\documentclass[a4paper,12pt,pdftex]{exam}

\newcommand{\ptitle}{Image statistics}
\input{../header.tex}
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
{email: jan.benda@uni-tuebingen.de}

\begin{document}

\input{../instructions.tex}


%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%

In you zip file you find a natural image called {\tt natimg.jpg}. 
\begin{questions}

  \question Load the image and extract all pixels as three dimensional
  vectors (red, green, and blue channel). 
  
  \question Perform a principal component analysis on these
  three-dimensional vectors.

  \question Try to find an interpretation of the principal components
  you find in terms of colors. Find a good way to visualize this. 

  \question What could be the biological significance of that (\cite{BG} can
  give you a clue)?

  \question How could you transform the picture to match the true
  representation in the retina (S-, M-, L- cones)?

\end{questions}

\begin{thebibliography}{1}
\bibitem{BG} Buchsbaum, G., \& Gottschalk, A. (1983). Trichromacy,
  opponent colours coding and optimum colour information transmission
  in the retina. Proceedings of the Royal Society of London B. Royal
  Society (Great Britain), 220(1218), 89–113.
\end{thebibliography}



\end{document}
