ANALYTICAL ON-LINE SYSTEMS IN CLOSE-RANGE PHOTOGRAMMETRY
foe
X ———X—DL—-X
T K
Using a truncation of T equivalent to Equa-
tion 10 the new operational formulas are
PARTIAL RETURN
x' = AT'Ax — ¢ = A\PTKAx — ¢
X =C + mKx ;
X = vx
(12)
Finally, if one desires, the whole orienta-
tion can follow the classical routine of the
relative-absolute orientation. The measure-
ments are arranged in two steps yielding in-
termediate model coordinates X after the rela-
tive orientation and final coordinates x after
the absolute orientation. With the notation of
R for the matrix of relative orientation, A for
the matrix of absolute orientation, L for the
matrix to level the model, and K for the matrix
of azimuthal rotation, one can write
P-AR , A-KL , P -— KLR
and eventually arrive at the following for-
mulas:
(a) after solving five parameters for R,, R,
x'= \RTA£ —-c ,
RELATIVE (13a)
X= mAï + dX ,
(b) after solving seven parameters for m, A,
dX
x= MLR) TAx me,
ABSOLUTE|X =mKx+dX ‚, (13b)
xX = vx ;
Mathematical considerations. Mathemati-
cal formulations suitable for applications in
close range photogrammetry are discussed in
detail by Wong (1975) in his invited paper to
the XIIIth ISP Congress. For this reason,
the analysis here is limited to some special
aspects typical of on-line systems.
In general, the basic equation for perspec-
tive bundles is the well known collinearity
condition which can be modified as an affin-
ity condition to fitthe relations in projections
with parallel beams. Both conditions can be
further extended to include the unknown
parameters of inner orientation and of image
distortions. For example a more general for-
mulation of the collinearity equation
(Abdel-Aziz and Karara, 1971; Jahn, 1975) in-
cluded the elements of interior orientation
extended by two additional parameters to
compensate for a general affine distortion of a
photograph.
87
An on-line analytical system can handle a
multiple orientation of images although the
final processing can obviously proceed only
in stereopairs sequentially formed from ap-
propriate combinations of images. The model
reconstruction is based on a simultaneous
micro-block adjustment using suitable mod-
els for the image geometries. This arrange-
ment has a great self-calibrating potential.
The procedure is applicable to multiple
stereoviews based on the use of mirrors, or to
several smaller sized pictures as long as they
can be simultaneously accommodated in the
photocarriers of the analytical on-line in-
strument.
An exclusive use of a single collinearity or
affinity condition leads to a uniform formula-
tion of the equation system. One can avoid
using an additional coplanarity condition for
intersections of conjugated rays, which is in-
adequate for a multiple orientation anyway.
In this instance the unknown coordinates of
intersected points are sequentially elimi-
nated from the solution in a point-by-point
procedure well known in photogrammetric
bundle adjustments.
In the formulation of the least squares ad-
justment it is advantageous to consider the
initial linearized system of condition equa-
tions with corrections v, unknown parame-
ters g, and condition residuals u
Av =Bg +u =0 (14)
as an equivalent to a system of parametric
equations based on quasi-observations u and
associated weights P
Bg--u-zw, P-(AAT- (15)
Weighting ofthe original observations is neg-
lected here. If required, their variance-
covariance matrix Q is introduced and then
the expression for P in Equation 15 is mod-
ified into (AQAT)-1!.
Assuming a suitable partitioning B — [B,
B,|andgt —(g? g7 ), the elimination of model
coordinates g, leads to an equivalent system
of quasi-observations u which are newly cor-
related through a weight matrix P,. This sys-
tem contains only orientation parameters g,
Bi +U = w >
P,-P —PB(BIPB)3BTP . (16
These equations are used to contribute se-
quentially towards the normal equations
BIP,B,g, + BIP,u =
In this scheme the given control
coordinates can be weighted with the estima-
tions of P, and regarded as additional con-
