DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 5.6 Moiré pattern
a form of aliasing in two dimensions,
results when a sampling
pattern (here the perforated
square) has a sampling density
that is too low for the image
content (here the dozen bars,
14° off-vertical). This figure is
adapted from Fig. 3.12 of
Wandell’s Foundations of Vision
(cited on page 195).
Sampling aperture
In a practical image sensor, each element acquires information
from a finite region of the image plane; the
value of each pixel is a function of the distribution of
intensity over that region. The distribution of sensitivity
across a pixel of an image capture device is
referred to as its sampling aperture, sort of a PSF in
reverse – you could call it a point “collection” function.
The sampling aperture influences the nature of the
image signal originated by a sensor. Sampling apertures
used in continuous-tone imaging systems usually peak
at the center of each pixel, fall off over a small distance,
and overlap neighboring pixels to some extent.
In 1915, Harry Nyquist published a landmark paper
stating that a sampled analog signal cannot be reconstructed
accurately unless all of its frequency components
are contained strictly within half the sampling
frequency. This condition subsequently became known
as the Nyquist criterion; half the sampling rate became
known as the Nyquist rate. Nyquist developed his
theorem for one-dimensional signals, but it has been
extended to two dimensions. In a digital system, it
takes at least two elements – two pixels or two scanning
lines – to represent a cycle. A cycle is equivalent to
a line pair of film, or two “TV lines” (TVL).
In Figure 5.6 in the margin, the black square punctured
by a regular array of holes represents a grid of small
sampling apertures. Behind the sampling grid is a set of
a dozen black bars, tilted 14° off the vertical, representing
image information. In the region where the
image is sampled, you can see three wide dark bars
tilted at 45°. Those bars represent spatial aliases that
arise because the number of bars per inch (or mm) in
the image is greater than half the number of apertures
per inch (or mm) in the sampling lattice. Aliasing can be
prevented – or at least minimized – by imposing
a spatial filter in front of the sampling process, as I will
describe for one-dimensional signals in Filtering and
sampling, on page 141, and for two dimensions in
Image presampling filters, on page 192.
46 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES