88 
straints in the same form of quasi-observation 
u as in Equation 16, but with modified weight 
matrices 
P,-P -PB,(P,.-B!pDB,)b7P (16a) 
An absolute enforcement of this coordinate 
constraint is feasible by increasing the 
diagonal values in P, to infinity, which will 
change the weight matrix P, into P. 
Any other auxiliary information concerning 
the orientation parameters g, should be 
added to the system again in the form of 
quasi-observations u which, this time, are as- 
sociated with a different matrix B, and with a 
weight matrix P. Otherwise, a full uniformity 
ofthe formation ofthe equations is preserved. 
The solution of normal equations is re- 
peated while regularly updating vector g, and 
quasi-observations u in each iteration. Upon 
applying P, from Equation 16 the unknown 
vector g, is rigorously eliminated in each step 
and is ultimately computed only after the 
completion of the iterative process by 
g: * —(BTPB,.)BTPu (17) 
Although possible, there is no need to update 
the model coordinates after each iteration. 
DETAILED COMPILATION 
The first two operational phases in a stan- 
dard on-line analytical process are concerned 
with the derivation ofa valid analytical model 
for image geometry and, by using it, with the 
analytical reconstruction of the model for ob- 
ject geometry. In both phases the on-line 
function proper is prepared and checked, but 
the essence of what is done is practically 
identical with the function of off-line analyti- 
cal procedures. Only after the models of both 
image and object geometries are derived are 
they ready to be used in a process of detailed 
photogrammetric compilation which repre- 
sents a typical real-time operation with all the 
characteristics of an on-line process. The con- 
trol of this operation is characterized by Equa- 
tion 2a or in a modified form by 
d, gi —> (x' x") 
Le gap RX 
eee 
With the computer performing all the three 
involved computations as given by Equations 
11 to 13 in a high frequency cycle, the 
operator retains the dynamic control of the 
system through x and, with a perfect illusion 
of continuity, receives his feedback from 
stereoobservations of computer positioned 
imaze details foi x' ead a". For the real-time 
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976 
operation the link (x — x') is most critical 
because it includes the image correction c 
= Dd and the computation is repeated for x’ 
and x". The second link (x—X) must be im- 
plemented with a frequency dependent on 
the type of output. If X is to be digitized and 
stored continuously, the required density of 
data should determine the computation fre- 
quency. When X is to be displayed or re- 
corded only occasionally, for discrete points, 
the frequency can be lowered. Depending on 
the user's need and sophistication, the 
X-digitization may also include additional 
operations, such as an interpolation of re- 
siduals remaining in control points. The 
graphical output following the conversion 
(x > %) is relatively less demanding as far as 
the computation frequency is concerned and, 
in general, it can be different for a plotting 
table or for a CRT-display. 
A few comments are in order on continuous 
digitizations. Some of the operations proceed 
under full control of the operator, some can 
be computer-assisted, and some may be fully 
controlled by the computer. The latter is pos- 
sible if the system includes an automatic cor- 
relator, but even in this instance the operator 
usually monitors the action and is ready to 
step in. This is typical for the Gestalt Photo 
Mapper (Hobrough 1971). The operator ter- 
minates the automatic correlation process in 
individual orthophoto patches and can mod- 
ify the derived height level if necessary. A 
reversed situation arises when the computer 
assists the operator by assuming control in a 
part of the operation. This is useful in profil- 
ing when the computer provides the basic 
constant drive in any desired direction or in a 
more general pattern and the operator con- 
trols the elevation. In parallel profiling the 
computer can duplicate the preceding pro- 
file, leaving the operator with relatively small 
adjustments. 
ADDITIONAL FUNCTIONS 
AUXILIARY OPERATIONS 
An on-line analytical system can also be 
used in further data processing and editing, 
mostly in a better way than a pure off-line 
system (Masry 1973). Some of these functions 
are performed directly during the real-time 
operation, some of them in periodically in- 
serted off-line time periods. One should men- 
tion a reduction of the data volume which is 
useful for any continuous digitization ulti- 
mately suffering from a high redundancy of 
data. A more sophisticated editing can 
smooth out the data stream, filter out the 
noise, provide some refinement with respect 
to already existing data, and do all necessary