coordinate system (X1,X2,X3) and (X1',X2',X3') above, this implies that where is the homogeneous representation of the point P in the coordinate system (X1',X2',X3'). Assuming also that the camera matrix is given by , the mapping from the coordinates in the (X1,X2,X3) system to homogeneous image coordinates becomes Consequently, the camera matrix which relates points in the coordinate system (X1',X2',X3') to image coordinates is a concatenation of a 3D rotation matrix and a 3-dimensional translation vector. This type of camera matrix is referred to as a normalized camera matrix, it assumes focal length = 1 and that image coordinates are measured in a coordinate system where the origin is located at the intersection between axis X3 and the image plane and has the same units as the 3D coordinate system. The resulting image coordinates are referred to as normalized image coordinates. The camera position Again, the null space of the normalized camera matrix, described above, is spanned by the 4-dimensional vector This is also, again, the coordinates of the camera center, now relative to the (X1',X2',X3') system. This can be seen by applying first the rotation and then the translation to the 3-dimensional vector and the result is the homogeneous representation of 3D coordinates (0,0,0). This implies that the camera center (in its homogeneous representation) lies in the null space of the camera matrix, provided that it is represented in terms of 3D coordinates relative to the same coordinate system as the camera matrix refers to. The normalized camera matrix can now be written as where is the 3D coordinates of the camera relative to the (X1',X2',X3') system. General camera matrix Given the mapping produced by a normalized camera matrix, the resulting normalized image coordinates can be transformed by means of an arbitrary 2D homography. This includes 2D translations and rotations as well as scaling (isotropic and anisotropic) but also general 2D perspective transformations. Such a transformation can be represented as a matrix which maps the homogeneous normalized image coordinates to the homogeneous transformed image coordinates : Inserting the above expression for the normalized image coordinates in terms of the 3D coordinates gives This produces the most general form of camera matrix See also 3D projection Camera resectioning References Geometry in computer vision