Eccentric Elliptical Contours in Total Hip Replacements
Stuart Kerrigan, Stephen James McKenna, Ian W. Ricketts, C.A. Wigderowitz · Worcester Research and Publications (University of Worcester) · 2004
Abstract. The active ellipses method for assessing wear in total hip replacements uses robust ellipse fitting to estimate ellipses around the contours of the femoral head and acetabular rim wire marker. In the case of the latter these ellipses can be very eccentric and the standard algebraic distance was shown to be inadequate. Unlike in robust estimation of a line the geometric distance from an ellipse to a point is not trivial to compute and thus numerous error of fit functions have been created. In this work several of these error of fit functions are compared, including a geometric error of fit function, on both synthetic data and by using the active ellipses on a set of test radiographs containing eccentric rims. The robust estimation using geometric error function was found to be the best performing in all but Gaussian noise (where a least squares fit using geometric error is the best) its performance was similar to that of a computationally cheaper error function known as the foci bisector distance to the extent where the two were almost interchangeable. 1