Robust Ellipsoid-specific Fitting via Expectation Maximization

TL;DR

This paper introduces a robust, outlier-resistant ellipsoid fitting method using kernel density estimation and EM, outperforming existing approaches in noisy, outlier-rich environments.

Contribution

A novel ellipsoid fitting approach that models data with KDE and employs EM for maximum likelihood estimation, enhancing robustness and eliminating the need for extra constraints.

Findings

Outperforms state-of-the-art methods in robustness against noise and outliers.

Parameter-free approach simplifies implementation and tuning.

Accelerated EM improves convergence speed.

Abstract

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 {\epsilon} 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/.