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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 ...@@ -268,6 +268,14 @@ When tested on a random set of 16 images, the ratio only changed from $0.3973$ t
    \end{center} \end{center}
    Our method created files that are on average 33.7\% smaller than PNG and 34.5\% smaller than LWZ compression on TIFF. 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} \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. 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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