The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
Direct least square fitting of ellipses
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-b/sup 2/=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.
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Cites
The algebraic eigenvalue problem
Wilkinson, J. H. (1965) · Cited by 5,833
The Algebraic Eigenvalue Problem
I., E., & Wilkinson, J. H. (1966) · Mathematics of Computation · doi:10.2307/2003558 · Cited by 5,140
Haralock, R. M., & Shapiro, L. G. (1991) · Addison-Wesley Longman Publishing Co., Inc. eBooks · Cited by 3,933
Optimization—Theory and Applications
Cesari, L. (1983) · Springer eBooks · doi:10.1007/978-1-4613-8165-5 · Cited by 2,559
Taubin, G. (1991) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.103273 · Cited by 1,147
Methods for Statistical Data Analysis of Multivariate Observations.
Sen, P. K., & Gnanadesikan, R. (1978) · Journal of the American Statistical Association · doi:10.2307/2286626 · Cited by 897
Least-squares fitting of circles and ellipses
Gander, W., Golub, G. H., & Strebel, R. (1994) · BIT · doi:10.1007/bf01934268 · Cited by 860
Recovery of parametric models from range images: the case for superquadrics with global deformations
Solina, F., & Bajcsy, R. (1990) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.44401 · Cited by 603
Methods for Statistical Data Analysis of Multivariate Observations
J, J. E. (1978) · Technometrics · doi:10.1080/00401706.1978.10489650 · Cited by 530
Fitting conic sections to scattered data
Bookstein, F. L. (1979) · Computer Graphics and Image Processing · doi:10.1016/0146-664x(79)90082-0 · Cited by 528
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Metadata
- Authors
- Fitzgibbon, A., Pilu, M., & Fisher, R. B.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 1999-05
- Volume
- 21
- Issue
- 5
- Pages
- 476-480
- ISSN
- 0162-8828 (ISSN-L)
- OpenAlex
- W2140427427
- Cited by
- 2,752
- References
- 17
- FWCI
- 32.08
- Type
- journal article
- Language
- en
- Open access
- closed
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- Fitzgibbon, A., Pilu, M., & Fisher, R. B. (1999). Direct least square fitting of ellipses. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/34.765658
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
