Filled in results.

docs/report.tex

@@ -349,7 +349,7 @@ value, and what value we decided on.
 
 The first parameter to decide on, is the $\sigma$ used in the Gaussian blur. To
 find this parameter, we tested a few values, by trying them and checking the
-results. It turned out that the best value was $\sigma = 1.1$.
+results. It turned out that the best value was $\sigma = 1.4$.
 
 \subsection{Parameter \emph{cell size}}
 
@@ -378,7 +378,13 @@ are not significant enough to allow for reliable classification.
 The neighbourhood to use can only be determined through testing. We did a test
 with each of these neighbourhoods, and we found that the best results were
 reached with the following neighbourhood, which we will call the
-()-neighbourhood.
+(12, 5)-neighbourhood, since it has 12 points in a area with a diameter of 5.
+
+\begin{figure}[H]
+\center
+\includegraphics[scale=0.5]{12-5neighbourhood.png}
+\caption{(12,5)-neighbourhood}
+\end{figure}
 
 \subsection{Parameters $\gamma$ \& $c$}
 
@@ -399,8 +405,41 @@ checks for each combination of values what the score is. The combination with
 the highest score is then used as our parameters, and the entire SVM will be
 trained using those parameters.\\
 \\
-We found that the best values for these parameters are $c = ?$ and
-$\gamma = ?$.
+The results of this grid-search are shown in the following table. The values
+in the table are rounded percentages, for easy displaying.
+
+\begin{tabular}{|r|r r r r r r r r r r|}
+\hline
+c $\gamma$ & $2^{-15}$ & $2^{-13}$ & $2^{-11}$ & $2^{-9}$ & $2^{-7}$ &
+	$2^{-5}$ & $2^{-3}$ & $2^{-1}$ & $2^{1}$ & $2^{3}$\\
+\hline
+$2^{-5}$ &       61 &       61 &       61 &       61 &       62 &
+       63 &       67 &       74 &       59 &       24\\
+$2^{-3}$ &       61 &       61 &       61 &       61 &       62 &
+       63 &       70 &       78 &       60 &       24\\
+$2^{-1}$ &       61 &       61 &       61 &       61 &       62 &
+       70 &       83 &       88 &       78 &       27\\
+ $2^{1}$ &       61 &       61 &       61 &       61 &       70 &
+        84 &       90 &       92 &       86 &       45\\
+ $2^{3}$ &       61 &       61 &       61 &       70 &       84 &
+        90 &       93 &       93 &       86 &       45\\
+ $2^{5}$ &       61 &       61 &       70 &       84 &       90 &
+        92 &       93 &       93 &       86 &       45\\
+ $2^{7}$ &       61 &       70 &       84 &       90 &       92 &
+        93 &       93 &       93 &       86 &       45\\
+ $2^{9}$ &       70 &       84 &       90 &       92 &       92 & 
+       93 &       93 &       93 &       86 &       45\\
+$2^{11}$ &       84 &       90 &       92 &       92 &       92 &
+       92 &       93 &       93 &       86 &       45\\
+$2^{13}$ &       90 &       92 &       92 &       92 &       92 &
+       92 &       93 &       93 &       86 &       45\\
+$2^{15}$ &       92 &       92 &       92 &       92 &       92 &
+       92 &       93 &       93 &       86 &       45\\
+\hline
+\end{tabular}
+
+We found that the best values for these parameters are $c = 32$ and
+$\gamma = 0.125$.
 
 \section{Results}
 
@@ -416,7 +455,17 @@ measure the time used to classify a license plate, not the training of the
 dataset, since that can be done offline, and speed is not a primary necessity
 there.\\
 \\
-The speed of a classification turned out to be ???.
+The speed of a classification turned out to be reasonably good. We time between
+the moment a character has been 'cut out' of the image, so we have a exact
+image of a character, to the moment where the SVM tells us what character it is.
+This time is on average $65$ ms. That means that this
+technique (tested on an AMD Phenom II X4 955 Quad core CPU running at 3.2 GHz)
+can identify 15 characters per second.\\
+\\
+This is not spectacular considering the amount of calculating power this cpu
+can offer, but it is still fairly reasonable. Of course, this program is
+written in Python, and is therefore not nearly as optimized as would be
+possible when written in a low-level language.
 
 \subsection{Accuracy}
 
@@ -427,16 +476,31 @@ accuracy score we possibly can.\\
 \footnote{
 \url{http://en.wikipedia.org/wiki/Automatic_number_plate_recognition}},
 commercial license plate recognition software score about $90\%$ to $94\%$,
-under optimal conditions and with modern equipment. Our program scores an
-average of ???.
+under optimal conditions and with modern equipment.\\
+\\
+Our program scores an average of $93\%$. However, this is for a single
+character. That means that a full license plate should theoretically
+get a score of $0.93^6 = 0.647$, so $64.7\%$. That is not particularly
+good compared to the commercial ones. However, our focus was on getting
+good scores per character, and $93\%$ seems to be a fairly good result.\\
+\\
+Possibilities for improvement of this score would be more extensive
+grid-searches, finding more exact values for $c$ and $\gamma$, more tests
+for finding $\sigma$ and more experiments on the size and shape of the 
+neighbourhoods.
 
 \section{Conclusion}
 
 In the end it turns out that using Local Binary Patterns is a promising
-technique for License Plate Recognition. It seems to be relatively unsensitive
+technique for License Plate Recognition. It seems to be relatively indifferent
 for the amount of dirt on license plates and different fonts on these plates.\\
 \\
-The performance speedwise is ???
+The performance speed wise is fairly good, when using a fast machine. However,
+this is written in Python, which means it is not as efficient as it could be
+when using a low-level languages.
+\\
+We believe that with further experimentation and development, LBP's can
+absolutely be used as a good license plate recognition method.
 
 \section{Reflection}