Journal
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
Volume 72, Issue -, Pages -Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIM.2023.3315361
Keywords
Index Terms-Distance metric; ellipsoid fitting; least-square method; random sample consensus (RANSAC); surface fitting
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In this article, a novel ellipsoid fitting method using a combination of axial distance and Sampson distance is proposed. The method shows higher robustness against outliers and consistently high accuracy in comparison to other representative fitting methods.
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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