A Degenerate Conic-Based Method for a Direct Fitting and 3-D Pose of Cylinders with a Single Perspective View

In this paper, we address the problem of the pose recovery of a straight homogeneous circular cylinder (SHCC) from its apparent contour in a single 2-D image. In many real-world situations, one may encounter cylindrical objects especially in man-made structures. Object models based on surfaces of revolution, in particular cylinders, are suitable for many fields, like the automatic assembly, the human motion capture and also in medical image-based robotic guidance. To model the geometry of a SHCC, we first introduce a singular matrix which represents this degenerate quadric and we show it can be expressed with the Plucker coordinates of its symmetry axis. We demonstrate that the perspective projection of a SHCC is related to the pose parameters and for this model-based pose estimation problem, we present a degenerate conic-based fitting method which has some connections with the estimation of the fundamental matrix. We provide a closed-form solution for the pose determination (4 dof). Compared to earlier works in this field, the proposed approach exhibits some geometric properties of SHCCs, it can deal with partial occlusions of apparent contours and it provides an efficient direct pose solution for the symmetry axis. Simulated data and real images are used to validate the fitting and pose computation. Finally, to highlight the effectiveness of the proposed method to deal with apparent contours in a poor structured environment, we apply this work to the localization of instruments used in laparoscopic surgery.