Therefore, analytical methods are usually preferred to conduct comparative analysis of video coding and transmission schemes. There are drawbacks here as well, as it is difficult to quantify how better is one scheme from another, by relying only on these measures, and there are certain images that mislead such statistical evaluations. Thus, subjective testing could be used in conjunction to the analytical evaluation, to provide the most reliable results.
The most common measure of the distortion of an image relative to a reference
image, is the Peak SNR (PSNR), a mean square error (
)
measure
defined as:
where M and N are the horizontal and vertical dimensions of the image, and
f and 
are the pel values matrices for the original and the
reconstructed frames, respectively.
Generally speaking, values of PSNR over 40 dB correspond to reconstructed images that are near perfect quality, that is, they seem identical to the original. Practical video coding schemes are producing images with lower average PSNR values, usually in the range of 32-40 dB. It has to be noted, however, that for the same average PSNR, distortions due to transmission errors are much more frustrating than distortions due to video coding. Therefore, some selected reconstructed frames will be illustrated in the next chapter for comparison, in addition to the PSNR statistics.
![\begin{gather}\mbox{PSNR} = 10\log_{10}\left( \frac{255^2}{\mbox{MSE}}\right) \h...
...}{M N} \sum_{j=1}^{N} \sum_{i=1}^{M}
[f(i, j) - \hat{f}(i, j)]^{2}
\end{gather}](img45.gif)