340
(II) These transformations are in the structural sense far more easy, because
input and output are equally structured - that means, the same space.
Examples:
digital geometric transformations;
pure feature transformations.
Whereas with transformations of case (I) the mathematical background is
necessary to correctly transform between the various descriptions, in case (II)
the mathematical means are necessary to define the concrete instruction.
Table 3 allocates the three questions "Where from, where to, how".
Algorithmic approaches of digital photogrammetry are given in /2/.
From the integral view of geoinformatics analogies arise to data structuring
and algorithmization in remote sensing, photogrammetry and cartography.
Algebraic aspects (addition, multiplication, linearity) as well as topological
ones (metrics, norm, scalar product) meld in the defined structures. The mathe
matical problems can be integrated into generalizations of the Euclidean space.
Because functional analysis derives special solutions from general ones over
structural identities, it is this analysis, which allows a closed description.
The basic idea of allocating numbers to events and processes leads to a uniform
calculus of representing analogue and digital realizations.
Literature
/1/ Proß, E.: Die Integration digitaler Komponenten der Fernerkundung, Photo
grammetrie und Kartographie innerhalb der Geoinformatik sowie deren Be
schreibung durch mathematische Mittel und Methoden.
Flabilitation (in preparation).
/2/ Proß, E.: Konsequenzen einer photogrammetrischen Betrachtungsweise bei
der Lösung spezieller Aufgaben der Digitalphotogrammetrie mit seriellen
Rechnern. Vermessungstechnik, Berlin 38 (1990) 7, S. 224 - 226.
