Full text: Modern trends of education in photogrammetry & remote sensing

193 
t3= 0 Indicates that T Is singular respectively, 
T*=T-1 of (2.3.1) cannot exist and Illustrates the 
Impossibility of reconstruction of a spatial object 
from one single Image. But because of det(T) = 0 
the homogeneous systems (2.3.3) become resolvable 
and produce the affine coordinates uom of the two 
centers of projection. 
Using (2.3.5) the relations 
Ti UM* 
To + tri-TojuM^ÍTz-To )um 2 -toUM 3 
and, consequently, for each Image the two equations 
{U 1 (tl-tO)~T1lUM 1 +U 1 (T2 —to)UM 2 ~U 1 tOUM 3 =-U 1 to 
u 2 (tl-to)ynL+{U 2 (T 2 *t0)-t2)UM 2 -U 2 tOUM 3 =-U 2 tO, 
arise. These are, just as usual, four equations for 
the three unknown spatial affine coordinates um 1 . 
In this way every pair of homologous points of P« , 
Ps delivers a point of the model space Pm, from 
which the desired orthonormal coordinates may be 
found by an inverse affine transformation. 
3. Final remarks. 
This paper intended to show by means of two 
examples, how projective geometry influences the 
conventional methods of photogrammetry. The most 
important difference is, that the number of control 
points or correlation points and, consequently, the 
expenditure of work increases. On the other side 
non-metric cameras or measuring devices can be used 
and all relations are linear. Therefore, projective 
methods will also be very useful 1 for photogram- 
metry by digital images and stereovideometry. 
From the educational point of view, the disadvan 
tage of a rather abstract geometry exists. However 
on the other hand a more general insight is gained, 
which enables also the deduction of the special 
relations of or thononnal ized metric systems. More 
over, a lot of problems will result from practical 
applications and will give new stimulations to 
photograrmnetri c i nvest i gat i on. 
References: 
Brandstätter G.: Fotogrametria proyectiva, pro 
cesamiento de imágenes digitales, métodos de tele- 
deteccíon. VI curso de geodesia superior, instututo 
de astronomía y geodesia, Universidad Complutense 
de Madrid, octubre 1989 
Fuchs H.: Projektive Geometrie; Anwendungen in 
Photogrammetrie und Robotik. Mitteilungen der geo 
dätischen Institute der Technischen Universität 
Graz, Folge 63, August 1988 
Hohenberg F. u. J. Tschupik: Die geometrischen Grundla 
gen der Photogrammetrie - in Handbuch der Vermes 
sungskunde Jordan/Eggert/Kneissl, Band IIIa/3, J.ß, 
Metzlersche Verlagsbuchhandlung, Stuttgart 1972 
Rinner K.: Studien über eine allgemeine vorausset 
zungslose Lösung des Folgebildanschlusses. 
Österreichische Zeitschrift für Vermessungswesen, 
Sonderheft 23, Wien 1963 
Wolf P.R.: Elements of Photogrammetry. International 
Student edition, Mc Graw-Hill Kogakusha ltd., 1974
	        
Waiting...

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.