ANALYTICAL ON-LINE SYSTEMS IN CLOSE-RANGE PHOTOGRAMMETRY 
decide on data rejections or remeasurements 
with the full advantage of comparing the digi- 
tal results with the observed optical 
stereomodel. 
ANALYTICAL FORMULATIONS 
GENERAL CONCEPTS 
As a basic rule for formulations and pro- 
gramming in on-line analytical systems one 
can state that simple and fast computations 
are preferable. However, this applies mainly 
to the real-time operations where the time 
aspects are most critical. Depending on the 
type of the computer used, this programming 
may be necessary at the lower level language, 
such as the assembler, while the other pro- 
grams seem to be handled well with higher 
level languages like FORTRAN, with the con- 
venience of their easier reading and potential 
modifications by the user. 
The variety of conditions in close-range 
photogrammetry requires that an on-line 
analytical system be supported by a set of 
program modules for formulations fitting all 
possible image geometries. The modules 
should provide ready-to-use solutions just by 
selecting the suitable type. For the recon- 
struction phase a more universal and flexible 
formulation is needed to accommodate differ- 
ent conditions, in the process of the 
operator-computer interaction. 
In general, two different groups of variables 
characterize the image-object relationship in 
on-line analytical systems: 
- inner geometry [x', d] 
- outer geometry [X, g] 
Here, vector x' = (x',y')" represents the 
image coordinates, d is a vector of distortion 
parameters typical of the imaging system, X 
— (X,Y,Z) is a vector of object coordinates, and 
g is a vector of parameters of exterior orienta- 
tion. In a symbol form one can write for the 
imaging process 
X &d x" 
and for the reconstruction process 
(sao d) Ee X 
(1) 
(2) 
After deriving the unknowns g with the use of 
suitable control points and with a previous 
knowledge of d, one can start the routine in- 
tersection of individual model points X from 
stereoobservations x', x") 
(x', x") dag X (3) 
Some or even all of the parameters d can be 
considered as unknown and determined to- 
85 
gether with g during phase (2); however, in 
most instances parameters d are predeter- 
mined in separate calibrations. 
IMAGE GEOMETRY 
The imaging process performs a suitable 
conversion of data from a three-dimensional 
object space into a two-dimensional image 
space. This conversion is always achieved by 
the use of physical means which represent a 
real projecting system. This is true for both 
basic modes of instantaneous or sequential 
imaging. Depending on the position of the 
effective projection center, one can 
categorize the projection as central or parallel 
(Kratky, 1975b). The imaging rays are consid- 
ered as straight lines which can be broken in 
the effective projection centers, or in a more 
general way as curved lines substituting for 
suitable trajectories or flux lines of a physical 
field, e.g., in electron microscopy. 
To unify the various possibilities one can 
always base the photogrammetric reconstruc- 
tion on scaled projections using straight lines 
derived from corrected image coordinates. 
Whenever applicable the corrections should 
also include the effect of the original cur- 
vilinear projection. This approach yields 
x'+c= 1 PTAxX (4) 
where c are corrections for image distortions, 
p is scale factor which is variable in central 
projections and constant in parallel projec- 
tions, and AX = (AX,AY,AZ)T are object coor- 
dinates reduced with respect to a suitable 
reference point. Projection matrix P(3,2) rep- 
resents the orientation of the projection bun- 
dle or beam in the object coordinate system. 
In the central projection, P forms the upper 
part of the exterior rotation matrix P for the 
photograph, and the reference point for AX is 
given by the projection center (Jaksic, 1967). 
In the parallel projection matrix P is a product 
of a matrix O for oblique parallel projection 
and of the rotation matrix P 
PT = O PT 
where 
1:0: £ 
O = (5) 
0 1:79 
and (€, n) are parameters of the oblique paral- 
lel projection (Kratky, 1975b). Only the left 
part of Equation 4 is important for the first 
phase of on-line operations as a preparation of 
the model reconstruction. 
The image distortion is ususally described 
by a linear transformation