\section{results}

\subsection{Overall ROC}
The overall ROC can be found in Figure \ref{fig:overallROC}. To define the false acceptance rate the point on the ROC closest to the northwest corner of the plot. This point is equal to the optimal threshold value. This point results in a false acceptance rate of $0.36\%$ and a correct acceptance rate of $99.62\%$. There is a total of 9358 matches which failed to capture. Together with a total of 383780 matches the failure to capture rate (FCR) is $1.2\%$ assuming that the software only failed to capture on only one of the two pictures. 
\begin{figure}[ht]
\centering
\includegraphics[width=.9\linewidth]{image/overall_ROC}
\caption{ The overall ROC}
\label{fig:overallROC}
\end{figure}

\subsection{Individual ROC’s}
18 out of the 31 individuals have a perfect ROC. Which means that the highest impostor score is lower than the lowest genuine score. An example of a perfect ROC can be found in Figure \ref{fig:nd1S04934_ROC}. All images from these 18 individuals are analyzed. In all of these images the person looks directly into the camera. A part of the eyes is visible and no parts of the face are covered. Not all ROC’s are perfect and further examination will be done later. The results from MATLAB give the feeling that Verilook has a lower success rate for woman. A different ROC in figure~\ref{fig:genderROC} supports this suspicion. There is a clear difference between these ROCs, one should note that the graphs are zoomed. The different scores are split up in table~\ref{tab:gender} and there is a clear difference between the success rate of males and females. This is probably due to the relative small amount of subjects and a Chi-square test gives a p-value of $0.106$. Although the p-value is too high for a significant difference it should be noted that a bigger subject group can generate a significant difference.

\begin{figure}[ht]
\centering
\includegraphics[width=.9\linewidth]{image/gender_ROC}
\caption{General ROC combined with gender specific ROCs}
\label{fig:genderROC}
\end{figure}
\begin{table}[ht]
\centering
\begin{tabular}{|c|c|c|}
\cline{2-3}
\multicolumn{1}{c|}{} & Male & Female \\
\hline
Perfect & 12 & 7 \\
\hline
Not Perfect & 4 & 8 \\
\hline
\end{tabular}
\caption{Cross table with gender scores}
\label{tab:gender}
\end{table}

\begin{figure}[ht]
\centering
\includegraphics[width=.8\linewidth]{image/nd1S04934_ROC}
\caption{A perfect ROC}
\label{fig:nd1S04934_ROC}
\end{figure}

To find out why certain individuals did not get a perfect score it crucial to inspect each of these cases. Figure~\ref{fig:nd1S04341_ROC} is the ROC of subject nd1S04341. This deviation is caused by one matching score of zero. In figure \ref{fig:nd1S04341} are the corresponding pictures. The main difference between this pictures is the visibility of the ears, further are there no significate difference.
\begin{figure}[ht]
\centering
\includegraphics[width=.8\linewidth]{image/nd1S04341_ROC}
\caption{ROC of subject nd1S04341}
\label{fig:nd1S04341_ROC}
\end{figure}
\begin{figure}[ht]
\begin{minipage}[th]{.49\linewidth}
\centering
\vspace{0pt}
\includegraphics[width=\linewidth]{image/04341d147}
\end{minipage}\hfill
\begin{minipage}[th]{.49\linewidth}
\centering
\vspace{0pt}
\includegraphics[width=\linewidth]{image/04341d154}
\end{minipage}\hfill
\caption{Pictures of subject nd1S04341}
\label{fig:nd1S04341}
\end{figure}

Another interesting result is the impact of visibility of the face. A expamle is subject nd1S04406, the ROC of this subject can be found in figure~\ref{fig:nd1S04406_ROC}. There are a few genuine scores which a relative low. One of these matching scores in the matching score between the pictures in Figure~\ref{fig:nd1S04406}. There are a few differences between these pictures. The first is the visibility of the left part of the face. In the left picture a bigger part of the face is covered with hair. Another significate diffent is the visablity of the ears. Furthermore, only in the left picture, the teeth are shown. 
\begin{figure}[ht]
\centering
\includegraphics[width=.8\linewidth]{image/nd1S04406_ROC}
\caption{ROC of subject nd1S04406}
\label{fig:nd1S04406_ROC}
\end{figure}
\begin{figure}[ht]
\begin{minipage}[th]{.49\linewidth}
\centering
\vspace{0pt}
\includegraphics[width=\linewidth]{image/04406d61}
\end{minipage}\hfill
\begin{minipage}[th]{.49\linewidth}
\centering
\vspace{0pt}
\includegraphics[width=\linewidth]{image/04406d36}
\end{minipage}\hfill
\caption{Pictures of subject nd1S04406}
\label{fig:nd1S04406}
\end{figure}

The pictures in figure~\ref{fig:nd1S04508} have also a relative low matching score. The left picture is a little bit overexposed, making the skin a little bit lighter. Furthermore, the teeth are not visible on the right picture. In figure~\ref{fig:nd1S04508_ROC} is the ROC of this individual. 
\begin{figure}[ht]
\centering
\includegraphics[width=.8\linewidth]{image/nd1S04508_ROC}
\caption{ROC of subject nd1S04508}
\label{fig:nd1S04508_ROC}
\end{figure}
\begin{figure}[ht]
\begin{minipage}[th]{.49\linewidth}
\centering
\vspace{0pt}
\includegraphics[width=\linewidth]{image/04508d52}
\end{minipage}\hfill
\begin{minipage}[th]{.49\linewidth}
\centering
\vspace{0pt}
\includegraphics[width=\linewidth]{image/04508d71}
\end{minipage}\hfill
\caption{Pictures of subject nd1S04508}
\label{fig:nd1S04508}
\end{figure}

If the Verilook software was not able to find a face it returned a score of minus one. These negative scores were not used when calculating the ROC but saved in to a different variable. There are eight images in total which have an no-face count larger then 10. Overall do all pictures have a no match rate of 7 or 8 because both pictures get a minus one score if only one of pictures fail to contain a face. Figure~\ref{fig:nd1S04484} shows subject nd1S04484 with a no-face count of 618. While there are 620 pictures in total this picture is matched a total of 619 times which means that only once Verilook was able to recognize a face but failed the other 618 times. In figure~\ref{fig:nd1S04746} a picture of subject nd1S04746 is shown with a no-face count of 395. Again this case Verilook could not detect the face consistently. Analyzing both pictures it is easy to conclude that light a large factor. Lighting is probably the main reason in figure~\ref{fig:nd1S04484} for Verilook to fail even though the subject is looking directly into the camera. Searching for similar pictures where the no-face count is around the 600 it shows settings where the subject wears white clothing. The white clothing results in a lower exposure time which gives a bad lighted face. The subject in figure~\ref{fig:nd1S04746} has a better lighting but does not directly look in to the camera. This leads to presuming that Verilook is depending on random tests to find faces and that this causes a couple of pictures fail only partially.

\begin{figure}[ht]
\begin{minipage}[th]{.49\linewidth}
\centering
\vspace{0pt}
\includegraphics[width=\linewidth]{image/04484d141}%NoFace:618
\caption{Picture of subject nd1S04484}
\label{fig:nd1S04484}
\end{minipage}\hfill
\begin{minipage}[th]{.49\linewidth}
\centering
\vspace{0pt}
\includegraphics[width=\linewidth]{image/04746d23} %NoFace:395
\caption{Picture of subject nd1S04746}
\label{fig:nd1S04746}
\end{minipage}\hfill
\end{figure}

All pictures and all ROC’s can be found in Appendix 1.