Tiling Lena with Different Tile Sizes

Images of Lena below were compressed to almost the same size slightly different tile sizes. Note that the compression with odd-size tiles in these experiments are not Part1 compliant: the wavelet transform was done on each tile as if it had offset 0; this allowed to keep all border pixels as "low-frequency".

The PPM to (old) JPEG conversion was done with the highest quality available (in 'xv'), so there should be no visible old JPEG artifacts, but there are links to decompressed PPM files just in case.

The images at the bottom are "difference images". They've been gamma-corrected to illuminate the noise.

Note that the tiles are way too small for normal compression. As you can see here, the resulting images are hardly any better than old jpeg ones with the same sizes.

Alex Zatsman

Common parameters:

Image Dimension	512 x 512
Transform Levels	3
Wavelet Transform	Irreversible 9/7
Number of Guard Bits	3
Color Transform	Irreversible
Number of Layers	1
Entropy Parameters	None (no bypass, no terminations, etc.)
Quantization	Derived with Delta=0.05
Original Images	PPM, JPEG

64x64 vs. 65x65

Tile Size 64 x 64 Compressed Size 20627 BPP 0.6295 PSNR 31.94 PPM Image here	Tile Size 65 x 65 Compressed Size 20639 BPP 0.6299 PSNR 31.98 PPM Image here

The following plots show the sum of squared errors for each row/column of the image between the noiseless encoded image and the decoded image for tilesizes of 64 and 65. Peaks in the MSE for rows correspond to artifacts located at  a tile top/bottom boundary. Peaks in MSE for columns correspond to artifacts located at a tile left/right boundary.

Note that these results seem to agree with results shown by Dr. Jianxin Wei with respect to reducing tile boundary artifacts.

Xgraph compatible datafile containing the numeric data for the graph above is available here.

Xgraph compatible datafile containing the numeric data for the graph above is available here.

128x128 vs. 129x129

Tile Size 128 x 128 Compressed Size 11003 BPP 0.336 PSNR 30.59 PPM Image here	Tile Size 129 x 129 Compressed Size 11010 BPP 0.336 PSNR 30.52 PPM Image here

Xgraph compatible datafile containing the numeric data for the graph above is available here.

Xgraph compatible datafile containing the numeric data for the graph above is available here.

Here are "old JPEG" files with similar size: 11085 bytes (quality=13) and 20792 bytes (quality=39):

Xgraph compatible datafile containing the numeric data for the graph above is available here.

Xgraph compatible datafile containing the numeric data for the graph above is available here.