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Geometric inversion approcah for visual curve estimattion

The trade-off between bias and variance is a key issue for statistical learning and estimation. Robust algorithm could be achieved by increasing the bias, such as the circle estimation problem in our paper. Estimating circles under finite sampling data points is an important task in many applications in computer vision area. In this paper, we provide a novel regression method based on the inversion transform. A circle can be translated into a line by the inversion transform, where the inversion centre is a point belonging to the sampling data set. After that, current analysis tools for fitting line can be directly used to the task of fitting the circle. Both experimental results and theoretical analysis show that our method could achieve better performance compared with the Hough transform.