BALLISTIC RESEARCH LABORATORIES 
. REPORT NO. 1065 
HHSchmid/dp 
Aberdeen Proving Ground, Md. 
July 1959 
A GENERAL ANALYTICAL SOLUTION TO THE 
PROBLEM OF PHOTOGRAMMETRY 
ABSTRACT 
An analytical treatment of the general problem of photogrammetry is 
developed. which only requires that object point, center of projection and 
corresponding image point are collinear for any one ray present in a specific 
photogrammetric measuring procedure. The corresponding formulas, expressing 
the geometrical relation existing between the spatial coordinates of the 
object, the plate coordinates of the corresponding image and the elements of 
orientation, are the bases for a rigorous least squares adjustment, whereby 
both the image-coordinates measured on & comparator, and the given control 
data may be considered as erroneous. The corresponding system of normal 
equations, which is shown to be typical for any photogrammetric measuring 
problem is used to form a system of reduced normal equations, the unknowns 
of which are either the elements of orientation or the spatial coordinates of 
the model. The application of matrix caleulus not only simplifies the presen- 
tation but reduces the "bookkeeping effort", while establishing the corre- 
Sponding program for electronic computers. A special chapter deals with the 
problem of incorporating additional geometric conditions as they may exist 
between any one or &ll of the unknowns of the solution. The application of 
the described method for the special cases of "strip and block triangulation" 
is treated, whereby attention is given to the problem of solving the corre- 
sponding system of reduced normal equations. For an unlimited strip, a 
rigorous solution is presented, which is based on the stepwise elimination of 
certain groups of the unknowns. Finally, an iterative solution is given which 
makes use of thé relaxation method.