International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 
many years and many applications. However, polynomial 
transformations should not be taken into consideration for 
precise image registration. In some cases, polynomial 
transformations can be used, e.g. an affine one could be used to 
transform an already geocoded image from one UTM zone to an 
adjacent one, or to register multi temporal images acquired by 
the same sensor under very similar imaging conditions, like it 
happens for Landsat TM. They can also be used, if the terrain is 
not rough and can be approximated by an appropriate 
polynomial. 
Polynomial and image warping methods are based on the use of 
2-D tie-points between datasets to be registered. Image 
distortions caused by the terrain topography are usually not 
taken into account. Following for instance a geometric 
interpretation of a polynomial-based rectification, an image is 
mapped onto an artificial “tie-point”-surface defined by the 
points being used. This may cause severe displacements in 
comparison to a precise orthorectification of the image onto the 
real terrain or the reference ellipsoid surface, respectively (see 
Figure 2). 
3.2, Parametric Methods 
Parametric techniques are based on the use of sensor-specific 
mapping models in order to relate image and map data. For 
representation of the terrain surface, a digital elevation model 
(DEM) is usually incorporated into these methods. These are 
the essential prerequisites to establish a precise relation between 
a point on ground and the related pixel in an image (Figure 3). 
Images can then be registered either in image or map geometry. 
Registration of images in map geometry is in general achieved 
through geocoding to a common geometry referring to a defined 
map projection. Registration in image geometry is achieved 
through a combination of geocoding (image-to-map) and map- 
to-image registration techniques. Geocoding is the standard 
approach, as the output can be immediately compared to other 
geocoded products. 
Fig. 3. Scheme of parametric relation between image and real 
topography, represented by a DEM. 
3.2.1. Geometric Modelling 
Parametric methods rely on the availability of a sensor-specific 
imaging model. The establishment of models to map image to 
object space and vice versa is called geometric modelling in our 
terminology and is the essential preparatory step for further 
registration or geocoding. 
In the geometric modelling task, any relevant sensor-specific 
parameters must be provided in order to establish a precise 
relation between an image pixel and the corresponding ground 
location. Such parameters include both information on the 
sensor geometry (e.g. pixel size, focal length etc.) as well as the 
position and attitude of the sensor during image acquisition. 
Latter information is delivered as ancillary information together 
with the image data for the majority of current remote sensing 
sensors. The information on sensor geometry, position and 
attitude is used to derive initial approximations for the 
parameters of the geometric model (initial imaging model). 
However, the geometric parameters being provided are 
generally not accurate enough, or part of the relevant imaging 
parameters is even missing. Ground control points (GCPs) 
measured in the image and the reference coordinate system are 
therefore usually required in order to derive approximations for 
the missing geometric imaging parameters and to accurately 
estimate the entire set of imaging parameters through the 
application of least squares adjustment procedures. This leads to 
an optimised imaging model (see Figure 4). 
The accuracy resulting from optimised imaging models is 
mainly driven by the localisation accuracy of the GCPs in the 
image, which depends on the ability to exactly identify the