\documentclass[a4paper, 10pt]{article}
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\usepackage{subcaption}
\usepackage[htt]{hyphenat} % allow hyphen inside texttt to avoid overfull hbox warnings
\usepackage[english, french]{babel}
\usepackage[margin=0.5in]{geometry} % default margins are too big for my taste: too much wasted space http://kb.mit.edu/confluence/pages/viewpage.action?pageId=3907057
\usepackage{amsmath} % provides underset

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\title{lipase}
\author{Guillaume Raffy \and Véronique Vié }
\begin{document}
    \selectlanguage{english}

    \maketitle

    \section{catalog images}

        image prefix :
        \selectlanguage{french}
        \begin{description}
            \item[AF]
            \item[blé] coupes de blé
            \item[CA] coupe d'amande
            \item[FE] feuille d'épinard
            \item[GGH] globule gras humain
            \item[CRF] chloroplastes de feuille d'épinard
            \item[OL] oléosome
            \item[DARK] dark
            \item[white]
        \end{description}

        \begin{description}
            \item[cin1] cinétique 1
                \begin{description}
                    \item[\texttt{phiG\_40x\_1}] cinétique avant et après injection enzyme gastrique
                    \item[\texttt{phiG\_40x\_Zstack20um\_1}] stack
                \end{description}

                \begin{tabular}{l|r|p{0.4\textwidth}}
                    file name  & time & action \\
                    \hline
                    \texttt{phiG\_40x\_1} & 0 mn & on commence à enregistrer et on attend 10mn (pour le bleaching)\\
                    & 10 mn & debut injection phase gastrique (poussée) \\
                    & 13 mn & la phase gastrique (le petit tuyau contient $20 \mu l$) arrive dans la cellule d'un coup (1 nanol) \\
                    & 15 mn & on arrête l'injection \\
                    \cline{1-1} \texttt{phiG\_40x\_Zstack20um\_1} & 50 mn & on fait un stack\\
                    \cline{1-1} \texttt{phiG\_I\_40x\_1} & 51 mn & début d'injection phase intestinale (poussée)\\
                    & x mn & on arrête l'injection \\
                    \cline{1-1} \texttt{phiG\_I\_40x\_Zstack20um\_1} & 90 mn & on fait un stack
                \end{tabular}


            \item[cin2] autre échantillon similaire à cin1
            \item[cond5678] condition non réalistes
        \end{description}
        \selectlanguage{english}

    \section{computing background image for trap sequences}

        Trap sequences show traps at fixed positions with particles that move over time, as shown in figure \ref{fig:trap_sequence1}. In order to detect the particles, we can subtract from each image a background image, which is an image of the scene without any particle.

        If we suppose that particles are moving fast enough, we can estimate this background image $B$, as :

        \begin{equation}
            B(x,y) = \underset{t\in {1 \ldots T_{max}}}{\mathrm{median}} \{I(x,y,t)\} 
        \end{equation}
        where $I(x,y,t)$ is the value of the input sequence at time $t$ and on pixel position $(x,y)$ and $T_{max}$ is the number of frames in the sequence.

        \begin{figure}
            \centering
            \begin{subfigure}[b]{0.3\textwidth}
                \includegraphics[width=1.0\textwidth]{graphics/res_soleil2018_GGH_GGH_2018_cin2_phiG_I_327_vis_-40_1_Pos0_img_000000000_DM300_nofilter_vis_000.png}
                %\includegraphics[width=\textwidth]{1.png}
                \caption{Frame 0}
                %\label{fig:1}
            \end{subfigure}
            ~
            \begin{subfigure}[b]{0.3\textwidth}
                \includegraphics[width=1.0\textwidth]{graphics/res_soleil2018_GGH_GGH_2018_cin2_phiG_I_327_vis_-40_1_Pos0_img_000000019_DM300_nofilter_vis_000.png}
                %\includegraphics[width=\textwidth]{1.png}
                \caption{Frame 19}
                %\label{fig:1}
            \end{subfigure}
            ~
            \begin{subfigure}[b]{0.3\textwidth}
                \includegraphics[width=1.0\textwidth]{graphics/res_soleil2018_GGH_GGH_2018_cin2_phiG_I_327_vis_-40_1_Pos0_img_000000039_DM300_nofilter_vis_000.png}
                %\includegraphics[width=\textwidth]{1.png}
                \caption{Frame 39}
                %\label{fig:1}
            \end{subfigure}


            \caption{Example of trap sequence (\texttt{res\_soleil2018/GGH/GGH\_2018\_cin2\_phiG\_I\_327\_vis\_-40\_1/Pos0})}
            \label{fig:trap_sequence1}
        \end{figure}
        

\end{document}