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Image Compression Using Space-Filling Curves

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

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  1. Image Compression Using Space-Filling Curves Michal Krátký, Tomáš Skopal, Václav Snášel Department of Computer Science, VŠB-Technical University of OstravaCzech Republic

  2. Presentation Outline • Motivation • Properties of Space-Filling Curves (SFC) • Experiments • lossless compression (RLE, LZW) • lossy compression (delta compression) • Conclusions ITAT 2003

  3. 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

  4. Space-Filling Curves (examples) ITAT 2003

  5. 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

  6. „C-ordered“ Lena „Hilbert“ Lena „Random“ Lena „Z-ordered“ Lena „Spiral“ Lena „Snake“ Lena Images scanned along SFC ITAT 2003

  7. 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

  8. SFC symmetry, jumping factor Symmetry:C-curve = Snake < Random < Z-curve < Spiral < HilbertJumping factor:Hilbert = Spiral = Snake < C-curve < Z-curve < Random ITAT 2003

  9. Experiments, lossless compression • neighbour color redundancy, applicability to RLE ITAT 2003

  10. Experiments, lossless compression • pattern redundancy, applicability to LZW ITAT 2003

  11. Experiments, lossy compression • delta compression, 6-bit delta  delta histograms Max. deltas = error pixels Tall “bell” = low entropy ITAT 2003

  12. C-curve errors Z-curve errors Snake curve errors Experiments, lossy compression • visualization of error pixels (all color components) ITAT 2003

  13. Random curve errors Spiral curve errors Hilbert curve errors Experiments, lossy compression • visualization of error pixels (all color components) ITAT 2003

  14. Experiments, lossy compression • entropy evaluation  arithmetical coding ITAT 2003

  15. 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

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