attached. The relationship with the latter is obtained from the photographs of-the downward-looking small 
camera and the survey camera. Little interest has been shown in this development by the manufacturers. 
J. Kure. In Saudi Arabia, 30,000 line km cover half the country in a net of 150 x 50 km polygons for 1:50,000 
mapping. Only one line of ground levelling exists, and 1000 km away is the Red Sea surface. Three stages of 
smoothing (statoscope, clearances, APR) were applied in a computer programme, and some data was rejected. 
Results may be summarized: statoscope € — 2m, clearance € = 2.5 m, APR 0 = 2m, overall rmse 1.3 m. 
A number of check points were picked up and none were in error by more than 3m. The stability of the 
isobaric surfaces appeared to have been much better than expected. The Henry collection does not allow for 
changes in the surface with time, or changes with drift during a strip. With strips of up to 150 models this was 
significant. The higher accuracy of the laser profiler will demand better knowledge of isobaric surfaces. 
F. Ackermann. We are developing a programme for adjustments with APR and statoscope data, but cannot 
report results yet. 
Tuesday August 1 1972, 9:00 
Invited Paper: “Systematic Image Errors in Aerial Triangulation"' by K. Kubik. 
E.H. Thompson. Errors are random, constant or correlated. I do not like the term systematic. The correlation 
is two-dimensional serial correlation, rather neglected by statisticians who have covered linear serialization. 
H.H. Schmid. It should be borne in mind that a least squares adjustment gives a consistent set of results, rather 
than the correct result. The distribution of residuals gives an estimation of systematic error, but a 
variance-covariance matrix should be used to estimate the variances of the parameters. The study of 
pseudo-inverses has an application in this work, and which will define the inner structure and correlation 
within the system. 
E.H. Thompson. It must not be overlooked, however, that least square methods have considerably improved 
the results of blocks of aerial triangulation. Some correlation of residuals found in the dispersion matrix may 
be due to algebraic processes, and not entirely correlation of the observations. 
G.H. Schut. Simple polynomials were derived by G. de Masson d'Autume to correct for certain assumed strip 
deformations. I tested these, and they need minor modification, but, in general, they give the required effect. 
Kubik considers deformation at the photograph, and different polynomials are required to correct for these 
deformations. Anderson and Ramey used an actual example of film deformation and camera calibration to 
apply to the simulated block data. H. Ziemann has endeavoured to fit polynomials to this deformation, and a 
very high degree polynomial is required (24 terms). The use of high degree polynomials can be expected to 
give unsatisfactory results, and we may have to look for other methods. 
G. Ducher. Monsieur G. de Masson d'Autume regrets his absence, and I would like to describe his paper. 
Corrections were applied at the plates in an experiment, and the effects investigated for Kubik's four types. The 
separation of systematic and random errors is difficult. High degree polynomials may lead to inappropriate, 
or even indeterminate, equations. We will apply corrections, based on a statistical analysis of results of the first 
adjustment in a repeated computation, after first being filtered for random errors. A few iterations should be 
enough to reach stability, but this is early in the investigation at IGN. In conjunction with a better knowledge 
of the nature and magnitude of systematic errors, there should be an improvement in accuracy. 
E.H. Thompson. It is not so much that the determination of higher degree polynomials is poor, as that they 
are not appropriate, and the coefficients are often not significant. 
K. Kubik. The four types of deformation I considered are not supposed to represent actual deformation. I used 
them as an example. 
G.H. Schut. The use of a smoothing method, as discussed by Mr. de Masson d'Autume in his presented paper, 
may be the best solution to the problem of systematic errors. There are many publications on smoothing 
methods in other disciplines, and these are worth investigating. 
H. Ziemann. If you have no influence on photography, then you must make the best of the errors in it. I think 
errors can be reduced, by the use of a reseau, or else the inclusion in the project of a test field for the system 
calibration. The deformations in typical practical examples of photography are very variable, and do not 
conform to any particular pattern. A new and improved camera with a reseau should be useful; at present I