Databases Reference
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F I GU R E 18 . 15
Original Elif image.
Example18.6.2:
The image Elif, shown in Figure
18.15
, was encoded using the fractal approach. The original
imagewas of size 256
256, and each pixel was coded using 8 bits. Therefore, the storage space
required was 65,536 bytes. The compressed image consisted of the transformations described
above. The transformations required a total of 4580 bytes, which translates to an average rate
of 0.56 bits per pixel. The decoding process started with the transformations being applied to
an all-zero image. The first six iterations of the decoding process are shown in Figure
18.16
.
The process converged in nine iterations. The final image is shown in Figure
18.17
. Notice
the difference in this reconstructed image and the low-rate reconstructed image obtained using
the DCT. The blocking artifacts are for the most part gone. However, this does not mean that
the reconstruction is free of distortions and artifacts. They are especially visible in the chin
and neck region.
×
In our discussion (and illustration) we have assumed that the size of the range blocks is
constant. If so, how large should we pick the range block? If we pick the size of the range
block to be large, we will have to send fewer transformations, thus improving the compression.
However, if the size of the range block is large, it becomes more difficult to find a domain
block that, after appropriate transformation, will be close to the range block, which in turn will
increase the distortion in the reconstructed image. One compromise between picking a large
or small value for the size of the range block is to start out with a large size and, if a good
enough match is not found, to progressively reduce the size of the range block until we have
either found a good match or reached a minimum size. We could also compute a weighted
sum of the rate and distortion
J
=
D
+
β
R
