  The presence of outliers can significantly degrade the performance of ellipse
fitting methods. We develop an ellipse fitting method that is robust to
outliers based on the maximum correntropy criterion with variable center
(MCC-VC), where a Laplacian kernel is used. For single ellipse fitting, we
formulate a non-convex optimization problem to estimate the kernel bandwidth
and center and divide it into two subproblems, each estimating one parameter.
We design sufficiently accurate convex approximation to each subproblem such
that computationally efficient closed-form solutions are obtained. The two
subproblems are solved in an alternate manner until convergence is reached. We
also investigate coupled ellipses fitting. While there exist multiple ellipses
fitting methods that can be used for coupled ellipses fitting, we develop a
couple ellipses fitting method by exploiting the special structure. Having
unknown association between data points and ellipses, we introduce an
association vector for each data point and formulate a non-convex mixed-integer
optimization problem to estimate the data associations, which is approximately
solved by relaxing it into a second-order cone program. Using the estimated
data associations, we extend the proposed method to achieve the final coupled
ellipses fitting. The proposed method is shown to have significantly better
performance over the existing methods in both simulated data and real images.
