Xmin$ X S Xmax (7)
min
in which X, and X, are known vectors,
To avoid solving a quadralic programming problem
we can substitute the variables according to fol-
lo wing expresion:
X = Ent Caen” End SSP (8)
In this case the formulas for the derivatives of
normal equations with respect io. the new variables
are: EC = S 2 (9)
This approach permits to solve the optimization
problem without constrains and in a more simple
way.
Accetding ta this approach the algorithm and the
corresponding piograHm ior oplimizaliun vf camera
station configuration for personal computer IBM PC
was elaborated (O. Kortchagina, 1991,. Chibu-
nichev, O.Kortchagina, 1992). This programm permits to
fulfil the following tasks: 1) The desing of starting
configuration of the fotogrammetric network. This
process is perfomed automaticaly for simple shapes
of the abjects (cylinder, sphere, cube and so on) and
in interactive mode for the objects o f comlex shapes.
2) The photogrammetric network optimization with
aulo matic change of photographs number in block. 3)
The bundle block adjustment for checking results of
optimization process.
EXAMPLES
Some examples of photogrammetric network desing
is illustrated in table 1 for the cylinder of 10m
diameter. Here f,u, m,,m,,mz are the initial data, and
s,D,m,,my,m, are the resultsof the design (f is the
focus of the camera; s is the number of photos; D is
the object-to- camera distace; m,,my,mz are standard
errors of object points determination after bundle
block adjustment using simulated photographs wich
correspond fo the optimal configuration of camera
statio ns.
Table |. Object points precision obtained after optimization process
req. precision simulation
o e e
m.m, mz 5 D m, m, mz
t
(mm) (mm) (mm)(mm)(mm) (m) (mm) (mm) (mm)
200 0.01 5 3 5 5 .17.2 i? 09 2.1
200 0.005 5 33 $ 5 17.2 0.6 20.4. 0.9
200 0.001 0.1 0.1 0.1 5 17.2 0.1 0.1 0.1
100 0.01 8 3 5 5 ¥7.2 2.3 ).7 2.9
100 0.005 5 3 5 5 17.2 2. 0.9 1.5
100 0.001 0.1 0.1 0.1 6 6.9 0.1 0.1 0.1
IN this table we can see that in some cases the
precision of the network after optimization is higher
than the required precision for 5 photos. The
programm reduces auto maticly the number of photos
to 4, becouse the required precision permits to do it.
But in these cases the overlap restriction works,
therefore these varianis of network are considered
0 ptimal.
Let's consider steps of the designing process for one
of the examples. Suppose that f = 100mm, # =
0.001mm, m, m,» mz- 0.1mm (the latter example in
table 1). Figure ! clearly demonstrates steps of the
desing process of the photogrammetric network with
such parameters. The first step (starting confi-
guration of camera station) is perfomed automaticly
on the basis of the approximate formula relating the
value of the standard errors of XYZ coordinates, to
the scale of photography and the precision of the
image coordinates measurements (C.Praser, 1984),
The location of the intermediate camera stations was
obtained as a result of the solution of the target
function (2). In this case the optimization process
was interrupted because of the overlap restriction
(the precision of the object point was my = 2mm, my =
2mm, m= 4mm at this moment). Therefore the sixth
camera station was added and the optimization
process wae continued. This process wae finished
only where the precision ichievos the required
values.
i
i
o> starting configuration of camera station
o— intermediate camera station during optimization
process
o> final camera station design
Pig. 1 Steps of design process.
These examples demonstraite that this method may
be used for photogrammetric netwark design. But it
is necessary to perform its comprehensive inves-
tigation.
REPERENCES
Chibunichev A., 1981. Conditionality of normal
equations in bundle block adjustment. (ig6GyuuueB
A., O6yCAOBHEHBOCTL HOPMANDEbIX ypaBHSHEÉR, BOo3-
EHKANMEKXK OPN ypaBHHBAHHH doTOrpaMMeTpEHWe-
CKEX ceTe B no cnocoliy caag30x. M an. ayaon. "l'en ge-
3223 H aspooTOcheMKa", 4: 87-93).
Chibunichev A., 1990, Optimization of photogram-
metric network design of industrialobjects (Hg6Gynumz-
"en A. OnTRMHSaNHES HpoexTRpOBaEBRS $oTOTpaMMeT:
DE"SeCKEX ChPMOK EHXKeHepHHX COOpyXxeHzR. Man.
By3os "leo ge3ma gH aspodorTOocoosMERa", 5: 87-95).
Chibunichev ÀA., Kortichagina O., 1992, Algorithm of
aptimal design of photogrammetric network for in-
dustrial objects. (Hub&ynumuues A., Kopsuaruzua O.
AXTOPETM npoerTEpoBaHHu ONTHMaAZXbHOÀÓ boTOrpaM:
METPHEYBCEOR CHOMEN HHAKBHSDpHBIK OO bexToB. Was.
By30B. "l'eogesua gu aspotoTocseMka", 1992, N 4.).
