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\documentclass [a4paper, 10pt] { article}
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\usepackage [utf8] { inputenc}
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\usepackage { graphicx}
\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
\hyphenation { tu-yau}
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\title { lipase}
\author { Guillaume Raffy \and Véronique Vié }
\begin { document}
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\selectlanguage { english}
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\maketitle
\section { catalog images}
image prefix :
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\selectlanguage { french}
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\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}
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\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}
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\end { document}