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In this paper, a new method for determining the position and orientation of the object in respect to the camera coordinate using the image is presented. True picture of the camera is obtained by a nonlinear mapping between the three-dimensional world and two-dimensional image. Some researchers assumed linear mapping to make approximation of position and orientation easier, but restrictions were imposed on the object size. Also the use of nonlinear mapping and geometric relationships between object and its image is so challenging and difficult task, but increase the accuracy and do not raises the limit on the size of the object. The case in which an object is placed in front of the camera can become different according to the orientation type and its distance from the main axis of the camera. In this paper, to determine 6DOF position and orientation of an object using its image, a system of nonlinear equations with ten equations and 5 unknowns is extracted. In solving nonlinear equations, it is important to choose an appropriate algorithm to minimize the error and needs little time. With regard to the non-exact values in practical test, the kind of optimization algorithm is proposed and. Then a way for selecting initial guess is proposed to always have a solution and reduce the run time. Accuracy of extracted equations is shown by determining 6 DOF position and orientation of one theodolite.

Keywords: Position and orientation determining, object coordinates, camera mathematical and geometrical equation, determining orientation matrix.

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