Robust Ellipse Fitting Based on Maximum Correntropy Criterion With Variable Center

TL;DR

This paper introduces a robust ellipse fitting method based on the maximum correntropy criterion with variable center, effectively handling outliers and extending to coupled ellipses with improved accuracy demonstrated through simulations and real images.

Contribution

It develops a novel robust ellipse fitting approach using MCC-VC, with efficient convex approximations and a new method for coupled ellipses fitting via data association estimation.

Findings

Significantly better performance than existing methods in simulations.

Effective handling of outliers in real image data.

Extension to coupled ellipses with improved accuracy.

Abstract

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.