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Image Compression Using Space-Filling Curves - PowerPoint PPT Presentation
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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
Michal Krátký, Tomáš Skopal, Václav Snášel
Department of Computer Science, VŠB-Technical University of OstravaCzech Republic
Presentation Outline
- Motivation
- Properties of Space-Filling Curves (SFC)
- Experiments
- lossless compression (RLE, LZW)
- lossy compression (delta compression)
- Conclusions
ITAT 2003
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
Space-Filling Curves (examples)
ITAT 2003
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
„Hilbert“ Lena
„Random“ Lena
„Z-ordered“ Lena
„Spiral“ Lena
„Snake“ Lena
Images scanned along SFCITAT 2003
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
Symmetry:C-curve = Snake < Random < Z-curve < Spiral < HilbertJumping factor:Hilbert = Spiral = Snake < C-curve < Z-curve < Random
ITAT 2003
Experiments, lossy compression
- delta compression, 6-bit delta delta histograms
Max. deltas
= error pixels
Tall “bell”
= low entropy
ITAT 2003
Z-curve errors
Snake curve errors
Experiments, lossy compression- visualization of error pixels (all color components)
ITAT 2003
Spiral curve errors
Hilbert curve errors
Experiments, lossy compression- visualization of error pixels (all color components)
ITAT 2003
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
