Eccentric Elliptical Contours in Total Hip Replacements

The active ellipses method for assessing wear in total hip replacements uses robust ellipse fitting to
localise 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. 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 active ellipses on a set of test radiographs containing eccentric rims.
Least squares estimation using a geometric error function was most accurate in the presence of Gaussian noise.
However, least median of squares estimation using a geometric error function was most accurate in the presence
of outliers. Furthermore, its performance was similar to that of a computationally cheaper error function known
as the foci bisector distance to the extent that the two were almost interchangeable.