DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 5.7 Bitmapped
graphic image, rotated
Nyquist explained that an arbitrary signal can be reconstructed
accurately only if more than two samples are
taken of the highest-frequency component of the signal.
Applied to an image, there must be at least twice as
many samples per unit distance as there are image
elements. The checkerboard pattern in Figure 5.1 (on
page 43) doesn’t meet this criterion in either the
vertical or horizontal dimensions. Furthermore, the
titlebar element doesn’t meet the criterion vertically.
Such elements can be represented in a bilevel image
only when they are in precise registration – “locked” –
to the imaging system’s sampling grid. However, images
captured from reality almost never have their elements
precisely aligned with the grid!
Point sampling refers to capture with an infinitesimal
sampling aperture. This is undesirable in continuoustone
imaging. Figure 5.7 in the margin shows what
would happen if a physical scene like that in Figure 5.1
were rotated 14°, captured with a point-sampled
camera, and displayed with a box distribution. The
alternating on-off elements are rendered with aliasing
in both the checkerboard portion and the titlebar.
(Aliasing would be evident even if this image were to
be reconstructed with a Gaussian.) This example
emphasizes that in digital imaging, we must represent
arbitrary scenes, not just scenes whose elements have
an intimate relationship with the sampling grid.
A suitable presampling filter would prevent (or at least
minimize) the Moiré artifact of Figure 5.6, and prevent
or minimize the aliasing of Figure 5.7. When image
content such as the example titlebar and the desktop
pattern of Figure 5.2 is presented to a presampling
filter, blurring will occur. Considering only bitmapped
images such as Figure 5.1, you might think the blurring
to be detrimental, but to avoid spatial aliasing in
capturing high-quality continuous-tone imagery, some
overlap is necessary in the distribution of sensitivity
across neighboring sensor elements.
Having introduced the aliasing artifact that results from
poor capture PSFs, we can now return to the display
and discuss reconstruction PSFs (spot profiles).
CHAPTER 5 IMAGE STRUCTURE 47