Tuning of conic parameters using Tikhonov regularization and L-Curve simulation

In this article, a method to infer the parameters of a conic given a set of rectangular coordinates that belong to the geometric entity is shown. The methodology consists of solving a Tikhonov regulation problem where the unregulated term introduces the non-linear nature of the conical body and the regulated the restriction associated to the discriminant of the quadratic equation, then the solution is computed minimizing the resulting cost function where the Regularization parameter is tuned using the L-Curve technique. The model was validated with synthetic and real data from digital images, as well as subject to comparison against other state of the art alternatives. The results show that the method is robust against atypical values and the phenomenon of occlusion present in the data.