DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 18.9 Response of
[1, 1] FIR filter operating
in the vertical domain,
scaled for unity gain, is
shown. This is a two-line
(1H) comb filter. Magnitude
falls as cos ω.
⎡1
1⎤
⎢ ⎥
⎣⎢
1 1⎦⎥
⎡1
2 1⎤
⎢ ⎥
⎢2
4 2⎥
⎢
⎣
1 2 1⎥
⎦
Figure 18.10 Separable
spatial filter examples
⎡1
1 1⎤
⎢ ⎥
⎢1
1 1⎥
⎢
⎣
1 1 1⎥
⎦
⎡0
0 1 0 0⎤
⎢
⎥
⎢0
1 1 1 0⎥
⎢1
1 1 1 1⎥
⎢
⎥
⎢0
1 1 1 0⎥
⎢
⎣0
0 1 0 0
⎥
⎦
Figure 18.11 Inseparable
spatial filter examples
1
0.5
0
0
0.5LA Frequency, ω, C/PW
LA (=1·fS )
(picture) samples per line, and these two samples are
presented to a comb filter like that of Figure 16.19, on
page 156, but having 639 zero-samples between the
two “ones,” then the action of the comb filter will be
identical to the action of a filter having two taps
weighted [1, 1] operating in the vertical direction. In
Figure 16.12, on page 153, I graphed the frequency
response of a one-dimensional [1, 1] filter. The graph in
Figure 18.9 above shows the response of the comb
filter, expressed in terms of its response in the vertical
direction. Here magnitude response is shown normalized
for unity gain at DC; the filter has a response of
about 0.707 (i.e., it is 3 db down) at one-quarter the
vertical sampling frequency.
Spatial filtering
Placing a [1, 1] horizontal lowpass filter in tandem with
a [1, 1] vertical lowpass filter is equivalent to computing
a weighted sum of spatial samples using the weights
indicated in the matrix on the left in Figure 18.10.
Placing a [1, 2, 1] horizontal lowpass filter in tandem
with a [1, 2, 1] vertical lowpass filter is equivalent to
computing a weighted sum of spatial samples using the
weights indicated in the matrix on the right in
Figure 18.10. These are examples of spatial filters. These
particular spatial filters are separable: They can be
implemented using horizontal and vertical filters in
tandem. Many spatial filters are inseparable: Their
computation must take place directly in the two-dimensional
spatial domain; they cannot be implemented
using cascaded one-dimensional horizontal and vertical
filters. Examples of inseparable filters are given in the
matrices in Figure 18.11.
CHAPTER 18 IMAGE DIGITIZATION AND RECONSTRUCTION 191