Robust ellipse fitting based on Lagrange programming neural network and locally competitive algorithm

Given a set of 2-dimensional (2D) scattering points, obtained from the edge detection process, the aim of ellipse fitting is to construct an elliptic equation that best fits the scattering points. However, the 2D scattering points may contain some outliers. To address this issue, we devise a robust ellipse fitting approach based on two analog neural network models, Lagrange programming neural network (LPNN) and locally competitive algorithm (LCA). We formulate the fitting task as a nonsmooth constrained optimization problem, in which the objective function is an approximated l₀-norm term. As the LPNN model cannot handle non-differentiable functions, we utilize the internal state concept of LCA to avoid the computation of the derivative at non-differentiable points. Simulation results show that the proposed ellipse fitting approach is superior to several state-of-the-art algorithms.