materials are measured.