A general accuracy measure for quality of elliptic sections fitting

Abstract

Least squares (LS) fitting, the most widespreadly used approach for ellipses, operates by minimizing the sum of squares of some error term measured at each data point. It is not an easy task to measure the accuracy of any fitting method in fitting elliptical sections since they rely on different error criteria. There is no unique criterion valid for any fitting method for quantifying for ellipse fitting. For this reason, there is a need for a general measure that can be used to compare the accuracy of fitted ellipses using different methods. In this work, an error measure is proposed which can be used both to measure the accuracy of any ellipse fitting method and to compare the accuracy of the ellipses fitted with different (i.e. algebraic or geometric) methods. This measure is generated from the widely known orthogonal least squares fitting (OLSF) method revising the computation scheme of initial values for the orthogonal contacting points for an ellipse in the study. This is a flexible error measure since it always computes orthogonal distance residuals between data points and the optimal ellipse and can then be used to compare the performance of different ellipse fitting methods. By computing this measure it is possible to obtain the precision of the ellipse parameters with respect to the orthogonal distance residuals. This measure is applied to the measurement of the outer section of a piston and results indicate the effectiveness of the criterion.