Ian Dowman 
Failure - for airborne raw 3-line imagery an interpolation of the flight path is highly problematic because of the 
sometimes very rough turbulence during flight. Thus, RF will have a limited use only, and one needs to use 
resampled imagery. 
Uncertainly - accuracy assessment is limited to using check points. Errors are not related to physical perturbations so 
that there is no clear indication on what to change if, for example, the errors at the check points are too high; 
lack of complete and rigorous error propagation information. 
Complexity - in defining function and number of points required, possibly leading to instability and further loss of 
accuracy; 
Not the best method for frame images. 
There is no unanimity amongst the vendors which have been contacted on the role of RFs. The consensus seems to be 
that rigorous models are preferred but RFs are inevitable for some sensors. There is no strong feeling that RFs should 
be adopted as a universal transfer standard. 
The information gathered so far indicates that there is a role for RFs but not that they should be the only standard. 
Amongst photogrammetrists there is a very strong feeling that there is a need for a standard which incorporates a 
rigorous sensor model. 
Key RF performance questions requiring further research and testing are: 
* How robust are they? 
* How accurate are they? What are the sources of error? 
* Once a USM is defined for a particular sensor, can this be used for all data from that sensor? What happens if the 
sensor is unstable (e.g. IRS), can the parameters be changed and the model still be robust? Are USMs for a sensor 
model independent of terrain? 
Due to the many variables and their interactions affecting RF performance, including sensor characteristics, imaging 
geometry, image size, terrain elevation range, and the validity of the rigorous sensor’s mathematical model, it is 
unrealistic that a theoretical mathematical analysis can answer many of the above questions. Empirical testing is 
required. (The following section documents some of the testing performed to date.) However, the following 
observations can be made: 
1. Although RFs with denominators can be unstable, a numerator only USM should be stable assuming the fit 
procedure is adequate, i.e., enough redundancy of fit points, enough fit planes covering the possible range of 
elevation, and fit points that span (or exceed) the image (segment). However, unstable results are still possible if 
the polynomial is evaluated outside its valid ground space domain. 
2. The general sources of RF error are fitting error relative to the rigorous model, and of course, any error in the 
rigorous model itself, primarily modeling error and error in the sensor support data. Fitting errors are generally 
due to an inadequate polynomial representation (terms selected), interpolation error (evaluation at points other 
than those used in the fitting grid), and an inadequate fitting procedure. 
3. In general, it's not feasible to predefine an RF (i.e., terms or coefficients used) that will work for any image from 
a given sensor other than for some sensors with benign imaging geometry and reasonably invariant image size. 
However, a fitting process can be predefined like BAE's USM that should work for all images from almost any 
sensor. However, for a desired fit accuracy, the resultant polynomial order and possibly number of image 
segments can vary. 
There are other issues which are raised but which can probably only be answered from experience of use with RFs: 
* . Would they be accepted by the user community if they are too complex? What might be acceptable to NIMA 
might not be acceptable to the average DPW/IPS user. 
* Could a basic set of physical systematic errors, which should be corrected before employing USMs, be defined? 
4. TEST RESULTS 
Kratky (1989) used polynomials to carry out the transformation from object co-ordinates to image co-ordinates of 
SPOT data in the real time loop of an analytical plotter. The transformation can be rigorously determined in advance 
for a 5 x 5 grid for three levels of elevation, covering the full elevation range of the ground scene. A suitable 
polynomial function is derived to fit the spatial grid through a least squares solution, so defining parameters which can 
be applied in real time conversions. Kratky states that 'Absolute errors of the transformation are within IdZ! < 0.2m 
  
258 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.