2. Algorithmization for serial computers 
In processing digital images the primary contradiction between the sequen 
tial storage of digital images and a logical two-dimensionality of real 
images becomes obviously. Leaving out future digital two-dimensional storages 
and two-dimensionally working computers, so at present only an algorithmical 
solution of this contradiction is possible. 
These contradictions can be solved on two levels: 
(1) reduction of higher-dimensional algorithms to an one-dimensional 
principle or 
(2) more-dimensional data supply for special array processors. 
Most present solutions move on level (1), because these solutions are only 
limited in regard of the possibilities of computer technology (e. g. main 
memory size, access time, "free moving" in the data set). Future solutions 
will more tend to level (2), whereby the processes in the computer are 
becoming more an more similar to those, proceeding in the human eye-brain- 
system. Increasingly methods of artificial intelligence will be used thereby 
(see also /2/). For methods of digital image processing - i. e., for digital 
photogrammetric methods, too - the position discretization in equal distances 
is a decisive precondition for constructively reaching algorithmic solutions. 
This regularity transforms - from the mathematical point of view - the repre 
sentation form from integrals to series. Exactly this transition provides the 
functional analytical path to an uniform model of analogue and digital methods. 
The most important mathematical backgrounds for this are the existence of a 
discrete eigenfunction system in the form of harmonic functions as well as the 
HILBERT space equivalence between the spaces of the square-integral functions 
L 2 and the square-summable series l 2 (see /1, 3/). 
3. Examples for algorithmic reduction 
In /4/ a row-invariant transformation method is presented. Thereby local 
scale variations, which shall correct the area distortions, are carried out 
by local stretchings and shrinkings within the image row - hence realized 
one-dimensionally. On account of the charakteristics of the correction 
function (small increase, piecewise linearizable) this transformation can be 
realized as a direct transformation without extensive resampling. Also in /4/