Robust Ellipsoid-specific Fitting via Expectation Maximization
This work addresses a domain-specific problem in machine vision for applications like object detection and shape approximation, offering incremental improvements in robustness and accuracy.
The paper tackles the problem of robust ellipsoid fitting in 3D environments with noise and outliers by proposing a method based on kernel density estimation and maximum likelihood estimation solved via Expectation-Maximization, achieving results that are more robust against noise, outliers, and large axis ratios compared to state-of-the-art approaches.
Ellipsoid fitting is of general interest in machine vision, such as object detection and shape approximation. Most existing approaches rely on the least-squares fitting of quadrics, minimizing the algebraic or geometric distances, with additional constraints to enforce the quadric as an ellipsoid. However, they are susceptible to outliers and non-ellipsoid or biased results when the axis ratio exceeds certain thresholds. To address these problems, we propose a novel and robust method for ellipsoid fitting in a noisy, outlier-contaminated 3D environment. We explicitly model the ellipsoid by kernel density estimation (KDE) of the input data. The ellipsoid fitting is cast as a maximum likelihood estimation (MLE) problem without extra constraints, where a weighting term is added to depress outliers, and then effectively solved via the Expectation-Maximization (EM) framework. Furthermore, we introduce the vector ε technique to accelerate the convergence of the original EM. The proposed method is compared with representative state-of-the-art approaches by extensive experiments, and results show that our method is ellipsoid-specific, parameter free, and more robust against noise, outliers, and the large axis ratio. Our implementation is available at https://zikai1.github.io/.