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Reversible compression of low order bits in digital images
(Method is patented in U.S. 7315266)
The compression of high quality photographic images is performed based on similarities
in rows, columns, colors or separated repeated fragments. There is, however, one more correlation
that is slipped out of attention or researchers. It is correlation between high order
bits and low order bits within RGB structure. This correlation exists not in every
image but in many of them, for example in
known published 24 Kodak images used by many companies for compression benchmarks
( bitjazz , for example).
This correlation is so strong that image palette can be used as look up table for
prediction of low order bits based on high order counter part and low order bits can
be compressed separately and independently from high order bits. This leads to possibility
of improvement of any existing algorithm by excluding low order bits and processing
them separately. The details along with code sample can be found in the article
Reversible Compression of Low Order Bits in Digital Images
Table 2. below contains the comparison of compression ratios with and without
separate processing of low order bits. The images are compressed by the method close to one
published in article of S.A. Martucci 'Reversible
compression of HDTV images using median adaptive prediction and arithmetic coding' in Proceedings
of IEEE ISCAS, May 1990, pp. 1310-1313. The ratios are shown in coupled figures as
2.26/2.69. The number shown on the top 2.26 is compression ratio when only mentioned above method
is applied. The number below 2.69 is compression ratio achieved when same algorithm was used along with
suggested technique of separate processing of low order bits. Average improvement is about 18 percent.
Both methods are lossless. Establishing a record was not an objective. The goal was to compare results
for separate processing of low order bits,
because the same technique can be used along with other, possibly, more effective
methods (wavelet transforms, for example). Some comparison to other software is shown in
table 1. The number in the table is total size of all 24 files when compression is
applied separately to each of them. All original images are 768 * 512 RGB (that is 28,311,552 bytes).
The list of companies is limited to those whose programs are easy
available for test. It is not even close to some sort of exhaustive set and there are
other companies and software versions that claim better compression but not freely
available for testing or need significant time to install and test. To avoid misleading of visitors
I have to add that very impressive compression by PAQ8P achieved for very long time such as about
36 seconds per image, while all other programs did it for sort of reasonable time between 1 and 3 sec.
Table 1. Overall compression for 24 images with different programs
| Method | Martucci 1990 | JPEG2000 | WinRK 2.1.6 |
This article | HD Photo | PAQ8P | BMF v.1.1 Option -F |
| Reference | IEEE ISCAS |
Luratech |
WinRK |
this method |
dpktools.zip |
PAQ8P |
BMF |
| Size | 12,005,203 | 11,327,776 | 11,945,646 |
10,196,432 |
12,855,465 | 8,281,918 | 10,992,592 |
Table 2. Individual compression ratios with and without separate processing of low-order bits
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| 2.26 / 2.69 |
2.39 / 2.91 |
2.81 / 3.29 |
2.33 / 2.78 |
2.04 / 2.35 |
2.33 / 2.75 |
2.68 / 3.17 |
2.08 / 2.38 |
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2.58 / 3.14 |
2.54 / 3.07 |
2.37 / 2.85 |
2.70 / 3.16 |
1.91 / 2.21 |
2.15 / 2.52 |
2.42 / 2.74 |
2.63 / 3.17 |
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| 2.48 / 3.02 |
2.01 / 2.36 |
2.30 / 2.77 |
2.97 / 3.25 |
2.28 / 2.73 |
2.17 / 2.55 |
2.60 / 2.97 |
2.22 / 2.56 |
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