基于轴向距离与组合的鲁棒椭球拟合
Robust Ellipsoid Fitting Using Axial Distance and Combination
AI总结：
本文提出轴向距离度量并与Sampson距离组合，构建CAS椭球拟合方法，在合成与真实数据上验证其抗离群点鲁棒性更强、精度更高且速度接近采样一致性方法。
摘要：
在随机采样一致性（RANSAC）中，椭球拟合问题可以被表述为最小化点到模型距离的问题，该问题通过最大化模型得分来实现。因此，椭球拟合的性能受到距离度量的影响。本文提出了一种新的距离度量，称为轴向距离，它通过引入一个缩放因子从代数距离转换而来，以解决代数距离的非几何问题。轴向距离与Sampson距离之间存在互补性，因为在计算采样一致性的模型得分和加权最小二乘（WLS）拟合的权重时，二者的组合是一种更严格的度量。随后，通过使用轴向距离与Sampson距离的组合（CAS），提出了一种新的基于采样一致性的椭球拟合方法。我们在合成数据集和真实数据集上通过实验将所提方法与几种代表性拟合方法进行了比较。结果表明，所提方法对离群点具有更高的鲁棒性、持续较高的精度，并且速度接近基于采样一致性的方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
