2 
Eleventh Congress of the 
International Society for Photogramrnetrv 
Lausanne, Switzerland, July 8-20, 1968 
Invited paper for Commission III 
Review of Strip and Block Adjustment 
During the Period 1964-1967 
G. H. Schut 
Photogrammetric Research, Div. of Applied Physics, 
National Research Council, Ottawa, Canada 
Introduction 
he period 1964-1967 is characterized by 
the further development and the success 
ful completion of a number of computer pro 
grams for the simultaneous adjustment of 
aerial photographs in large blocks. Both the 
direct solution and the iterative solution of 
the resulting system of normal equations have 
proved to be entirely practical. 
Block adjustments in which models, sec 
tions or strips are adjusted as units are still 
far more common. They can be divided into 
two main groups: adjustment of models or 
sections by means of similarity transforma 
tions, and adjustment of strips or parts of 
strips by means of polynomial transforma 
tions of higher than the first degree. 
The proponents of the adjustment of photo 
graphs view this adjustment as the most 
rigorous solution and as the main trend in 
computational photogrammetry. Others re 
gard the similarity transformation of models 
as the true or rigorous least squares adjust 
ment and the ultimate solution, and they 
predict a decrease of interest in the poly 
nomial adjustment. Nevertheless, the poly 
nomial adjustment has many adherents and 
is much used because it is the easiest to pro 
gram and to use, and because it gives a very 
satisfactory accuracy for topographic map 
ping. 
Any interest that may still exist in the 
analog adjustment of input data has not re 
sulted in more than one published paper. 
Simultaneous Adjustment 
of Photographs 
1. USE OF THE COLLINEARITY CONDITION 
References [5] to [23] deal with the simul 
taneous adjustment of photographs in blocks 
or strips. References [24] to [31] discuss the 
solution of the large system of normal equa 
tions in this adjustment. 
Already before the London Congress, H. H. 
Schmid and D. C. Brown used the condition 
of collinearity of image point, perspective 
centre, and object point for the simultaneous 
adjustment of a set of photographs. This 
condition leads to the linearized equation 
v + Bb = t (1) 
in which 
v is the vector of corrections to the'photo- 
graph coordinates, 
5 is the vector of corrections to the 
parameters of camera orientation and 
to the coordinates of object points, 
B is a matrix of coefficients, and 
e is the vector of residuals of the photo 
graph coordinates in the non-linear con 
dition equations. 
The normal equations become 
-Pv + k =0 
v + Bb = E 
B l k = 0 (2a) 
in which P is the weight matrix of the ob 
served photograph coordinates and is com 
puted as the inverse of the covariance matrix. 
Further, k is the vector of Lagrange multi 
pliers or correlates, and the superscript t indi 
cates the transpose. Elimination of v gives 
P l k + Bb = e 
B‘k = 0. (2b) 
Subsequently, elimination of k gives 
B l PBb = B l Pz. (2c)