Identification of circles from datapoints using the Legendre transform

In this paper we present a method of reconstructing the circle parameters from a set of datapoints on a plane. The method is based on the geometrical Legendre transform. We test the method under various scenarios using Monte Carlo generated data. These scenarios include variation of the noise hits percentage, uncertainties in the hit position and the number of datapoints. The technique is proven to be robust and provide quickly and efficiently very accurate results. Furthermore, the use of the geometrical Legendre transform method for the identification of two overlapping circles is shown.