# Robust Ellipsoid-specific Fitting via Expectation Maximization

arXiv: https://arxiv.org/abs/2110.13337 · HTML: https://mlsanity.com/paper/2110.13337/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 42 references that are in the map.
- First posted on arXiv 26 Oct 2021.

## Builds on (most cited first, 2 of 2)

- [Generic Primitive Detection in Point Clouds Using Novel Minimal Quadric Fits](https://mlsanity.com/paper/1901.01255/) (2019)
- [Real-time 3D scene description using Spheres, Cones and Cylinders](https://mlsanity.com/paper/1603.03856/) (2016)

## Built on by (most cited first, 1 of 1)

- [A Bayesian Approach Toward Robust Multidimensional Ellipsoid-Specific Fitting](https://mlsanity.com/paper/2407.19269/) (2024)

## Abstract (arXiv)

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/.