Added stuff on usage of different neighbourhoods.

docs/report.tex

@@ -94,8 +94,8 @@ Rewrite this section once we have implemented this properly.
 \subsection{Transformation}
 
 A simple perspective transformation will be sufficient to transform and resize
-the characters to a normalized format. The corner positions of characters in the
-dataset are supplied together with the dataset.
+the characters to a normalized format. The corner positions of characters in
+the dataset are supplied together with the dataset.
 
 \subsection{Reducing noise}
 
@@ -141,8 +141,9 @@ by the n(with i=i$_{th}$ pixel evaluated, starting with $i=0$).
 This results in a mathematical expression:
 
 Let I($x_i, y_i$) an Image with grayscale values and $g_n$ the grayscale value
-of the pixel $(x_i, y_i)$. Also let $s(g_i, g_c)$ (see below) with $g_c$ = grayscale value
-of the center pixel and $g_i$ the grayscale value of the pixel to be evaluated.
+of the pixel $(x_i, y_i)$. Also let $s(g_i, g_c)$ (see below) with $g_c$ =
+grayscale value of the center pixel and $g_i$ the grayscale value of the pixel
+to be evaluated.
 
 $$
   s(g_i, g_c) = \left\{
@@ -236,12 +237,12 @@ noise in the margin.
 In the next section you can read more about the perspective transformation that
 is being done. After the transformation the character can be saved: Converted
 to grayscale, but nothing further. This was used to create a learning set. If
-it doesn't need to be saved as an actual image it will be converted to a
+it does not need to be saved as an actual image it will be converted to a
 NormalizedImage. When these actions have been completed for each character the
 license plate is usable in the rest of the code.
 
 \paragraph*{Perspective transformation}
-Once we retrieved the cornerpoints of the character, we feed those to a
+Once we retrieved the corner points of the character, we feed those to a
 module that extracts the (warped) character from the original image, and
 creates a new image where the character is cut out, and is transformed to a
 rectangle.
@@ -274,11 +275,18 @@ surrounding the character.
 \subsection{Creating Local Binary Patterns and feature vector}
 Every pixel is a center pixel and it is also a value to evaluate but not at the 
 same time. Every pixel is evaluated as shown in the explanation
-of the LBP algorithm. The 8 neighbours around that pixel are evaluated, of course
-this area can be bigger, but looking at the closes neighbours can give us more
-information about the patterns of a character than looking at neighbours
-further away. This form is the generic form of LBP, no interpolation is needed 
-the pixels adressed as neighbours are indeed pixels.
+of the LBP algorithm. There are several neighbourhoods we can evaluate. We have
+tried the following neighbourhoods:
+
+\begin{figure}[h!]
+\center
+\includegraphics[scale=0.5]{neighbourhoods.png}
+\caption{Tested neighbourhoods}
+\end{figure}
+
+We chose these neighbourhoods to prevent having to use interpolation, which
+would add a computational step, thus making the code execute slower. In the
+next section we will describe what the best neighbourhood was.
 
 Take an example where the 
 full square can be evaluated, there are cases where the neighbours are out of 
@@ -311,9 +319,10 @@ available. These parameters are:\\
 	$\sigma$  			& The size of the Gaussian blur.\\
 	\emph{cell size}	& The size of a cell for which a histogram of LBPs will
 	                      be generated.\\
+	\emph{Neighbourhood}& The neighbourhood to use for creating the LBP.\\
 	$\gamma$			& Parameter for the Radial kernel used in the SVM.\\
 	$c$					& The soft margin of the SVM. Allows how much training
-						  errors are accepted.
+						  errors are accepted.\\
 \end{tabular}\\
 \\
 For each of these parameters, we will describe how we searched for a good
@@ -339,7 +348,14 @@ the feature vectors will not have enough elements.\\
 In order to find this parameter, we used a trial-and-error technique on a few
 cell sizes. During this testing, we discovered that a lot better score was
 reached when we take the histogram over the entire image, so with a single
-cell. therefor, we decided to work without cells.
+cell. Therefore, we decided to work without cells.
+
+\subsection{Parameter \emph{Neighbourhood}}
+
+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.
 
 \subsection{Parameters $\gamma$ \& $c$}
 
@@ -351,7 +367,7 @@ different feature vector than expected, due to noise for example, is not taken
 into account. If the soft margin is very small, then almost all vectors will be
 taken into account, unless they differ extreme amounts.\\
 $\gamma$ is a variable that determines the size of the radial kernel, and as
-such blablabla.\\
+such determines how steep the difference between two classes can be.\\
 \\
 Since these parameters both influence the SVM, we need to find the best
 combination of values. To do this, we perform a so-called grid-search. A
@@ -445,7 +461,7 @@ plates. Upon completion all kinds of learning and data sets could be created.
 \subsection{How it went}
 
 Sometimes one cannot hear the alarm bell and wake up properly. This however was
-not a big problem as no one was affraid of staying at Science Park a bit longer
+not a big problem as no one was afraid of staying at Science Park a bit longer
 to help out. Further communication usually went through e-mails and replies
 were instantaneous! A crew to remember.