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.

翻译：在随机采样一致性（RANSAC）框架下，椭球拟合问题可表述为点-模型距离的最小化问题，该过程通过最大化模型得分实现。因此，椭球拟合的性能受距离度量影响。本文提出一种新型距离度量——轴向距离，该距离通过引入缩放因子对代数距离进行转换，以解决代数距离的非几何问题。轴向距离与桑普森距离存在互补性，因为两者组合在计算样本一致性的模型得分和加权最小二乘（WLS）拟合的权值时，构成更严格的度量标准。在此基础上，本文提出基于轴向距离与桑普森距离组合（CAS）的新型样本一致性椭球拟合方法。通过合成数据集与真实数据集的实验，将所提方法与多种代表性拟合方法进行对比。结果表明，所提方法对异常值具有更强的鲁棒性，始终保持高精度，且运算速度接近基于样本一致性的方法。