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Image Compression Using Space-Filling Curves. Michal Kr átký, Tomáš Skopal , Václav Snášel Department of Computer Science, VŠB-Technical University of Ostrava Czech Republic. Presentation Outline. Motivation Properties of Space-Filling Curves (SFC) Experiments

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image compression using space filling curves

Image Compression Using Space-Filling Curves

Michal Krátký, Tomáš Skopal, Václav Snášel

Department of Computer Science, VŠB-Technical University of OstravaCzech Republic

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

ITAT 2003

space filling curves
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

ITAT 2003

motivation
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 errorswhen using lossy compression

ITAT 2003

images scanned along sfc

„C-ordered“ Lena

„Hilbert“ Lena

„Random“ Lena

„Z-ordered“ Lena

„Spiral“ Lena

„Snake“ Lena

Images scanned along SFC

ITAT 2003

properties of sfc

distance shrinking distance enlargement

Properties of SFC
  • SFCs partially preserve topological properties of the vector space. The topological (metric) quality of SFC:Points „close“ in the vector space are also „close“ on the curve.
  • Two anomalies in a SFC shape:
    • “distance enlargements”in every SFC
    • symmetry of SFC:correlation of anomalies in all dimensions
    • jumping factor:number of “distance shrinking” occurences(jumps over neighbours)

ITAT 2003

sfc symmetry jumping factor
SFC symmetry, jumping factor

Symmetry:C-curve = Snake < Random < Z-curve < Spiral < HilbertJumping factor:Hilbert = Spiral = Snake < C-curve < Z-curve < Random

ITAT 2003

experiments lossless compression
Experiments, lossless compression
  • neighbour color redundancy, applicability to RLE

ITAT 2003

experiments lossless compression10
Experiments, lossless compression
  • pattern redundancy, applicability to LZW

ITAT 2003

experiments lossy compression
Experiments, lossy compression
  • delta compression, 6-bit delta  delta histograms

Max. deltas

= error pixels

Tall “bell”

= low entropy

ITAT 2003

experiments lossy compression12

C-curve errors

Z-curve errors

Snake curve errors

Experiments, lossy compression
  • visualization of error pixels (all color components)

ITAT 2003

experiments lossy compression13

Random curve errors

Spiral curve errors

Hilbert curve errors

Experiments, lossy compression
  • visualization of error pixels (all color components)

ITAT 2003

experiments lossy compression14
Experiments, lossy compression
  • entropy evaluation  arithmetical coding

ITAT 2003

conclusions
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

ITAT 2003