Lossless binary image compression using logic functions and spectra

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Lossless binary image compressionusing logic
functions and spectra

• Bogdan J. Falkowski
• Computers and Electrical Engineering, Vol. 30,
  2004, pp 1743.
• Speaker Ho, Yu An (???)
• Date 2004/07/26

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Outline

• Introduction
• Cube Encoding
• Boolean switching function
• Novel technique
• Experimental results
• Conclusions

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Introduction
010000001010111
Reduce size
0101011010111
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Cube encoding (1/3)
Data structure for internal representation of
cube.
Example
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Cube encoding (2/3)
10 01 00 00
Cube encoding
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Cube encoding (3/3)
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Optimum polarity for the fixed polarity
Reed-Muller (FPRM) expansion (1/4)
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Optimum polarity for the fixed polarity
Reed-Muller (FPRM) expansion (2/4)
Chosen 101
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Optimum polarity for the fixed polarity
Reed-Muller (FPRM) expansion (3/4)
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Novel technique

• File extraction
• Image differencing
• Segmentation and classification
• Partitioning into rectangular regions
• Coding scheme

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File extraction
Multiple of 16 to handle images of different
sizes.
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Image differencing
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Segmentation and classification
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Partitioning into rectangular regions
disjoint
non-disjoint
0 all-black, 1 all-white or 2 mixed
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Coding scheme
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Coding scheme
Vertices (5,5)
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Coding scheme
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Coding scheme
Each mixed block is split into four smaller
blocks.
Type A
Type B
Type C
Type D
Type E
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Coding scheme
A 0s, B 1s and C cube
The number of 1s is less than three, minterm
coding is applied. The number of 1s is greater
than two but less than nine, coordinate data
coding is applied. If the GPMPRM expansion
contains less than three cubes, the block is
compressed as cubes.
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Minterm coding
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Coordinate Data Coding
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GPMPRM Cubes
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Coding scheme
The number of 1s is less than seven, coordinate
data coding is applied.
Example
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Coding scheme
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Pattern Coding
Example
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Reference Row Technique
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Experimental results (1/2)
Comparison of compression ratios for binary images
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Experimental results (2/2)
Timings for compression and decompression of
binary images in seconds.
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Conclusions

• A new technique for the lossless compression of
  binary images has been proposed.
• The presented method can be used for gray code
  image compression.

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