Robust ellipsoid fitting using combination of axial and Sampson distances

M Han, J Kan, G Yang, X Li - IEEE Transactions on …, 2023 - ieeexplore.ieee.org
M Han, J Kan, G Yang, X Li
IEEE Transactions on Instrumentation and Measurement, 2023ieeexplore.ieee.org
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
article, 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 …
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 article, 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 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.
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