# Direct least squares fitting of ellipses

@article{Fitzgibbon1996DirectLS, title={Direct least squares fitting of ellipses}, author={Andrew W. Fitzgibbon and Maurizio Pilu and Robert B. Fisher}, journal={Proceedings of 13th International Conference on Pattern Recognition}, year={1996}, volume={1}, pages={253-257 vol.1} }

This paper presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4ac-b/sup 2/=1 the new method incorporates the ellipticity constraint into the normalization factor. The new method combines several advantages: 1) it is ellipse-specific so that even bad data will always return an ellipse; 2) it can be solved naturally by a…

## 774 Citations

NUMERICALLY STABLE DIRECT LEAST SQUARES FITTING OF ELLIPSES

- Computer Science
- 1998

This paper presents a numerically stable non-iterative algorithm for fit ting an ellipse to a set of data points. The approach is based on a least squares minimization and it guarantees an…

Robust Legendre Moments Ellipse Fitting from Noisy Image

- Computer Science
- 2008

A new statistical approach based on the expansion of the probability density function in terms of Legendre polynomials which guarantees the extraction of an ellipse even for high rate of outliers and an important level of noise.

Numerically Stable Direct Least Squares Fitting of Ellipses

- Computer Science
- 1998

This paper presents a numerically stable non-iterative algorithm for fitting an ellipse to a set of data points based on a least squares minimization which leads to a simple, stable and robust fitting method which can be easily implemented.

Constrained Least Squares Fitting of Ellipse

- Computer Science2010 International Conference on Computational Intelligence and Software Engineering
- 2010

A new efficient algorithm for fitting an ellipse to scattered points by minimizing the algebraic distance subject to the constraint of length of semi-minor axis and incorporating the ellipticity constraint into the normalization factor is presented.

Ellipse-specific direct least-square fitting

- Computer ScienceProceedings of 3rd IEEE International Conference on Image Processing
- 1996

This article presents the first direct method for specifically fitting ellipses in the least squares sense, which is directly solved by a generalised eigen-system, has a desirable low-eccentricity bias, and is robust to noise.

Direct least square fitting of ellipsoids

- Computer ScienceProceedings of the 21st International Conference on Pattern Recognition (ICPR2012)
- 2012

Experimental results demonstrate the validity of the proposed approach and the extension from 2D to 3D for ellipsoid-specific fitting is not easy as mentioned in the main text.

Non-linear least squares ellipse fitting using the genetic algorithm with applications to strain analysis

- Geology
- 2008

Constrained Ellipse Fitting with Center on a Line

- EngineeringJournal of Mathematical Imaging and Vision
- 2015

This work makes use of a constrained algebraic cost function with the incorporated “ellipse center on given line”-prior condition in a global convergent one-dimensional optimization approach and shows computational efficiency and numerical stability.

Geometric interpretation and precision analysis of algebraic ellipse fitting using least squares method

- Computer ScienceActa Geodaetica et Geophysica Hungarica
- 2012

This approach is based on coordinate description of the ellipse geometry to determine the error distances of the fitting method based on combined least squares method and the experimental results revealed that it might be a good choice for precision estimation of theEllipse fitting method.

High Accuracy Ellipse-Specific Fitting

- Computer SciencePSIVT
- 2013

A new method is proposed that always fits an ellipse to a point sequence extracted from images by random sampling of data points and has higher accuracy than the methods of Fitzgibbon et al. and Szpak et al., the two methods so far proposed to always return an ellIPse.

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