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Geometric Least Squares Fitting of Circle and Ellipse

: Ahn, S.J.; Rauh, W.


International journal of pattern recognition and artificial intelligence 13 (1999), No.7, pp.987-996
ISSN: 0218-0014
Journal Article
Fraunhofer IPA ()
Orthogonal Distance Fitting; Circle Fitting; Ellipse Fitting; Singular Value Decomposition; Nonlinear Least Squares; Gauss-Newton iteration

The least squares fitting of geometric features to given points minimizes the squares sum of error-of-fit in predefined measures. By the geometric fitting, the error distances are defined with the orthogonal, or shortest, distances from the given points to the geometric feature to be fitted. For the geometric fitting of circle and ellipse, robust algorithms are proposed which are based on the coordinate descriptions of the corresponding point on the circle/ellipse for the given point, where the connecting line of the two points is the shortest path from the given point to the circle/ellipse.