Camera Coordinate System
Assume an object point X (4x1 homogenous coordinates) is mapped to the image coordinates x (3x1 homogenous coordinates) by multiplication of the projection matrix P (3x4):
x = PX
The matrix P is composed of the rotation matrix (3x3), the translation t vector (3x1) and the camera matrix (3x3). The matrix P (3x4) is shaped as follows
P = K[R|t].
Thereby the translation is t = -RC. C (3x1) represents the coordinates of projective center of the camera with respect to the object COS. The z-axis of the camera is oriented in viewing direction.
Exterior orientation parameters for the .ori format
Image Coordinate System
Let X_cam = [R|t]X be the coordinates of an object point in the cam system. X_cam(3x1) can be mapped to homogenous image coordinates using the camera matrix K
x = KX_cam.
K is shaped as follows:
Thereby f_x, f_y represent focal lengths in pixels. Parameters c_x, c_y represent the offsets to the principle point in terms of pixel dimensions. The parameter s_x specifies the skew parameter. In the image COS (0,0) corresponds to the center of the upper left pixel.
Image coordinate system
Interior orientation parameters for the .ori format