DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 18.1 Horizontal domain
Figure 18.2 Vertical domain
Figure 18.3 Temporal domain
Figure 18.4 Spatial domain
Image digitization
and reconstruction 18
In Chapter 16, Filtering and sampling, on page 141,
I described how to analyze a signal that is a function of
the single dimension of time, such as an audio signal.
Sampling theory also applies to a signal that is
a function of one dimension of space, such as a single
scan line (image row) of a video signal. This is the horizontal
or transverse domain, sketched in Figure 18.1 in
the margin. If an image is scanned line by line, the
waveform of each line can be treated as an independent
signal. The techniques of filtering and sampling in
one dimension, discussed in the previous chapter, apply
directly to this case.
Consider a set of points arranged vertically that originate
at the same displacement along each of several
successive image rows, as sketched in Figure 18.2.
Those points can be considered to be sampled by the
scanning process itself. Sampling theory can be used to
understand the properties of these samples.
A third dimension is introduced when a succession of
images is temporally sampled to represent motion.
Figure 18.3 depicts samples in the same column and
the same row in three successive frames.
Complex filters can act on two axes simultaneously.
Figure 18.4 illustrates spatial sampling. The properties
of the entire set of samples are considered all at once,
and cannot necessarily be separated into independent
horizontal and vertical aspects.
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