  In random sample consensus (RANSAC), the problem of ellipsoid fitting can be
formulated as a problem of minimization of point-to-model distance, which is
realized by maximizing model score. Hence, the performance of ellipsoid fitting
is affected by distance metric. In this paper, we proposed a novel distance
metric called the axial distance, which is converted from the algebraic
distance by introducing a scaling factor to solve nongeometric problems of the
algebraic distance. There is complementarity between the axial distance and
Sampson distance because their combination is a stricter metric when
calculating the model score of sample consensus and the weight of the weighted
least squares (WLS) fitting. Subsequently, a novel sample-consensus-based
ellipsoid fitting method is proposed by using the combination between the axial
distance and Sampson distance (CAS). We compare the proposed method with
several representative fitting methods through experiments on synthetic and
real datasets. The results show that the proposed method has a higher
robustness against outliers, consistently high accuracy, and a speed close to
that of the method based on sample consensus.
