Discussion of Address by E.H. Thompson 
F.A. Ackermann. Verbatim recording is difficult and frequently unsatisfactory, and puts a burden on the editor. 
I think a brief summary of the discussion should be prepared by the secretary of the symposium and published 
in the proceedings. 
This was agreed upon as guidance for future symposia, to be applied at the President’s discretion. 
S. Degual introduced his presented paper **Use of the Galileo Digital Stereocartograph for Analytical Aerial 
Triangulation”. The configuration recommended for triangulation is a Stereocomparator linked with a Loben 
8K computer with fast paper tape recorder. Parallax is eliminated at 5 to 12 points, and the computer performs 
the relative orientation and subsequently removes parallax from the stereo model. Pass points and control 
points are observed, and xyz model co-ordinates are punched on tape. The next pass through the computer 
connects the models together, and performs a linear transformation on up to 12 control points. This is often 
sufficient; but, in further cases, a third phase is block adjustment, which can be on the same computer, provided 
the 32K version is used. In response to a question, the reason for using paper tape is that it is cheapest. Punched 
cards, magnetic tapes or discs may be used. 
C. Togliatti introduced the presented paper by F. Sanso “An Exact Solution of the Rototranslation Problem”. 
The problem is to obtain a similarity transformation, which includes a possible large rotation, without the use 
of initial approximations or iteration. Quaternion algebra is used, which offers the advantage of allowing the 
same representation for both vectors in 3-D and rotations. Both co-ordinate systems are referred to the centroid 
of common points as origin, thus eliminating the translation. The quaternion of the rotation is found as the 
eigenvector associated with the smallest eigenvalue of a 4 x 4 symmetric matrix. The 3 x 3 Rodrigues matrix 
of the rotation is formed from the components of this quaternion. The accuracy of the iterative determination 
of the eigenvalues, and the influence of measuring errors on the computed rotation, are studied also. 
G.H. Schut. I draw attention to my publications on this subject, the latest being “Strip Formation from 
Independent Models"', (Photogrammetric Engineering, July, 1968). Quaternions are here replaced by 4 x 4 
matrices. The four parameters of the Rodrigues matrix are determined from exact linear equations, four for 
each control point. There is no need to compute eigenvalues and eigenvectors. Recent tests show that the results 
are virtually indistinguishable from least squares minimization of residuals at the control points. 
U. Rauhala introduced his presented paper “New Solutions for Fundamental Calibration and Triangulation 
Problems”. The paper considers the use of generalized polynomial and harmonic interpolation in calibration 
and triangulation problems, and combines photogrammetric and ground survey observations in one 
adjustment. The advantage is that better arrangements can be made for the isolation and reduction of errors 
due to targetting, misidentification of targets, and of errors in observations. Tests indicate a high accuracy in 
the determination of co-ordinates of new points. 
T. Leberl. I think interpolation methods such as these are only an advantage with a regular pattern of points, 
and employ high order polynomials with all the dangers of obtaining poor results, even though the residuals 
at these points may be small. 
U. Rauhala. Interpolation is very effective with regular points. Irregular distribution is a disadvantage, but not 
more so than with other methods. The danger can be reduced by normalizing the polynomials, and using a 
k-vector technique. 
Wednesday July 26 1972, 14:00 
Invited Paper: “Experimental Research in Block Triangulation’ - Summary of Working Group Reports into 
use of Simulator Data in Aerial Triangulation. 
Co-Chairmen: J.M. Anderson and E.H. Ramey. 
Discussion 
R. Forstner. We used the lowest number of check points, because we used the same ones for all cases A,B,C. 
Therefore, in cases A and B, we did not use all the available checks, though other participants did.