Databases Reference
In-Depth Information
T A B L E 14 . 11
Alternate four subimages.
Low-Low Image
Low-High Image
10
12
13
11
0
0
−
0.5
−
0.5
11
9.5
9
9.5
1
−
0.5
−
2
1.5
11
8
6
6
3
3
1
−
1
12
9
7
6
0
−
1
−
1
0
High-Low Image
High-High Image
0
−
2
1
3
0
0
0
0
0
−
1.5
0
1.5
0
0.5
1
−
0.5
0
−
1
−
1
1
0
0
0
0
0
0
−
1
0
0
−
2
1
0
are as uniform as possible. For example, if we did not have the relatively large values in the
first column of the high-low subimage, we could choose a quantizer with a smaller step size.
In this example, this effect is limited to a single row or column because the filters use a
single past value. However, most filters use a substantially larger number of past values in the
filtering operation, and a larger portion of the subimage is affected.
We can avoid this problem by assuming a different “past.” There are a number of ways
this can be done. A simple method that works well is to reflect the values of the pixels at the
boundary. For example, for th
e seq
uence 6 9 5 4 7 2
···
, which is to be filtered with a three-tap
filter, we assume the past as
96
695472
. If we use this approach for the image in
Example
14.12.1
, the four subimages would be as shown in Table
14.11
.
Notice how much sparser each image is, except for the low-low image. Most of the energy
in the original image has been compacted into the low-low image. Since the other subimages
have very few values that need to be encoded, we can devote most of our resources to the
low-low subimage.
···
14.12.1 Decomposing an Image
Earlier a set of filters was provided for one-dimensional subband coding. We can use those
same filters to decompose an image into its subbands.
Example14.12.2:
Let's use the eight-tap Johnston filter to decompose the Sinan image into four subbands. The
results of the decomposition are shown in Figure
14.29
. Notice that, as in the case of the
image in Example
14.12.1
, most of the signal energy is concentrated in the low-low subimage.
However, there remains a substantial amount of energy in the higher bands. To see this more
clearly, let's look at the decomposition using the 16-tap Johnston filter. The results are shown
in Figure
14.30
. Notice how much less energy there is in the higher subbands. In fact, the
high-high subband seems completely empty. As we shall see later, this difference in
energy
compaction
can have a drastic effect on the reconstruction.
