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Commit 4503d4c2 authored by Super-Klass's avatar Super-Klass
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formulas for compression limit

parent 3f1102b8
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    ......@@ -268,6 +268,14 @@ When tested on a random set of 16 images, the ratio only changed from $0.3973$ t
    \end{center}
    Our method created files that are on average 33.7\% smaller than PNG and 34.5\% smaller than LWZ compression on TIFF.
    For estimation of limits of compression, we use information theory. Expected length of source code: $ L = \sum_{x} p(x)l(x)\\$ $l(x)$ is a length of codeword, corresponding to state x. $p(x) = \frac{n_x}{N}$, $n_x$ - number of elements for state $x$, N - total number states. From information theory we have: $L \geq H$ Where $H = -\sum_{x} p(x)\log_2{p(x)}$ - Shannon entropy.
    From the previous formula: $ L = \frac{\sum_{x} n_x l(x)}{N} \geq -\sum_{x} p(x)\log_2{p(x)}$.
    From that we have:
    $ \text{compression rate} \geq \frac{NH}{\text{uncompr size}}
    $
    After averaging over 224 images, compression limit is 0.37.
    \section{Discussion}
    The files produced through this method are much smaller than the ones produced by the others, but this comes at great computational costs in its current implementation.
    ......
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