Direct least square fitting of ellipses

Author

Fitzgibbon, Andrew ; Pilu, Maurizio ; Fisher, Robert B.

Author_Institution

Dept. of Sci. Eng., Oxford Univ., UK

Volume

21

Issue

5

fYear

1999

fDate

5/1/1999 12:00:00 AM

Firstpage

476

Lastpage

480

Abstract

This work 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-b²=1, the new method incorporates the ellipticity constraint into the normalization factor. The proposed method combines several advantages: It is ellipse-specific, so that even bad data will always return an ellipse. It can be solved naturally by a generalized eigensystem. It is extremely robust, efficient, and easy to implement

Keywords

computational complexity; curve fitting; eigenvalues and eigenfunctions; least squares approximations; algebraic distance; computational expense; direct least square ellipse fitting; ellipticity constraint; general conics; generalized eigensystem; normalization factor; scattered data; Application software; Computer vision; Eigenvalues and eigenfunctions; Fitting; Iterative algorithms; Iterative methods; Least squares methods; Pattern recognition; Robustness; Scattering;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/34.765658

Filename

765658