A novel method to register images onto 3D data, such as 3D point cloud, 3D vectors, and 3D surfaces, is proposed. The proposed method estimates the exterior orientation of a camera with respective to the 3D data though fitting pairs of the normal vectors of two planes passing a focal point and 2D and 3D lines extracted from an image and the 3D data, respectively. The fitting condition is that the angle between each pair of the normal vectors has to be zero. This condition can be represented as a numerical formula using the inner product of the normal vectors. This paper demonstrates the proposed method can estimate the exterior orientation for the image registration as simulation tests.