Application Of Ellipse Fitting Methods To The Edge Of Saturn's Ring

The least squares fitting minimizes the squares sum of error-of-fit in predefined measures. There are two main categories of Least-Squares (LS) fitting problems for geometric features, algebraic and geometric fitting, and these are differentiated by their respective definition of the error distances involved. 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 ellipse, rigorous and robust nonparametric algorithm is carried out, which is called Least-squares orthogonal ellipse fitting. It is based on the coordinate description of the corresponding point on the geometric feature for the given point, where the connection line of the two points is the shortest path from the given point to the geometric feature to be fitted.On the basis of the theory of existing ellipse fitting, the least-squares orthogonal ellipse is implemented and used for an astronomical image in this thesis. According to the edge-detection of the planet, this orthogonal ellipse fitting method is applied to Saturn to obtain its center position. After comparison with other ellipse fitting methods, such as algebraic fitting and ellipse-definition fitting, experimental results show that the least-squares orthogonal ellipse fit is effective.