(13) (S+W) à = € -We 
When the number of photos is not excessively large this 6mx6m system can 
be solved by standard methods of inversion to yield | 
(14) op (sudes), 
With the vector of corrections to the elements of orientation thus established, 
each vector of corrections to the approximate coordinates of object points can 
be computed sequentially from 
(15) 8j = (N;*W;) (€5 - Wje;) - 10,8 je 1,253225 70 
The corrections resulting from (14) and (15) may be employed to generate 
refined approximations, thus initiating an iterative process that can be 
carried to convergence. Thereupon, the covariance matrix A of the adjusted 
elements of orientation and the covariance matrix A; of the adjusted 
coordinates of the jth point can be evaluated from 
(16) A +a, 
v. joe rus e T 
The above development provided the basis for the practical utili- 
zation of the bundle adjustment in the early 1960's. In applications 
involving relatively small numbers of photographs (e.g., terrestrial appli- 
cations) the solution of the reduced system of normal equations presented 
no practical difficulties; here, a straightforward process of Gaussian 
elimination was altogether adequate. However, in applications to aerial 
blocks the direct solution of the reduced system of normal equations by 
standard methods became increasingly impractical with increasing numbers 
of photos and was clearly unfeasible (even with large and advanced computers) 
for blocks containing many hundreds of photos. The first practical resolution 
of this basic difficulty was developed in Brown, Davis and Johnson (1964). 
Here, specific advantage was taken of the characteristic sparseness of the 
N submatrix associated with aerial blocks. Instead of operating on the 
reduced system of normal equations (8), Brown, Davis and Johnson reverted to 
the general system (3) and instead of attempting to effect a direct solution 
of this system, they employed the indirect method of Block Successive Over 
Relaxation (BSOR). The effectiveness of this approach depended on the use 
of an indexing scheme whereby (a) only the nonzero submatrices of the normal 
equations would be formed and (b) these would be stored and operated on in a 
collapsed form as illustrated in Figure 1b. By eliminating all superfluous 
operations on zero matrices this process drastically reduced storage require- 
ments, and greatly facilitated the formation and solution (by BSOR) of the 
normal equations. As a consequence, by 1966 it became practical to adjust 
blocks containing more than 1000 photos by means of the operational computer 
program implementing the 'collapsed' BSOR reduction (Davis 1965)). 
Bm