Robust ellipse fitting via alternating direction method of multipliers

The edge point errors, especially outliers, introduced in the edge detection step, will cause severe performance degradation in ellipse fitting. To address this problem, we adopt the ℓ_p-norm with p < 2 in the direct least square fitting method to achieve outlier resistance, and develop a robust ellipse fitting approach using the alternating direction method of multipliers (ADMM). Especially, to solve the formulated nonconvex and nonlinear problem, we decouple the ellipse parameter vector in the nonlinear ℓ_p-norm objective function from the nonconvex quadratic constraint via introducing auxiliary variables, and estimate the ellipse parameter vector and auxiliary variables alternately via the derived numerical methods. Simulation and experimental examples are presented to demonstrate the robustness of the proposed approach.