1. Rectangle Image Compression Jiří Komzák Department of Computer Science and Engineering, Czech Technical University (CTU)

2. Overview Introduction Existing Methods Rectangle Method Description Rectangle Method Specifics Comparison To Existing Methods Future Work

3. Introduction Compression Need –storage space is always small –limited bandwidth of networks History –text applications at first –extension into 2 and more dimensions Compression - redundancy reduction

4. Introduction Compression ratio = compressed/original size Fast Decompression Need Lossless Compression - allows exact reconstruction Use of Spatial Context

5. Existing similar methods Lossless compression –RLE –Quad-trees –Space Filling Curves Lossy compression –integral transforms - DCT, DWT –Iterated Function Systems - repeatedly used transformations (fractal compression)

6. Existing similar methods RLE - horizontal strings Quad-trees - squares

7. Existing similar methods Space Filling Curves –area is covered by a parametric function (Hilbert Curve) –quad-tree is a special case of space filling function Hilbert Curve

8. Rectangle Method Description Lossless method based on idea similar to RLE but in two dimensions Splits image into rectangles with identical colors

9. Rectangle Method Description Compressed image and image with first eight rectangles

10. Rectangle Method Description Simple row strings remain in areas with big color variability Method of finding rectangles - heuristic Rectangles with same color can overlap to cover more pixels

11. Rectangle Method Description Fully coded image and illustration of overlapping

12. Rectangle Method Parameters sizes - influence code efficiency –minimal rectangle size - number of noncoded pixels in just created rectangle –minimal length of noncoded string of pixels split control and data bytes –for consequential use of other compression is useful to save it separately

13. Method Specifics strong in coding horizontal lines as well as vertical ones and rectangular areas poor in coding continuos-tone images (no coding) suitable for images „painted by hand“ or cartoons (images with larger areas with identical color) unsymmetrical - encoding takes more time vs. decoding is very fast

14. Images used for testing (Waterloo BragZone - http://links.uwaterloo.ca/bragzone.base.html)

15. Results - Comparison BMP - Windows Bitmap RLE - Windows Bitmap with RLE QT - Quad-tree (my implementation) GIF - Graphics Interchange Format RC - Rectangle Compression all values are ratios of file sizes multiplied by 100% better than BMP, RLE, QT other than GIF

16. Results - Comparison - ARJ’d BMP - Windows Bitmap RLE - Windows Bitmap with RLE QT - Quad-tree (my implementation) GIF - Graphics Interchange Format RC - Rectangle Compression RC-S - Rectangle Compression with Control and Data Bytes Saved Separately better than QT, GIF worse than BMP RC-S is better than RC all values are ratios of file sizes after using ARJ compressor multiplied by 100%

17. Future Work Implementation of optional arithmetic or LZW coding Extension into 3D Lossy compression –how determine significance of pixels –separation of noise and thin lines or texture