Results of Compression Tests
Summary:
Since I have collected over 100 data files and could concievably make thousands
of plots of the data, this page does not contain every single detail of the
compressors performance--there are probably a few details I have yet to
stumble upon! This page summarizes the main aspects of the compressor's
performance in as concise a way as possible. I have included the data files
and analysis software on the following page so that, if so inclined, one
can examine the data in more detail.
Do the PMEM Pages Perform As Expected ?
In general, a given image (busy, sky, atmospheric) compresses best under the
PMEM page designed for that image type when a B value of 0 is used. This
can be seen in the collage of test images. Also apparent in these
collages, however, is the fact that some images unexpectedly compress better
under a different page than expected. These fall into two main categories:
1) In the set of atmospheric images, there are a large number of pictures of
the moon which show up. In general, these images were taken at low phase
angle, and hence have a relatively low amount of contrast. Since the
atmospheric PMEM page (page 3) is designed for intermediate entropy values
(which most atmospheric images fall into), this is not as anomalous as it
may first seem. The difference in compression ratio between the atmospheric
PMEM page (page 3) and the busy page (page 0) for these images is generally
around 2 or less, so these images are borderline cases.
2) In the set of sky images, there are numerous images of Venus in which
Venus takes up the majority of the image frame and there is little black
sky. There is very little contrast in these images, however, and the
atmosphere of Venus appears very smooth (possibly a little out of focus).
Since the sky page (page 2) is designed for low entropy images, the fact that
these images compress best under the sky page is not surprising. The difference in compression ratio between the sky PMEM page (page 2) and the atmospheric
page (page 3) for these images is generally small, so these images are
also borderline cases.
How Does B value Affect the Choice of PMEM Page ?
When a Busy image is compressed at high levels, a large amount of
high spatial frequency information is discarded and the resulting data
can be more effectively coded for with an atmospheric PMEM page.
This effect seems to come into play only at high B values (~10) where the
data loss is so high that it is unlikely such values would be used. Even then,
the increase in compression ratio is generally small.
A similar effect probably also occurs in which atmospheric images will
compress better with
the sky page at high B values, but the fact that the sky page has a different
set of scale factors than the other pages makes a comparison between the two
pages difficult.
Difference Between PMEM Pages 0 and 1
PMEM page 1, as mentioned before, has a scaled quantization matrix which is
designed to discard more high frequency information from an image than the flat
matrix in PMEM page 0. While no detailed analysis has been performed thus far,
it can be shown that an image compressed under PMEM page 0 can be compressed
under PMEM page 1 with a lower B value and have essentially the same compression
ratio and RMS difference value. The difference, however, is that
compression with PMEM page 1 would better preserve the low spatial frequency
components of the image while compression under PMEM page 0 would
better preserve the high spatial frequency components of the image. This
factor should be taken into account if there are instances when either
high or low spatial frequency information is important for certain types of
analysis.
When is an Image a `Sky Image' ?
While no detailed analysis has been performed, a rough estimate can be placed
on how much black sky must be present in an image for it to qualify as a
'sky image'.
Moon Images: ~8/9 must be black sky (moon must comprise less than ~1/9 of
the image)
Venus Images: ~3/4 must be black sky (Venus must comprise less than ~1/4 of
the image)
The fact that Venus can be larger than the moon and still be a sky image is
due to the fact that Venus is generally a lower entropy target than the moon.
Relation Between Image Entropy and Compression Ratio / Data Loss
The general relationship between image entropy and the RMS difference between
the original and decompressed image is linear, while the relationship between
image entropy and compression ratio is liner in a log-log plot. A program
(available on the downloads page) which plots the RMS and compression ratio
values vs. entropy and displays the best fit lines and equations. The
four plots show the results for each PMEM page and the corresponding image type
at a B value of zero.
There is obviously a large amount of scatter in most of the plots. This
indicates that image entropy, as computed here, is not the best predictor
of compression ratio and RMS loss. I am currently working on an improved
prediction factor which takes into account scene contrast as well as the ratio
of black sky in an image. This may improve the correlation and decrease
scatter, but it will be impossible to obtain an exact relationship.
Relation Between B Value and Compression Ratio / Data Loss
In general, the effect of increasing B value on compression performance can
be demonstrated with the following plot. It is based on best fit lines
to the data for atmospheric images compressed with the atmpspheric PMEM page,
but plots constructed with data for the other image types have the same
general curve shapes.
Generally, the slope of the RMS difference lines increases and the compression
ratio curves flatten as the B value increases. Also, the spacing of both the
RMS lines and the compression ratio curves generally increases as B value increases. The following groups of plots show the data for specific images
from each image type (busy, sky, and atmospheric).
The following plot is for a busy image of the moon compressed under the busy
table (PMEM page 0). Essentially all of the busy images I used have the same
general compression profiles as in the following plot--a fairly flat response
at low B values and a relatively rapid increase in compression ratio and RMS
difference at higher B values.
The following two plots are for a moon and Venus sky image compressed under
the sky page (PMEM page 2).
In general, sky images have a rather chaotic response to increasing B value.
The compression ratio increases with B value, as expected, but the RMS
difference value often shows very little increase or an actual decrease
as B increases (the decrease is more prevalent in moon images than in Venus
images). The decrease in RMS difference does not occur with any other
combination of image type and PMEM page. The reason for this is unclear, as increasing B value should discard more information from an image and thus
increase the RMS loss. The test procedure and programs were checked multiple
times, however, so this behavior is definitely a quality of sky images
compressed under PMEM page 2 and not an error in the testing procedure.
The implication of this, obviously, is that increasing the B value (from 3 to 5,
for example) in the case of sky images will almost always give better
compression performance (higher ratio with the same or lower amounts of loss).
The final 2 plots are for a venus and a moon atmospheric image compressed under
PMEM page 3 (the atmospheric page). At low phase angle, remember, the moon
compresses best under the atmospheric PMEM page. For moon images, the
ratio and RMS curves are very similar to the curves for busy images. For
Venus images, however, there is generally a sharp jump in compression ratio
between B = 3 and B = 5 and the RMS curve stays relatively flat up to a B value
of 10. This sharp jump in compression ratio occurs with only a small increase
in RMS difference, so it would generally be advantageous to use a B value of 5
rather than a B value of 3 for imaging targets similar to Venus (Saturn and
Titan?).
Effect of GOB Length on Compression Ratio
As the GOB length decreases, more error correction headers are included
in the compressed image file and the total compression ratio decreases. The
plot below shows the actual data for three images of different entropies
compressed with a range of GOB values. Once the GOB length drops below
about 50, there is a sharp dropoff in compression ratio.
The next plot of the same data is done with the recoprocal of the compression
ratio plotted against the recoprical of the GOB length (L). A linear
relationship exists when the data is plotted this way. The Y intercept is
the recoprical of the compression ratio with no GOB headers. The slope is
a constant ranging from .080 to .095. I have thus far been unable to find
a direct relationship between the slope and any of the other factors involved
in compression.
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