Real-time geometric fitting and pose estimation for surface of revolution

This paper presents a novel ellipse fitting method to simultaneously estimate the Euclidean pose and structure of a surface of revolution (SOR) by minimizing the geometric reprojection error of the visible cross sections in image space. This geometric error function and its Jacobian matrix are explicitly derived to enable Levenberg-Marquardt (LM) optimization. With the obtained pose and structure, the Euclidean shape of a SOR can be reconstructed by generating the ellipse tangency to the apparent contour of the SOR. Given the real size of several visible cross sections, this approach can be extended to perform a real-time 3D tracking of the SOR. Additionally, this technique can be also generalized to fitting for imaged parallel circles. Sufficient experiments validate the accuracy and the real-time performance of the proposed method.