Experimental results and discussion
This section compares binary tree predictive coding with JPEG and GIF for lossy
and lossless coding of several test images. The test set includes monochrome
and color, photographic, graphic and mixed images of various sizes.
Results for the test images are given on the pages listed below. Each
page includes
- a JPEG or GIF thumbnail version of the test image,
large enough to judge the salient features of the image (for one of
the high-resolution inputs, the "thumbnail" is 256 x 256!).
- lossless coding results for GIF and BTPC. BTPC 2 results are given in
all cases, BTPC 1 results for monochrome images only (a color version has
not been developed), and GIF results for all cases except photographic color
images where color quantization would be necessary and the process therefore
not lossless.
- a graph plotting the rate-distortion performance of BTPC 1 (monochrome
only), BTPC 2, and JPEG (Independent JPEG Group, Version 5, default
parameters).
The rate-distortion graphs plot Peak Signal to Noise ratio against
bits per pel. For the color images the PSNR is the average over
the three (red, green, blue) color planes. The luminance PSNR is significantly
higher. Bits per pel for color images refers to 24-bit pels, so
1.2 bpp for a color image means 20:1 compression. The sixth data point from
the right on the JPEG graphs represents coding at the usual default quality of
75.
The JPEG coder [14] rescales its outputs to the range [0,255], so to
ensure a fair comparison, all images were first scaled to this range.
As mentioned earlier, both JPEG and BTPC used Huffman rather
than arithmetic coding.
Monochrome photographic
Monochrome Lenna 256 x 256
Monochrome Lenna 512 x 512
Monochrome Gold Hill 256 x 256
Monochrome Gold Hill 512 x 512
Monochrome Barbara 256 x 256
Monochrome Barbara 512 x 512
Monochrome Cameraman 256 x 256
Monochrome other continuous image types
Monochrome Magnetic Resonance Image 256 x
256
Monochrome Synthetic Aperture Radar 512 x
512
Monochrome text and graphics
Monochrome Quick Brown Fox Text 256 x 256
Monochrome World Map Graphic 372 x 619
Monochrome France Presentation Graphic 496 x 672
Monochrome multimedia
Monochrome Library Multimedia 352 x 464
Color photographic
Color Lenna 512 x 512
Color Baboon 512 x 512
Color Portraits 2048 x 2048
Color text and graphics
Color CSC Graphic 500 x 400
Color multimedia
Color X desktop multimedia 2048 x 2048
Lossless Compression
Overall, BTPC achieves a significantly lower lossless compression rate
than GIF for the photographic and mixed images, and a higher rate for the
graphical images.Lossy Compression
On average, BTPC's performance on photographic images is close to JPEG's.
At the usual JPEG default quality of 75 the only images for which BTPC is
inferior are
the 512 x 512 monochrome Barbara, and the magnetic resonance image.
The first of these has large areas of regular spatial frequencies which
JPEG's transform coder can exploit. The second is very well recovered by both
coders and the difference is marginal. On some images (e.g. Cameraman),
BTPC's superiority is substantial.
For the graphical and mixed images BTPC
consistently outperforms JPEG. Even in the Library image, which has the
most photographic content, the improvement is more than 1 bpp at 36dB.
Lossy coding with BTPC degrades graphics, but in a monotonic and consistent
way, and coding at the rate achieved by GIF usually results in invisible
degradations.
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