act 
ic 
ite 
vay 
Lng 
ic 
d, 
ind 
ng 
Ire 
"ms 
en 
it 
Ch 
be 
in 
re 
st 
.nt 
th 
h- 
ve 
al 
th 
an 
ire 
re 
ime 
‘he 
is 
il. 
)l- 
‚th 
In order to answer these questions we need a model for the digitizing 
process that allows us to make an analysis and decide what parameters 
are of interest. Here, firstly quality measures of photographic images 
and their relation to the digital image will be considered. Then a 
general model of a digitizer is presented. The model consists of two 
parts. The first models the quantization in space and the second 
quantization of the grey levels in the image. 
The models are based on statistical optics and signal theory. Some of 
the fundamental theorems are valid only when restrictions are imposed 
on the input signal or the image. Working with real images these 
underlying assumptions will sometimes be violated. 
3. RESOLUTION AND PIXEL SIZE 
3.1 Sampling in the Space Domain 
The digital image is constructed from the photograph by sampling at 
regular intervals. In each sampling point the intensity of the image 
is measured and converted to a number. According to the sampling 
theorem (O'Neill, 1963) it is sufficient to sample a function with an 
interval A < 1 / 2R, where R is the maximum frequency. Such sampling 
permits complete reconstruction of the original function and no 
information is lost. 
When digitizing an image the interval A equals the distance between 
the pixel centers. The formulation of the theorem quoted above applies 
to onedimensional signals. The image considered as a signal is 
two-dimensional. The frequency associated with images is the spatial 
frequency or lp/mm. With square pixels and arbitrary orientation of 
the lines in the image, the sampling must be made with the interval: 
A« 1:2 SER. ( 3.1 ) 
The sampling theorem is valid under the condition that the input 
signal is band limited. The lens in an optical imaging system works as 
a low-pass filter in the frequency domain. As a result the image will 
always be band limited. The problem is how to estimate R in the for- 
mula above to permit a proper choice of the sampling interval A. 
3.2 Resolution. Modulation Transfer and Threshold Modulation 
Image quality and performance of photographic systems are evaluated 
in terms of resolution, Modulation Transfer Functions (MTF) and 
granularity ( Brock, 1970 ). Interpreting frequency as lp/mm we can 
use resolution to decide how to sample the image in accordance with 
the sampling theorem quoted in the preceding section. Then the choice 
of R, or cut off frequency will give the appropriate sampling 
interval, or pixel size A. Working with lenses for photogrammetric 
purposes, in most cases the lens is the limiting factor. Thus the 
resolution of the lens could be taken as the criterion. A still better 
solution is to use system resolution. 
The Modulation Transfer Function describes how modulation transfer in 
141