Image Compression Using Space-Filling Curves

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Image Compression Using Space-Filling Curves

• Michal Krátký, Tomáš Skopal, Václav Snášel
• Department of Computer Science, VŠB-Technical
  University of OstravaCzech Republic

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Presentation Outline

• Motivation
• Properties of Space-Filling Curves (SFC)
• Experiments
• lossless compression (RLE, LZW)
• lossy compression (delta compression)
• Conclusions

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Space-Filling Curves

• bijective mapping of an n-dimensional vector
  space into a single-dimensional interval
• Computer Science discrete finite vector spaces
• clustering tool in Data Engineering, indexing,
  KDD

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Space-Filling Curves (examples)
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Motivation

• Traditional methods of image processing
  scanning rows or columns, i.e. along the C-curve
• Our assumption other scanning paths could
  improve the compression and could decrease errors
  when using lossy compression

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Images scanned along SFC
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Properties of SFC

• SFCs partially preserve topological properties of
  the vector space. The topological (metric)
  quality of SFCPoints close in the vector
  space are also close on the curve.
• Two anomalies in a SFC shape
• distance enlargements in every SFC
• symmetry of SFCcorrelation of anomalies in all
  dimensions
• jumping factornumber of distance shrinking
  occurences(jumps over neighbours)

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SFC symmetry, jumping factor
Symmetry C-curve Snake lt Random lt Z-curve lt
Spiral lt Hilbert Jumping factor Hilbert
Spiral Snake lt C-curve lt Z-curve lt Random
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Experiments, lossless compression

• neighbour color redundancy, applicability to RLE

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Experiments, lossless compression

• pattern redundancy, applicability to LZW

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Experiments, lossy compression

• delta compression, 6-bit delta ? delta histograms
• Max. deltas
• error pixels
• Tall bell
• low entropy

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Experiments, lossy compression

• visualization of error pixels (all color
  components)

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Experiments, lossy compression

• visualization of error pixels (all color
  components)

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Experiments, lossy compression

• entropy evaluation ? arithmetical coding

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Conclusions

• Choice of a suitable SFC can positively affect
  the compression rate (or entropy) as well as the
  quality of lossy compression.
• Experiments symmetric curves with low (zero)
  jumping factor are the most appropriate ? Hilbert
  curve