Collinearity equations play a very important role in photogrammetry and computer vision. It established the relationship between three points

that is

the camera projective center

an object point and its corresponding image point. In collinearity equations

a rotation matrix is usually used to describe the attitude of an image traditionally a rotation matrix is always represented by three Euler angles because of its vivid describing of the relationships between three axes. However

since the unit quarternion was presented by Hamilton in 1843

its use has extended into many application fields such as signal processing

mechanics

and aerospace. In order to discuss the application problem of unit quaternion in photogrammetry

research was carried out in this paper systemically into rigorous solution of collinearity equations by using unit quarternion based rotation matrices. Starting from the basic theories and its operations of unit quaternion

rigorous linearized expression of unit quaternion based collinearity equations are derived in detail and there is no need to derive the rotation matrix. Tests by using both simulated data and real image data indicate that linearized collinearity equations have many merits such as having a very simple form

being independent of initial values

and having a high convergent speed compared to two other rotation matrices orthe Euler angle based rotation matrix. So

unit quaternion based rotation matrix should be used widely in practical application.