^ 
> 
ie analysis it 
| in time di- 
—continuity) 
eness to the 
e image cube 
y mathemat- 
lation meth- 
| this fact is 
ion of prob- 
ds to finding 
| functionals 
es (e.g. least 
n [6] such a 
1onstrated. 
ne Pro- 
efine the ge- 
nages of the 
ning contin- 
' discrete on 
uently these 
in the image 
ith the help 
frequencies, 
tion calculus 
"he minimiz- 
R equations, 
ons (see also 
screte planes 
'ralization is 
and to get a 
s possible to 
ss of objects. 
in the image 
Xf the image 
respondence 
erence equa- 
| sense to the 
ive scheme it 
photogram- 
esses can be 
‚tions within 
and qualified 
ı dependence 
: use of prin- 
; with image 
jecause from 
  
  
space 
continuous discrete 
time 
: image digital 
continuous ; 
flow image flow 
: image digital 
discrete 5 : 8 
sequences images 
  
  
  
  
Figure 2: Structure Characterization 
the point of view of structure categories the discrete- 
ness and the continuum are different. 
Only an adaptive problem-depended digitalization in 
space and time leads to a regular grid structure for 
difference equation in zj, y; and t,: 
A(z), (mo i()zo 
By separation and with a multiindex (s) this equation 
is transfered into 
76) — A(z 9-7?) 
In an example in [2] comparing variation methods with 
least squares methods this technique is demonstrated. 
4 Outlook 
The modelling in real-time mapping encloses the def- 
inition of suitable photogrammetric principles of con- 
servation (image intensity, image energy, velocity field, 
...) and corresponding realizations, which are as a 
rule linear combinations of mathematical operators 
like an equation of weighted sums of operators, that 
must be effectively solved by iteration of difference 
equations determined by image convolutions. 
By using several images or a quasi-continuous image 
cube methods in real-time techniques essentially dif- 
fer. Another view to modelling realizes the image 
cube trajectories as parallaxes. The velocity is the 
first derivative at the time and the velocity variation 
is the second derivative or the acceleration. The par- 
allax can be interpreted as result of a projection in 
time direction within the image cube — also the dig- 
itized image flow corresponds to the parallax — and 
this results in the discretization distance in time direc- 
tion being rougher and also influencees the switching 
strategy between processing direction in an algorith- 
mic solution. 
457 
I hope that this paper could contribute to the discus- 
sion of mathematical principles , methods, and back- 
ground in modern mapping techniques and data base 
modelling. 
References 
[1] Foerstner,W.: Objektmodell fuer Fernerkundung 
und GIS, Jahrestagung der DGPF, Cologne, 1991 
[2] Hahn,M.; Pross,E.: Bildzuordnung nach dem 
Variationsprinzip — ein Vergleich mit Kleinste- 
Quadrate-Methoden, Zeitschrift fuer  Photo- 
grammetrie und Fernerkundung 4(60), pp. 116- 
123, Karlsruhe, 1992 
— 
wo 
à 
Leberl,F.: The Promise of Softcopy Photo- 
grammetry. In: Ebner, Fritsch, Heipke (Eds.): 
Digital Photogrammetric Systems, Wichmann, 
Karlsruhe 1991, pp. 3-14 
[4 
—À 
Novak,K.: Real-Time Mapping Technology, In- 
tern. Archives of Photogrammetry and Remote 
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[6] Mueller,B.; Hahn,M.: Parallel Processing — The 
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[6] Poggio, T.; Torre, V.; Koch,Ch. (1985): Computa- 
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317, pp. 314-319 
[7] Pross,E.: Describing Digital Photogrammetry by 
Functional Analytical Methods, Intern. Archives 
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[8] Pross,E.: Digitale Komponenten von Fernerkun- 
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[9] Pross,E.: Die Bedeutung der Funktionalanalysis 
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