Journal of Mathematical Imaging and Vision

, Volume 53, Issue 3, pp 364–382

# Constrained Ellipse Fitting with Center on a Line

• Patrick Waibel
• Jörg Matthes
• Lutz Gröll
Article

## Abstract

Fitting an ellipse to given data points is a common optimization task in computer vision problems. However, the possibility of incorporating the prior constraint “the ellipse’s center is located on a given line” into the optimization algorithm has not been examined so far. This problem arises, for example, by fitting an ellipse to data points representing the path of the image positions of an adhesion inside a rotating vessel whose position of the rotational axis in the image is known. Our new method 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. Further advantages of the algorithm are computational efficiency and numerical stability.

## Keywords

Ellipse fitting Constrained cost function Eigenvalue problem

## Notes

### Acknowledgments

The authors thank the anonymous reviewers for their valuable feedback. Especially, we would like to thank for providing parts of the proof for Theorem 2.

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