For the ortho-rectification, the part of the photo geometry between the optical center and the object is also need to know. The most important elements of this are the three-dimensional position of the optical center and the camera orientation. We have to know that the photo was taken from where and to which direction.
The location of the optical center is best to know in the wanted coordinate system of the later ortho-rectified image. The elevation of this point is also has to be known and given, practically from the sea level (the geoid). If we want to measure them during the flight, onboard an GPS instrument should be used, however its data can be applied only with some corrections. The exact position of the camera, valid at the time of the photo taking, should be interpolated from the continuous position string of the GPS. Besides, it has to be taken into correction (and this correction is never fully correct) that the GPS antenna and the optical center are not at the same place. Their position is fixed only in the coordinate system fixed to the aircraft, but its heading, roll and pitch affect the difference vector element in any external (ground-fixed) coordinate system.
The direction vector of the optical axis of the camera is also important to describe the image geometry, and their onboard recording is also can be attempted. For this, an inertial navigation system (INS) can be used. This contains gyroscopes (rotation sensors) and accelerometers (motion sensors) and records the actual angle difference in three dimensions from a reference direction, which is pre-set prior to the flight. In this case, it is again an exercise to get the orientation angle data exactly at the time of photo taking. The six elements of the external position are the three locations and the three orientation data; they can be input directly into the GIS system used for ortho-rectification.
In the practice of the geo-reference, however, these data are seldom presented, even with preliminary accuracy. Fortunately, the elements of the external orientation can be completed in indirect way. They can be estimated using ground control points, moreover, this method often provides better accuracy than the built-in navigation system. Most of the widely used GIS software packages offer the possibility of the estimation of the six external orientation parameters instead of their direct input. To perform this estimation, the ground control points should be given in the target coordinate system and the image positions of these points should be given also in the aerial photo. The target coordinate system, however, should be a projected one, latitude-longitude based geographic systems should be avoided here. The elevation of these point should be defined as precisely as possible; this affects the accuracy, and sometimes the possibility of the parameter estimation. The elevations can be obtained from elevation models or can be read from topographic maps. We have to be prepared to do a meticulous work with many clarifications, difficult point identifications and switching the already recorded points on and off, during the process (Figs. 55 & 56).
According to the recorded point data – three positional data and two image coordinates for each point – and the already defined interior orientation the software estimates and gives the six parameters of the external orientation. However, the parameter estimation is often burdened by significant error. Therefore, a dense control point system, covering the whole image, should be created. The closer the optical axis to the vertical, the better is the quality of the parameter estimation. If the image contains the horizon, it is almost impossible to estimate the elements of the external orientation. However, the image should be used as a whole – no part of it can be cropped out – to save the internal orientation data!