Results

(Our Results / Others Results)


Our Results

The results achieved in this project are shown in the table below. It is important to realize how computationally intensive the encoding of images is. An extremely high amount of computations are required in order to achieve only moderate results. The code used to compress the images in this project was written in MatLab and includes parts with as much as five nestled for-loops. To date, MatLab is not fast enough (even for a "fast" UNIX Station) to be able to do a preferable amount of computations in a reasonable time. Hence, the encoding algorithm needed not to include too many computations, which explains the poor quality of the images below. Examples of ways to cut down on number of computations are: search fewer domain blocks, use larger range and domain blocks, etc.

Image	Approximate Compression Ratio	MSE	PSNR
Lenna	13	467	21.4
Clown	13	547	20.7
Building	13	776	19.2

The mean-square-error (MSE) of an NxN image is defined as MSE=1/(N^2)*sum_over_n&m((x[m,n]-xc[m,n])^2) where x is the original image and xc is the compressed image.

The peak-signal-to-noise ratio (PSNR) of an 256x256 image is defined as PSNR = 10*log(255x255/MSE).



Compressed Images


Lenna


Clown


Building

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Others Results

Better results than the ones presented above can be achieved using faster software and/or faster computers, allowing more computations per time unit and a more careful encoding. Below are the results achieved by Zhao & Yuan (see bibliography) using the same hybrid method as described in this report. Results for non-hybrid methods are included for comparison.

Image	Compression Method	Compression Ratio	PSNR
Lenna	Same as described in this report	12.4	31.7
Lenna	Spatial domain fractals	17.4	24.9
Lenna	DCT domain fractals	18.5	26.1

Clearly, there is a reason why the hybrid method is a subject for research. Although the compression ratio does not differ very much between the different methods, the PSNR is much better for the hybrid method (it is important to remember that PSNR is measured in dB, and that a change from 24.9 to 31.7 may appear less remarkable than it actually is).