EllipseFitting

Ellipse fitting is a highly researched and mature topic. Surprisingly, however, no existing
method has thus far considered the data point eccentricity in its ellipse fitting procedure. Here,
we introduce the concept of eccentricity of a data point, in analogy with the idea of ellipse
eccentricity. We then show empirically that, irrespective of ellipse fitting method used, the root
mean square error (RMSE) of a fit increases with the eccentricity of the data point set. The main
contribution of the paper is based on the hypothesis that if the data point set were pre-processed
to strategically add additional data points in regions of high eccentricity, then the quality of a fit
could be improved. Conditional validity of this hypothesis is demonstrated mathematically using
a model scenario. Based on this confirmation we propose an algorithm that pre-processes the
data so that data points with high eccentricity are replicated. The improvement of ellipse fitting
is then demonstrate