Digital Signal Processing Reference
In-Depth Information
Fig. 6
Subsampling of an
image by a factor of two in
horizontal and vertical
direction
i(x,y,t)
o(x,y,t)
A
B
C
4.1
Motivation: Processing of Multidimensional Arrays
by Sliding Window Algorithms
Figure
6
exemplarily depicts a local image processing algorithm in form of image
subsampling. It aims to reduce the image size by a factor of two in both horizontal
and vertical direction. The input image is supposed to have six columns and four
rows. Consequently, the output image consists of three columns and two rows.
Node
A
is the source of the system representing an image interface such as an input
DVI connector. Node
A
thus forwards the unaltered image to the next node
B
.It
performs the proper subsampling, producing an output image having half the width
and height of the corresponding input image. Note
C
finally corresponds to a sink,
representing for instance an output DVI connector.
In principle the subsampling can be implemented by simply discarding every
other pixel in both horizontal and vertical direction. Section
3
introduced cor-
responding modeling techniques. However, such an approach typically leads to
computes the weighted mean value over a number of neighbor pixels. The weights
can be derived by corresponding filter design techniques. Mathematically, the output
image can thus be expressed as
α
2
∑
β
2
∑
b
=
−
β
1
i
)
(1)
∀
0
≤
x
<
w
o
:
o
(
x
,
y
,
t
)=
(
2
·
x
−
a
,
2
·
y
−
b
,
t
)
·
f
(
a
,
b
∀
0
≤
y
<
h
o
a
=
−
α
1
i
(
x
,
y
,
t
)
if 0
≤
x
<
w
i
,
0
≤
y
<
h
i
i
(
x
,
y
,
t
)=
(2)
...
otherwise
where
w
i
is the input image width,
w
o
=
w
2
is the output image width,
h
i
is the input image height,
h
2
is the output image height,
h
o
=
+
α
+
,
α
≥
α
1 is the filter width (typically
α
0),
1
2
1
2
+
β
+
,
β
≥
β
1 is the filter height (typically
β
0),
1
2
1
2
(
,
)
f
a
b
are the filter weights or coefficients,
