Robust Ellipsoid Fitting Using Axial Distance and Combination
This work addresses robust ellipsoid fitting for computer vision applications, representing an incremental improvement over existing sample-consensus methods.
The paper tackled the problem of robust ellipsoid fitting in RANSAC by proposing a novel axial distance metric and its combination with Sampson distance (CAS), resulting in higher robustness against outliers and consistently high accuracy with competitive speed.
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.