Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola

摘要

The least-squares fitting 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/sphere/ellipse/hyperbola/parabola, simple and robust nonparametric algorithms are proposed. These are based on the coordinate description of the corresponding point on the geometric feature for the given point, where the connecting line of the two points is the shortest path from the given point to the geometric feature to be fitted.