The contrast sensitivity function described in the Human vision section is given for frequencies in cycles/degree. As we want to compute our metric in image space, frequencies should be converted from cycles/degree to pixels/degree. This conversion is simple and follows straight forward from the viewing geometry for a given viewing distance. Actually the whole metric is viewing distance dependent. (The other above mentioned metrics are also viewing distance dependent, although it is not explicitly mentioned in the above papers). Consider, once more, our picture with the black and white stripes. Let the stripes be 1 cm wide now. You will agree, the stripes will be clearly and sharply distinguishable if the image is observed from 50 cm. But what happens if the viewing distance is, let's say, 100 meters. The image becomes gray again. Let us derive the cycles/degree to pixels/degree conversion now. Actually we are interested in how many pixels contains one visual degree. We will denote the viewing distance given in cm as d, the display size in cm as W, the display resolution in pixels as R, the width of the display portion covered by 1 visual degree given in cm as w, and the number of pixels in w as r (see fig. 8.1).
Now, according to the Shannon sampling theorem [Glas95], the maximum frequency that can be realized using r pixels is r/2 cycles.
Let us illustrate this conversion using the next example: Our
display device is a CRT monitor. The width of the monitor W is 34
cm. The display resolution is 1280 pixels, and the viewing distance
is 50 cm. We are interested in the number of pixels r contained in one
(
) visual degree. According to (8.2) r is:
Since the maximum displayable frequency is r/2, frequencies above
16.427 cycles/degree cannot be displayed. They represent the sub-pixel
range (see fig. 8.2). If we want to exploit our visual system
to its maximum we should move the maximum frequency toward 60
(remember that the contrast sensitivity function is practically 0
above 
, see section 2.3.5 Contrast Sensitivity
Function), either by increasing the viewing distance d, or
resolution R (see equation 8.2). If the distance d is
increased further, such that the maximum frequency goes above 60, we
are not able to see the individual pixels any more. Larger pixel areas
will become the essential image elements now. Note that if the changes
on the pixel basis are important we can decrease the viewing distance
d in order to move the maximum frequency near the peak of the
contrast sensitivity function A(f).
Figure 8.2: Subpixel range for maximum displayable frequency of 22 cycles/degre
