Databases Reference
In-Depth Information
F I GU R E 14 . 31
Decomposition of Sinan image using the the eight-tap
Smith-Barnwell filter.
14.12.2 Coding the Subbands
Once we have decomposed an image into subbands, we need to find the best encoding scheme
to use with each subband. The coding schemes we have studied to date are scalar quantization,
vector quantization, and differential encoding. Let us encode some of the decomposed images
from the previous section using two of the coding schemes we have studied earlier, scalar
quantization and differential encoding.
Example14.12.3:
In the previous example we noted the fact that the eight-tap Johnston filter did not compact
the energy as well as the 16-tap Johnston filter or the eight-tap Smith-Barnwell filter. Let's see
how this affects the encoding of the decomposed images.
When we encode these images at an average rate of 0.5 bits per pixel, there are 4
2
bits available to encode four values, one value from each of the four subbands. If we use the
recursive bit allocation procedure on the eight-tap Johnston filter outputs, we end up allocating
1 bit to the low-low band and 1 bit to the high-low band. As the pixel-to-pixel difference in
the low-low band is quite small, we use a DPCM encoder for the low-low band. The high-low
band does not show this behavior, which means we can simply use scalar quantization for the
high-low band. As there are no bits available to encode the other two bands, these bands can
be discarded. This results in the image shown in Figure
14.32
, which is far from pleasing.
However, if we use the same compression approach with the image decomposed using the
eight-tap Smith-Barnwell filter, the result is Figure
14.33
, which is much more pleasing.
To understand why we get such different results from using the two filters, we need to look
at the way the bits were allocated to the different bands. In this implementation, we used the
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