Databases Reference
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an image of an object with sharp edges in front of a relatively plain background. The number of
pixels that occur on edges is quite small compared to the total number of pixels. Therefore, if
we allocate bits based on average variances, the coefficients that are important for representing
edges (the high-frequency coefficients) will get few or no bits assigned to them. This means
that the reconstructed image will not contain a very good representation of the edges.
This problemcan be avoided by using a different approach to bit allocation known as
thresh-
old coding
[
195
,
104
,
196
]. In this approach, which coefficient to keep and which to discard is
not decided a priori. In the simplest form of threshold coding, we specify a threshold value.
Coefficients with magnitude below this threshold are discarded, while the other coefficients
are quantized and transmitted. The information about which coefficients have been retained is
sent to the receiver as side information. A simple approach, described by Pratt [
104
], is to code
the first coefficient on each line regardless of the magnitude. After this, when we encounter a
coefficient with a magnitude above the threshold value, we send two codewords: one for the
quantized value of the coefficient and one for the count of the number of coefficients since the
last coefficient with a magnitude greater than the threshold. For the two-dimensional case, the
block size is usually small, and each “line” of the transform is very short. Thus, this approach
would be quite expensive. Chen and Pratt [
196
] suggest scanning the block of transformed
coefficients in a zigzag fashion, as shown i
n
Figure
13.7
. If we scan an 8
8 block of quantized
transform coefficients in this manner, we will find that, in general, a large section of the tail
end of the scan will consist of zeros. This is because, generally, the higher-order coefficients
have smaller amplitude. This is reflected in the bit allocation table shown in Table
13.4
.Aswe
×
F I GU R E 13 . 7
The zigzag scanning pattern for an 8
×
8 transform.
