  Given a set of 2-dimensional (2-D) scattering points, which are usually
obtained from the edge detection process, the aim of ellipse fitting is to
construct an elliptic equation that best fits the collected observations.
However, some of the scattering points may contain outliers due to imperfect
edge detection. To address this issue, we devise a robust real-time ellipse
fitting approach based on two kinds of analog neural network, Lagrange
programming neural network (LPNN) and locally competitive algorithm (LCA).
First, to alleviate the influence of these outliers, the fitting task is
formulated as a nonsmooth constrained optimization problem in which the
objective function is either an l1-norm or l0-norm term. It is because compared
with the l2-norm in some traditional ellipse fitting models, the lp-norm with
p<2 is less sensitive to outliers. Then, to calculate a real-time solution of
this optimization problem, LPNN is applied. As the LPNN model cannot handle the
non-differentiable term in its objective, the concept of LCA is introduced and
combined with the LPNN framework. Simulation and experimental results show that
the proposed ellipse fitting approach is superior to several state-of-the-art
algorithms.

Image and Video Processing