U. Glaeser

FIGURE 28.5
image of reasonable quality, or to get a good progressively scanned sequence from an interlaced one, is
a nontrivial problem.
Image Sequences as Spatiotemporal Data
As discussed previously, the scanning process makes the precise specification of an image sequence
difficult (since every spatial point exists at a different time). Interlace complicates matters further. In the
remainder of this chapter, the simplifying assumption will be made that each point in a frame corresponds
to the same point in time. This is analogous to the digitization of motion picture film, or the sequence
which results from a CCD camera with a shutter. It is a reasonable assumption in progressive or interlaced
video systems when scene motion is slow compared to the frame rate. The series of frames are no longer
tilted in the spatiotemporal domain and can be “stacked” in a straightforward way to form a spatiotemporal
volume (see Fig. 28.5).
28.2 Some Fundamentals
Following are some notational conventions and basic principles used in the balance of this chapter. A
continuous sequence is denoted as u(
x,
y,
t),
v(
x,
y,
t),
etc., where x,
y are the continuous spatial variables
and t is the continuous temporal variable. Similarly, a discrete sequence is denoted as u(
m,
n,
p),
v(
m,
n,
p),
etc., where m,
n are the discrete (integer) spatial variables and p is the discrete (integer) temporal variable.
A 3-D System
As in 1-D and 2-D, a 3-D discrete system can be defined as
© 2002 by CRC Press LLC
An image sequence represented as a spatiotemporal volume, raytraced to exhibit its internal structure.
y( m, n, p)
= H[ x( m, n, p)
]
(28.1)
where H is the system function. In general, this function need be neither linear nor shift invariant. If
the system is both linear and shift invariant (LSI), it can be characterized in terms of its impulse response
h(
m,
n,
p).
The linear shift invariant system response can then be written as
∞
∑
∞
∑
∞
∑
y( m, n, p)
=
x( m′, n′, p′ )h( m– m′, n – n′, p – p′ )
m′=−∞ n′=−∞ p′=−∞
≡
x( m, n, p)
∗ h( m, n, p)
(28.2)