Z-shaped Perspective-Three-Line Problem's Unique Solution Conditions

Perspective-three-line (P3L) problem when three lines are coplanar and placed as Z-shaped is studied for camera pose determination from a single perspective view and 2-D to 3-D line correspondences. We find the problem's solution number depends on the location of optical center of the camera. If the optical center locates inside two conical cones or on a special plane, the problem has a unique solution, otherwise it has two possible solutions at most. The conclusions are proved via geometric method. The results show that line features can be applied to pose measurement in computer vision systems.