A simple vision algorithm for 3-D position determination using a single calibration object

We shall present a new method to determine the arbitrary 3-D location and orientation of a calibration object relative to the camera. Most of equations used to determine the 3-D position are simple and non-trigonometric. There is also no severe problem regarding the viewing angle. We choose a cube to be our calibration object whose dimensions are known. The basic theory behind our method for 3-D position determination is to express the 3-D line equations and the 3-D plane equations of the cube in terms of the 2-D coordinates of the vanishing points obtained from the perspective projection of the cube. Furthermore the given dimensions and edge perpendicularity property of the cube are used to determine the 3-D coordinates of the cube vertices. More importantly, in our method we iteratively modify the coordinates of the vanishing points on the image plane so that (a) the derived 3-D vertices comply with the given geometric constraints of the cube and (b) the cube image data given by the back projection is also in close agreement with what actually appears in the TV image. Thirty-six real images are used in the experiments to illustrate the performance of the proposed method and a Mitsubishi RM-101 robot arm is shown to be guided by the vision system to grasp the object, too.