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@@ -442,14 +442,14 @@ value, and what value we decided on.
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The first parameter to decide on, is the $\sigma$ used in the Gaussian blur. To
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find this parameter, we tested a few values, by trying them and checking the
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-results. It turned out that the best value was $\sigma = 1.4$.
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+results. It turned out that the best value was $\sigma = 1.9$.
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Theoretically, this can be explained as follows. The filter has width of
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-$6 * \sigma = 6 * 1.6 = 9.6$ pixels. The width of a `stroke' in a character is,
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-after our resize operations, around 8 pixels. This means, our filter `matches'
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-the smallest detail size we want to be able to see, so everything that is
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-smaller is properly suppressed, yet it retains the details we do want to keep,
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-being everything that is part of the character.
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+$6 * \sigma = 6 * 1.9 = 11.4$ pixels. The width of a `stroke' in a character is
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+after our resize operations around 10 pixels. This means, our filter in
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+proportion to the smallest detail size we want to be able to see, so everything
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+that is smaller is properly suppressed, yet it retains the details we do want
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+to keep, being everything that is part of the character.
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\subsection{Parameter \emph{cell size}}
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@@ -515,33 +515,35 @@ in the table are rounded percentages, for better readability.
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c $\gamma$ & $2^{-15}$ & $2^{-13}$ & $2^{-11}$ & $2^{-9}$ & $2^{-7}$ &
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$2^{-5}$ & $2^{-3}$ & $2^{-1}$ & $2^{1}$ & $2^{3}$\\
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\hline
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-$2^{-5}$ & 61 & 61 & 61 & 61 & 62 &
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- 63 & 67 & 74 & 59 & 24\\
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-$2^{-3}$ & 61 & 61 & 61 & 61 & 62 &
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- 63 & 70 & 78 & 60 & 24\\
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-$2^{-1}$ & 61 & 61 & 61 & 61 & 62 &
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- 70 & 83 & 88 & 78 & 27\\
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- $2^{1}$ & 61 & 61 & 61 & 61 & 70 &
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- 84 & 90 & 92 & 86 & 45\\
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- $2^{3}$ & 61 & 61 & 61 & 70 & 84 &
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- 90 & 93 & 93 & 86 & 45\\
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- $2^{5}$ & 61 & 61 & 70 & 84 & 90 &
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- 92 & 93 & 93 & 86 & 45\\
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- $2^{7}$ & 61 & 70 & 84 & 90 & 92 &
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- 93 & 93 & 93 & 86 & 45\\
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- $2^{9}$ & 70 & 84 & 90 & 92 & 92 &
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- 93 & 93 & 93 & 86 & 45\\
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-$2^{11}$ & 84 & 90 & 92 & 92 & 92 &
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- 92 & 93 & 93 & 86 & 45\\
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-$2^{13}$ & 90 & 92 & 92 & 92 & 92 &
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- 92 & 93 & 93 & 86 & 45\\
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-$2^{15}$ & 92 & 92 & 92 & 92 & 92 &
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- 92 & 93 & 93 & 86 & 45\\
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+$2^{-5}$ & 63 & 63 & 63 & 63 & 63 & 65 &
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+ 68 & 74 & 59 & 20\\
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+$2^{-3}$ & 63 & 63 & 63 & 63 & 63 & 65 &
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+ 70 & 80 & 60 & 20\\
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+$2^{-1}$ & 63 & 63 & 63 & 63 & 63 & 71 &
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+ 84 & 89 & 81 & 23\\
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+ $2^{1}$ & 63 & 63 & 63 & 63 & 70 & 85 &
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+ 91 & 92 & 87 & 45\\
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+ $2^{3}$ & 63 & 63 & 63 & 70 & 85 & 91 &
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+ 93 & 93 & 86 & 45\\
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+ $2^{5}$ & 63 & 63 & 70 & 85 & 91 & 93 &
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+ 94 & 93 & 86 & 45\\
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+ $2^{7}$ & 63 & 70 & 85 & 91 & 93 & 93 &
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+ 93 & 93 & 86 & 45\\
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+ $2^{9}$ & 70 & 85 & 91 & 93 & 93 & 93 &
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+ 93 & 93 & 86 & 45\\
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+$2^{11}$ & 85 & 91 & 93 & 93 & 93 & 93 &
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+ 93 & 93 & 86 & 45\\
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+$2^{13}$ & 91 & 93 & 93 & 92 & 93 & 93 &
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+ 93 & 93 & 86 & 45\\
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+$2^{15}$ & 93 & 93 & 92 & 92 & 93 & 93 &
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+ 93 & 93 & 86 & 45\\
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\hline
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\end{tabular} \\
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The grid-search shows that the best values for these parameters are $c = 2^5 =
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-32$ and $\gamma = 2^{-3} = 0.125$.
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+32$ and $\gamma = 2^{-3} = 0.125$. These values were found for a number of
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+different blur sizes, so these are the best values for this neighbourhood and
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+this problem.
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\section{Results}
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@@ -558,31 +560,32 @@ According to Wikipedia \cite{wikiplate}, commercial license plate recognition
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that are currently on the market software score about $90\%$ to $94\%$, under
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optimal conditions and with modern equipment.
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-Our program scores an average of $93.6\%$. However, this is for a single
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+Our program scores an average of $94.0\%$. However, this is for a single
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character. That means that a full license plate should theoretically
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-get a score of $0.936^6 = 0.672$, so $67.2\%$. That is not particularly
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+get a score of $0.940^6 = 0.690$, so $69.0\%$. That is not particularly
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good compared to the commercial ones. However, our focus was on getting
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-good scores per character. For us, $93.6\%$ is a very satisfying result.
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+good scores per character. For us, $94\%$ is a very satisfying result.
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\subsubsection*{Faulty classified characters}
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As we do not have a $100\%$ score, it is interesting to see what characters are
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classified wrong. These characters are shown in appendix \ref{fcc}. Most of
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-these errors are easily explained. For example, some 0's are classified as
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-'D', some 1's are classified as 'T' and some 'F's are classified as 'E'.
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+these errors are easily explained. For example, some `0's are classified as
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+`D', some `1's are classified as `T' and some `F's are classified as `E'.
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Of course, these are not as interesting as some of the weird matches. For
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-example, a 'P' is classified as 7. However, if we look more closely, the 'P' is
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-standing diagonally, possibly because the datapoints where not very exact in
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+example, a `P' is classified as `7'. However, if we look more closely, the `P'
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+is standing diagonally, possibly because the datapoints where not very exact in
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the XML file. This creates a large diagonal line in the image, which explains
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-why this can be classified as a 7. The same has happened with a 'T', which is
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-also marked as 7.
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+why this can be classified as a `7'. The same has happened with a `T', which is
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+also marked as `7'.
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-Other strange matches include a 'Z' as a 9, but this character has a lot of
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-noise surrounding it, which makes classification harder, and a 3 that is
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-classified as 9, where the exact opposite is the case. This plate has no noise,
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+Other strange matches include a `Z' as a `9', but this character has a lot of
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+noise surrounding it, which makes classification harder, and a `3' that is
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+classified as `9', where the exact opposite is the case. This plate has no noise,
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due to which the background is a large area of equal color. This might cause
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-the classification to focus more on this than on the actual character.
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+the classification to focus more on the background than on the actual
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+character. This happens for more characters, for instance a `5' as `P'.
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\subsection{Speed}
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Jayke Meijer