Robust Ellipse Fitting with Laplacian Kernel Based Maximum Correntropy Criterion

The performance of ellipse fitting may significantly degrade in the presence of outliers, which can be caused by occlusion of the object, mirror reflection or other objects in the process of edge detection. In this paper, we propose an ellipse fitting method that is robust against the outliers, and thus maintaining stable performance when outliers can be present. We formulate an optimization problem for ellipse fitting based on the maximum entropy criterion (MCC), having the Laplacian as the kernel function from the well-known fact that the $\ell _{1}$ -norm error measure is robust to outliers. The optimization problem is highly nonlinear and non-convex, and thus is very difficult to solve. To handle this difficulty, we divide it into two subproblems and solve the two subproblems in an alternate manner through iterations. The first subproblem has a closed-form solution and the second one is cast as a convex second-order cone program (SOCP) that can reach the global solution. By so doing, the alternate iterations always converge to an optimal solution, although it can be local instead of global. Furthermore, we propose a procedure to identify failed fitting of the algorithm caused by local convergence to a wrong solution, and thus, it reduces the probability of fitting failure by restarting the algorithm at a different initialization. The proposed robust ellipse fitting method is next extended to the coupled ellipses fitting problem. Both simulated and real data verify the superior performance of the proposed ellipse fitting method over the existing methods.