ORTHOGONAL DISTANCE FITTING OF ELLIPSES | Zendy

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ORTHOGONAL DISTANCE FITTING OF ELLIPSES

Author(s) -

Ik-Sung Kim

Publication year - 2002

Publication title -

communications of the korean mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.286

H-Index - 15

eISSN - 2234-3024

pISSN - 1225-1763

DOI - 10.4134/ckms.2002.17.1.121

Subject(s) - ellipse , mathematics , curve fitting , quadratic equation , data point , convergence (economics) , algorithm , function (biology) , least squares function approximation , coordinate descent , mathematical optimization , geometry , statistics , evolutionary biology , estimator , biology , economics , economic growth

We are interested in the curve fitting problems in such a way that the sum of the squares of the orthogonal distances to the given data points is minimized. Especially, the fitting an ellipse to the given data points is a problem that arises in many application areas, e.g. computer graphics, coordinate metrology, etc. In (1) the problem of fitting ellipses was considered and numerically solved with general purpose methods. In this paper we present another new ellipse fitting algorithm. Our algorithm is mainly based on the steepest descent procedure with the view of ensuring the con- vergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

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