Estimation of a rotationally symmetric mirror shape from a frontal image of the mirror

In structure from motion problems, mirror shape reconstruction from mirror image is very interesting. In this paper, we propose a method to estimate the shape of a rotationally symmetric mirror by calibrating a mirror image which has radially symmetric distortion. In the proposed method, the shape of mirror is represented by the set of solution of a differential equation, which is derived from distortion function computed by the calibration of radially symmetric distortion of an image on a rotationally symmetric mirror. The differential equation and the boundary condition are simplified under the assumption that the image on mirror is taken by orthographic projection camera. The experimental result for a real image is presented to demonstrate the performance of our reconstruction method, and the method is applied for reconstruction of the shape of the mirror painted on the Jan van Eyck´s Arnolfini Wedding which had drawn in the 15th century.