Euclidean reconstruction of a circular truncated cone only from its uncalibrated contours

We present a method to recover a circular truncated cone only from its contour up to a similarity transformation. First, we find the images of circular points, and then use them to calibrate the camera with constant intrinsic parameters from two or three contours of a circular truncated cone, or from a single contour of a circular truncated cylinder. Second, we give an analytical solution of the relative pose between each camera and the circular truncated cone. After the camera's intrinsic parameters and pose are recovered, the circular truncated cone or cylinder is reconstructed from one image. Experiments on both simulated data and real images are performed and validate our approach.