Haggrén - 3 
Orientations 
The orientation is the procedure where the transformation parameters from one coordinate system to a 
second coordinate system are determined. A 2-D orientation includes the shift and rotation of an object 
along a plane, and a 3-D orientation includes the determination of the position and attitude of an object in 
both coordinate systems. 
In photogrammetry, the orientations are described as interior or exterior orientations, or as relative and 
absolute orientations. The division to interior and exterior orientation relates to the camera body, whereas 
the relative and absolute orientations were introduced aside exterior orientations for the purpose of 
operating analog stereo plotters. In following both the traditional definitions of orientations are described 
and the recent definitions outlined with respect to procedural aspects. 
Interior orientation. The interior orientation is the determining of the interior perspective of the image 
as it is or was at the instant of recording. The datum for the orientation is most likely a calibrated camera 
coordinate system. The transformation results in a 3-D bundle of imaging rays. The collinearity condition 
will be fulfilled by compensating the non-linear imaging distortions which are given as functions of the 
camera coordinates. 
The ordinary four parameters for the interior orientation are the 2-D coordinates of the location of the 
principal point and the camera constant and the rotation around optical axis. In the case of affine 
transformation two further parameters are used, namely the aspect ratio and the angle between the 
coordinate axes. The number of non-linear distortion parameters vary largely upon purpose. 
In the case of analog images the interior orientation is an image related variable. As it regards the 
measuring procedure, the interior orientation is a preceding operation before the actual object 
measurements. It includes the observation of fiducial marks in the coordinate system of the measuring 
instrument first, and then an adjustment for solving the parameter values for interior orientation. The 
same values are then used for transforming the actual object measurements to the camera coordinate 
datum. The transformation will be different for all subsequent images and therefore the procedure has to 
be repeated separately. 
In the case of digital cameras the interior orientation is a camera related variable. In the case of imaging 
system, which is a combination of a video camera, a digitizer and cables in-between, perhaps a feature 
projector, the interior orientation is a system related variable. As it regards the measuring procedure, this 
simplifies the entire interior orientation largely, as the transformation parameters have to be determined 
only once for each camera or system. 
Exterior orientation. The exterior orientation is the determining of the exterior perspective of the image 
as it is or was at the instant of recording, i.e. by determining the position of the camera station and the 
attitude of the camera at that instant. By exterior orientation the bundles are oriented in such way that the 
collinearity condition will be fulfilled all along to the object space. After exterior orientation of at least 
two images, new object points and features can be coordinated in 3-D by intersection. The datum is 
external and usually a local one or an object model coordinate system. 
The ordinary six parameters for the exterior orientation are the 3-D coordinates of the projection Centre 
and the three rotations around the coordinate axes. The exterior orientation is determined directly by 
resection or indirectly by block adjustment. For resection, the 3-D object geometry should be known by at 
least three control points, but in the case of digital images more likely by a set of geometric object entities 
or features. In block adjustment, the exterior orientations are determined for several images 
simultaneously relative to a given external datum. In the case the object geometry is still largely unknown,