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+\documentclass[english,11pt,table,handout]{beamer}
+
+\input{dsa-style.tex}
+\usepackage{pgf}
+
+\newcommand{\Rule}[2]{\genfrac{}{}{0.7pt}{}{{\setlength{\fboxrule}{0pt}\setlength{\fboxsep}{3mm}\fbox{$#1$}}}{{\setlength{\fboxrule}{0pt}\setlength{\fboxsep}{3mm}\fbox{$#2$}}}}
+
+\newcommand{\Rulee}[3]{\genfrac{}{}{0.7pt}{}{{\setlength{\fboxrule}{0pt}\setlength{\fboxsep}{3mm}\fbox{$#1$}}}{{\setlength{\fboxrule}{0pt}\setlength{\fboxsep}{3mm}\fbox{$#2$}}}[#3]}
+
+\usepackage{url}
+
+\usepackage{qtree}
+
+\usepackage{datetime}
+
+\usepackage{amsfonts}
+\usepackage{mathtools}
+\usepackage{fancybox}
+\usepackage[linesnumbered]{algorithm2e}
+\usepackage{ragged2e}
+
+\lecture[3]{Local Processing on Images}{lecture-text}
+
+% \subtitle{Sequence Control}
+
+\date{09 September 2015}
+\newcounter{saveenumi}
+
+\usepackage{wrapfig}
+\usetikzlibrary{automata,arrows,positioning, chains, shapes.callouts, calc}
+
+\tikzstyle{mnode}=[circle, draw, fill=black, inner sep=0pt, minimum width=4pt]
+\tikzstyle{thinking} = [draw=blue, very thick]
+\edef\sizetape{1cm}
+\tikzstyle{tmtape}=[draw,minimum size=\sizetape]
+\tikzstyle{tmhead}=[arrow box,draw,minimum size=.5cm,arrow box
+arrows={east:.25cm, west:0.25cm}]
+\tikzset{
+  level/.style   = { ultra thick, blue },
+  connect/.style = { dashed, red },
+  notice/.style  = { draw, rectangle callout, callout relative pointer={#1} },
+  label/.style   = { text width=4cm }
+}
+
+\begin{document}
+
+\begin{frame}
+\selectlanguage{english}
+  \maketitle
+\end{frame}
+
+\begin{frame}\frametitle<presentation>{Overview}
+  \tableofcontents
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{Local processing}
+\frame
+{
+	\Huge
+	\begin{center}
+	\textcolor{blue}{\textbf{What is local processing?}}
+	\end{center}
+}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\frame
+{
+  \frametitle{What is local processing?}
+	\selectlanguage{english}
+	\begin{block}{Definition}
+		Local processing is an image operation where each pixel value $I(u, v)$ is changed by a \textbf{function} of the intensities of pixels in a neighborhood of the pixel $(u, v)$.
+	\end{block}
+		
+	\begin{figure}[!h]
+   	\includegraphics[scale=0.5]{localproc.png}
+	\end{figure}
+}
+
+\frame
+{
+	\frametitle{What is local processing?}
+	\begin{block}{Example of neighborhood}
+		\begin{itemize}
+			\item An image $I(u,v)$; a pixel $(u,v)$ and its neighborhood of $3\times 3 $ pixels
+		\end{itemize}
+	\end{block}
+	\centering
+	\begin{figure}[!h]
+		\includegraphics[scale=0.5]{neighborhood.png}
+	\end{figure}
+}
+
+\frame
+{
+	\frametitle{What is local processing?}
+	\begin{example}{Examples of some processing functions}
+	\begin{itemize}
+		\item Linear functions
+		\begin{enumerate}
+			\item Averaging function
+			\item Shifting function
+			\item Gaussian function
+			\item Edge detecting function
+		\end{enumerate}
+		\item Non-linear functions
+		\begin{enumerate}
+			\item Median function
+			\item Min function
+			\item Max function
+		\end{enumerate}
+	\end{itemize}
+	\end{example}
+}
+\frame
+{
+	\frametitle{What is local processing?}
+	\begin{itemize}
+		\item Example of an averaging function
+	\end{itemize}
+	\centering
+	\begin{figure}[!h]
+		\includegraphics[scale=0.5]{neighborhood.png}
+	\end{figure}
+	\begin{equation*}
+		I^{'}{(u,v)} = \frac{1}{9}\sum_{i=-1}^{1}{\sum_{j=-1}^{1}{I(u+i, v+j)}}
+	\end{equation*}
+	
+}
+
+\frame
+{
+	\frametitle{What is local processing?}
+	\begin{itemize}
+		\item Example of an averaging function
+	\end{itemize}
+	\centering
+	\begin{figure}[!h]
+		\begin{tabular}{cc}
+			\includegraphics[scale=0.11]{kyoto_gray.jpg} &
+			\includegraphics[scale=0.11]{kyoto_gray_smooth_9.jpg} \\
+			Input image & Output image
+		\end{tabular}
+	\end{figure}
+
+	\begin{itemize}
+		\item The output image is obtained by averaging the input with neighborhood of $9 \times 9$ pixels.
+	\end{itemize}
+}
+\frame
+{
+	\frametitle{What is local processing?}
+	\begin{itemize}
+		\item Example of an averaging function
+	\end{itemize}
+	\centering
+	\begin{figure}[!h]
+		\begin{tabular}{cc}
+			\includegraphics[scale=0.11]{kyoto_gray.jpg} &
+			\includegraphics[scale=0.11]{kyoto_gray_smooth_9.jpg} \\
+			Input image & Output image \\
+						& blurred, smoothed
+		\end{tabular}
+	\end{figure}
+	
+	\begin{equation*}
+	I^{'}{(u,v)} = \frac{1}{9\times 9}\sum_{i=-4}^{4}{\sum_{4=-4}^{4}{I(u+i, v+j)}}
+	\end{equation*}
+}
+\frame
+{
+	\frametitle{What is local processing?}
+	\begin{itemize}
+		\item Example of a median function (a non-linear function)
+	\end{itemize}
+	\centering
+	\begin{figure}[!h]
+		\begin{tabular}{cc}
+			\includegraphics[scale=0.57]{image_salt_peper.png} &
+			\includegraphics[scale=0.57]{image_salt_peper_denoise.png} \\
+			Input image & Output image\\
+				& Noises have been removed
+		\end{tabular}
+	\end{figure}
+	
+	\begin{itemize}
+		\item The output image is obtained by computing the median value of a set of pixels in a neighborhood of $5 \times 5$ pixels.
+	\end{itemize}
+}
+
+
+\section{Linear processing}
+\frame
+{
+	\Huge
+	\begin{center}
+		\textcolor{blue}{\textbf{Linear processing function}}
+	\end{center}
+}
+
+\subsection{Correlation}
+\frame
+{
+	\frametitle{Mean function}
+	Consider an averaging function on square window. In general, the window can have different size of each dimension. The output of the averaging is determined by.
+	
+	\begin{equation*} 
+	\begin{split}
+	I^{'}{(u,v)} &= \frac{1}{(2r+1) \times (2r+1)} \sum_{i=-r}^{r}{\sum_{-r}^{r}{I(u+i, v+j)}}
+	\end{split}
+	\end{equation*}
+	
+	$I^{'}(u,v)$ can be written as
+	
+	\begin{equation*} 
+	\begin{split}
+	I^{'}{(u,v)}	&= \sum_{i=-r}^{r}{\sum_{-r}^{r}{I(u+i, v+j).H_{corr}{(i,j)}}}
+	\end{split}
+	\end{equation*}
+}
+\frame
+{
+	\frametitle{Mean function}
+	\begin{enumerate}
+		\item $H_{corr}$ is a matrix of size $(2r+1) \times (2r+1)$ 
+		\item $H_{corr} = \frac{1}{(2r+1) \times (2r+1)} M_{identity}$
+		
+		and,
+		\item $M_{identity}$ : is an identity matrix of size $(2r+1) \times (2r+1)$
+	
+	\end{enumerate}
+	
+	\begin{example}
+	Matrix for averaging pixels in a neighborhood of size $5 \times 5$, i.e., $r= 2$.
+	$$
+		H_{corr} = \frac{1}{5 \times 5} \times 
+		\begin{bmatrix}
+			1 & 1 & 1 & 1 & 1 \\
+			1 & 1 & 1 & 1 & 1 \\
+			1 & 1 & 1 & 1 & 1 \\
+			1 & 1 & 1 & 1 & 1 \\
+			1 & 1 & 1 & 1 & 1 \\
+		\end{bmatrix}
+	$$
+	\end{example}
+}
+\frame
+{
+	\frametitle{From averaging function to others}
+	\begin{block}{A way to construct other linear processing functions}
+		If one changes $H_{corr}$ to other kinds of matrix, he obtains other linear function.
+	\end{block}
+	
+	\begin{example}
+	Edge detecting function (Sobel)
+	$$
+		H_{corr} = 
+		\begin{bmatrix}
+			1 & 0 & -1 \\
+			2 & 0 & -2 \\
+			1 & 0 & -1 \\
+		\end{bmatrix}
+		\quad 
+		H_{corr} = 
+		\begin{bmatrix}
+			1 & 2 & 1 \\
+			0 & 0 & 0 \\
+			-1 & -2 & -1 \\
+		\end{bmatrix}
+	$$
+	
+	Shifting function
+	$$
+	H_{corr} = 
+	\begin{bmatrix}
+		0 & 0 & 0 \\
+		0 & 0 & 1 \\
+		0 & 0 & 0 \\
+	\end{bmatrix}
+	$$
+	\end{example}
+}
+
+
+\frame
+{
+	\frametitle{Correlation}
+	
+	\begin{block}{Definition}
+		Input data:
+		\begin{enumerate}
+			\item Input image, $I(u,v)$
+			\item Matrix $H_{corr}{(i,j)}$ of size $(2r+1) \times (2r+1)$. In general, the size on two dimensions maybe different.
+		\end{enumerate}
+		\textbf{Correlation} is defined as follows:
+		\begin{equation*} 
+		\begin{split}
+		I_{corr}^{'}{(u,v)} &= \sum_{i=-r}^{r}{\sum_{-r}^{r}{I(u+i, v+j).H_{corr}{(i,j)}}}
+		\end{split}
+		\end{equation*}
+	\end{block}
+}
+
+
+\frame
+{
+	\frametitle{Correlation: How does it works?}
+	\selectlanguage{english}
+	\begin{figure}[!h]
+		\includegraphics[scale=0.57]{correlation.png}
+		\caption{Method for computing the correlation for one pixel}
+	\end{figure}
+}
+
+\frame
+{
+	\frametitle{Correlation: How does it works?}
+	\selectlanguage{english}
+	\begin{block}{A computation process}
+		For each pixel $(u,v)$ on the output image, do:
+		\begin{enumerate}
+			\item \textbf{Place} matrix $H_{corr}$ centered at the corresponding pixel, i.e., pixel $(u,v)$, on the input image
+			\item \textbf{Multiply} coefficients in matrix $H_{corr}$ with the underlying pixels on the input image.
+			\item \textbf{Compute} the sum of all the resulting products in the previous step.
+			\item \textbf{Assign} the sum to the $I^{'}(u,v)$.
+		\end{enumerate}
+	
+	\end{block}
+}
+
+
+\subsection{Convolution}
+\frame
+{
+	\frametitle{Convolution}
+	\selectlanguage{english}
+		
+	\begin{block}{Definition}
+		Input data:
+		\begin{enumerate}
+			\item Input image, $I(u,v)$
+			\item Matrix $H_{conv}$ of size $(2r+1) \times (2r+1)$. In general, the size on two dimensions maybe different.
+		\end{enumerate}
+		\textbf{Convolution} is defined as follows:
+		\begin{equation*} 
+		\begin{split}
+		I_{conv}^{'}{(u,v)} &= \sum_{i=-r}^{r}{\sum_{-r}^{r}{I(u-i, v-j).H_{conv}{(i,j)}}}
+		\end{split}
+		\end{equation*}
+	\end{block}
+}
+
+\frame
+{
+	\frametitle{Convolution}
+	\selectlanguage{english}
+	
+	\begin{block}{Natation}
+		\begin{itemize}
+			\item \alert{Operator *} is used to denote the convolution between image $I$ and matrix $H_{conv}$
+			\item That is
+			
+			\begin{equation*} 
+			\begin{split}
+			I_{conv}^{'}{(u,v)} &= I * H_{conv} \\
+				&= \sum_{i=-r}^{r}{\sum_{-r}^{r}{I(u-i, v-j).H_{conv}{(i,j)}}}
+			\end{split}
+			\end{equation*}
+		\end{itemize}
+		
+		
+	\end{block}
+}
+\frame
+{
+	\frametitle{Convolution}
+	\selectlanguage{english}
+	
+	\begin{alertblock}{Attention!}
+		\begin{itemize}
+			\item When $I$ is an gray image, both of $I$ and $H_{conv}$ are matrices.
+			\item However,  $I * H_{conv}$ is convolution between $I$ and $H_{conv}$, \textbf{instead of matrix multiplication}!
+	
+	\end{itemize}
+	
+	
+	\end{alertblock}
+}
+
+
+\frame
+{
+	\frametitle{Convolution and Correlation}
+	\selectlanguage{english}
+	
+	\begin{block}{Mathematics}
+		\begin{equation*} 
+		\begin{split}
+		I_{conv}^{'}{(u,v)} &= \sum_{i=-r}^{r}{\sum_{-r}^{r}{I(u-i, v-j).H_{conv}{(i,j)}}} \\
+		I_{corr}^{'}{(u,v)} &= \sum_{i=-r}^{r}{\sum_{-r}^{r}{I(u+i, v+j).H_{corr}{(i,j)}}}
+		\end{split}
+		\end{equation*}
+	\end{block}
+	In mathematics, convolution and correlation are different in the \textbf{sign} of $i$ and $j$ inside of $I(u+i, v+j)$ and $I(u-i, v-j)$
+}
+\frame
+{
+	\frametitle{Convolution and Correlation}
+	\selectlanguage{english}
+	
+	\begin{block}{Convolution to Correlation}
+		\begin{itemize}
+			\item Let $s=-i$ and $t=-j$ 
+			\item We have
+		\end{itemize}
+		\begin{equation*} 
+		\begin{split}
+		I_{conv}^{'}{(u,v)} &= \sum_{i=-r}^{r}{\sum_{-r}^{r}{I(u-i, v-j).H_{conv}{(i,j)}}} \\
+				&= \sum_{i=-r}^{r}{\sum_{-r}^{r}{I(u+s, v+t).H_{conv}{(-s,-t)}}} 
+		\end{split}
+		\end{equation*}
+	\end{block}
+	\begin{alertblock}{$H_{conv}{(-s,-t)}$ from $H_{conv}{(i,j)}$}
+		$H_{conv}{(-s,-t)}$ can be obtained from $H_{conv}{(i,j)}$ by either
+			\begin{itemize}
+				\item \textbf{Flipping} $H_{conv}{(i,j)}$ on x and then on y axis
+				\item \textbf{Rotating} $H_{conv}{(i,j)}$ around its center $180^0$
+			\end{itemize}
+	\end{alertblock}
+	
+}
+\frame
+{
+	\frametitle{Convolution and Correlation}
+	\selectlanguage{english}
+
+	
+	\begin{example}
+		Demonstration of rotation and flipping.
+		
+		$$
+		H = 
+		\begin{bmatrix}
+		1 & 2 & 3 \\
+		4 & 5 & 6 \\
+		7 & 8 & 9 \\
+		\end{bmatrix}
+		\quad
+		H_{flipped\_x} = 
+		\begin{bmatrix}
+		3 & 2 & 1 \\
+		6 & 5 & 4 \\
+		9 & 8 & 7 \\
+		\end{bmatrix}
+		$$
+		$H_{flipped\_x}$ is obtained from $H$ by flipping $H$ on x-axis.
+		
+		After flipping $H_{flipped\_x}$ around y axis
+		$$
+		H_{flipped_xy} = 
+		\begin{bmatrix}
+		9 & 8 & 7 \\
+		6 & 5 & 4 \\
+		3 & 2 & 1 \\
+		\end{bmatrix}
+		$$
+		
+		$H_{flipped\_xy}$ can obtained from $H$ by rotating $H$	$180^0$ around $H$'s center.
+		\end{example}
+}
+
+\frame
+{
+	\frametitle{Convolution and Correlation}
+	\selectlanguage{english}
+	
+	\begin{block}{Correlation to Convolution}
+	\begin{itemize}
+	\item Let $s=-i$ and $t=-j$ 
+	\item We have
+	\end{itemize}
+	\begin{equation*} 
+	\begin{split}
+	I_{corr}^{'}{(u,v)} &= \sum_{i=-r}^{r}{\sum_{-r}^{r}{I(u+i, v+j).H_{corr}{(i,j)}}} \\
+	&= \sum_{i=-r}^{r}{\sum_{-r}^{r}{I(u-s, v-t).H_{corr}{(-s,-t)}}} 
+	\end{split}
+	\end{equation*}
+	\end{block}
+	\begin{alertblock}{$H_{corr}{(-s,-t)}$ from $H_{corr}{(i,j)}$}
+	$H_{corr}{(-s,-t)}$ can be obtained from $H_{corr}{(i,j)}$ by either
+	\begin{itemize}
+	\item \textbf{Flipping} $H_{corr}{(i,j)}$ on x and then on y axis
+	\item \textbf{Rotating} $H_{corr}{(i,j)}$ around its center $180^0$
+	\end{itemize}
+	\end{alertblock}
+	
+}
+\frame
+{
+	\frametitle{Convolution-Correlation Conversion}
+	\selectlanguage{english}
+	\begin{alertblock}{Relationship}
+	\begin{enumerate}
+		
+		\item Convolution can be computed by correlation and vice versa.
+		
+		\item For example, convolution can be computed by correlation by: first, \alert{(a)} rotating the matrix $180^0$ and then \alert{(b)} computing the correlation between the rotated matrix with the input image.
+		
+	\end{enumerate}
+	
+	\end{alertblock}
+}
+
+\frame
+{
+	\frametitle{Convolution: How does it works?}
+	\selectlanguage{english}
+	\begin{block}{A Computation process}
+		\begin{enumerate}
+			\item \textbf{Rotate} matrix $H_{conv}$ around its center $180^0$ to obtain $H_{corr}$
+		\end{enumerate}
+		For each pixel $(u,v)$ on the output image, do:
+		\begin{enumerate}
+			\item \textbf{Place} matrix $H_{corr}$ centered at the corresponding pixel, i.e., pixel $(u,v)$, on the input image
+			\item \textbf{Multiply} coefficients in matrix $H_{corr}$ with the underlying pixels on the input image.
+			\item \textbf{Compute} the sum of all the resulting products in the previous step.
+			\item \textbf{Assign} the sum to the $I^{'}(u,v)$.
+		\end{enumerate}
+		
+	\end{block}
+}
+\frame
+{
+	\frametitle{MATLAB's function}
+	\selectlanguage{english}
+	\begin{example}
+		MATLAB's functions supports correlation and convolution
+		\begin{enumerate}
+			\item \alert{\textbf{corr2}}
+			\item \alert{\textbf{xcorr2}}
+			\item \alert{\textbf{conv2}}
+			\item \alert{\textbf{filter2}}
+			\item \alert{\textbf{imfilter}}
+		\end{enumerate}
+			MATLAB's function supports creating special matrix
+			\begin{enumerate}
+				\item \alert{\textbf{fspecial}}
+			\end{enumerate}
+	\end{example}
+}
+
+
+\subsection{Linear Filtering}
+\frame
+{
+	\frametitle{Linear Filtering}
+	\selectlanguage{english}
+	\begin{block}{Definition}
+		Linear filtering is a process of applying the \alert{\textbf{convolution}} between an matrix $H$ to input image $I(u,v)$.
+	\end{block}
+	\begin{block}{Model of a filter system}
+		\begin{figure}[!h]
+			\includegraphics[scale=0.57]{filtersys.png}
+			\caption{Filter image $I(u,v)$ with matrix $H$ to obtain $I^{'}(u,v)$} 
+		\end{figure}
+		
+		\centering
+		$I^{'}(u,v) =  I(u,v)*H(i,j)$
+	\end{block}
+}
+\frame
+{
+	\frametitle{Filter's kernel}
+	\selectlanguage{english}
+	\begin{block}{Definition}
+		In filtering, matrix $H$ is called the filter's kernel.
+	\end{block}
+	\begin{block}{Other names of $H$}
+		\begin{itemize}
+			\item Filter's kernel
+			\item Window
+			\item Mask
+			\item Template
+			\item Matrix
+			\item Local region
+		\end{itemize}
+	\end{block}
+}
+\subsection{Popular Linear Filter}
+\frame
+{
+	\frametitle{Popular Linear Filter: Mean filter}
+	\selectlanguage{english}
+	\begin{example}
+		Mean filter's kernel
+		\begin{itemize}
+			\item General case:
+		\end{itemize}
+		$$
+		H_{corr} = \frac{1}{(2r+1)^2} \times 
+		\begin{bmatrix}
+		1 & 1 & ... & 1 & 1 \\
+		1 & 1 & ... & 1 & 1 \\
+		... & ... & ... & ... & ... \\
+		1 & 1 & ... & 1 & 1 \\
+		1 & 1 & ... & 1 & 1 \\
+		\end{bmatrix}_{(2r+1) \times (2r+1)}
+		$$
+	\end{example}
+}
+
+\frame
+{
+	\frametitle{Popular Linear Filter: Mean filter}
+	\selectlanguage{english}
+	\begin{figure}
+		\begin{tabular}{cc}
+			\includegraphics[scale=0.53]{char.png} &
+			\includegraphics[scale=0.53]{char_mean_3_3.png} \\
+			Original image & Filtered with $H$'s size: $3 \times 3$
+		\end{tabular}
+	\end{figure}
+}
+
+\frame
+{
+	\frametitle{Popular Linear Filter: Mean filter}
+	\selectlanguage{english}
+	\begin{figure}
+		\begin{tabular}{cc}
+			\includegraphics[scale=0.53]{char_mean_5_5.png} &
+			\includegraphics[scale=0.53]{char_mean_11_11.png} \\
+			Filtered with $H$'s size: $5 \times 5$ & Filtered with $H$'s size: $11 \times 11$ 
+		\end{tabular}
+	\end{figure}
+}
+
+\frame
+{
+	\frametitle{Popular Linear Filter: Gaussian filter}
+	\selectlanguage{english}
+	\begin{block}{2D-Gaussian Function}
+		\begin{equation*}
+		\begin{split}
+				G(x,y, \sigma) &= \frac{1}{2\pi{\sigma}^2}  exp({-\frac{x^2 + y^2}{{2\sigma}^2}})
+		\end{split}
+		\end{equation*}
+	\end{block}
+	\begin{figure}
+		\includegraphics[scale=0.3]{gaussian.png}
+		\caption{2D-Gaussian Function}
+	\end{figure}
+}
+
+\frame
+{
+	\frametitle{Popular Linear Filter: Gaussian filter}
+	\selectlanguage{english}
+	\begin{example}
+		\begin{itemize}
+			\item $H$'s size is $3 \times 3$
+			\item $\sigma = 0.5$
+		\end{itemize}
+		$$
+		H = 
+		\begin{bmatrix}
+		0.0113   & 0.0838  &  0.0113\\
+		0.0838   & 0.6193  &  0.0838\\
+		0.0113   & 0.0838  &  0.0113
+		\end{bmatrix}
+		$$
+		\begin{itemize}
+			\item $H$'s size is $5 \times 5$
+			\item $\sigma = 0.5$
+		\end{itemize}
+		$$
+		H = 
+		\begin{bmatrix}
+		0.0000  &  0.0000  &  0.0002  &  0.0000  &  0.0000\\
+		0.0000  &  0.0113  &  0.0837  &  0.0113  &  0.0000\\
+		0.0002  &  0.0837  &  0.6187  &  0.0837  &  0.0002\\
+		0.0000  &  0.0113  &  0.0837  &  0.0113  &  0.0000\\
+		0.0000  &  0.0000  &  0.0002  &  0.0000  &  0.0000
+		\end{bmatrix}
+		$$
+	\end{example}
+}
+\frame
+{
+	\frametitle{Popular Linear Filter: Gaussian filter}
+	\selectlanguage{english}
+	\begin{figure}
+		\begin{tabular}{cc}
+			\includegraphics[scale=0.53]{char_mean_11_11.png} &
+			\includegraphics[scale=0.53]{char_gaussian_11_11_05.png} \\
+			Filtered with Mean filter  & Filtered with Gaussian filter \\
+			$H$'s size: $11 \times 11$ & $H$'s size: $11 \times 11$ \\
+									& 	$\sigma =0.5$
+		\end{tabular}
+	\end{figure}
+}
+
+\frame
+{
+	\frametitle{Popular Linear Filter: Shifting filter}
+	\selectlanguage{english}
+	\begin{example}
+		\begin{itemize}
+			\item In order to shift pixel $(u,v)$ to $(u-2, v+2)$, use the following kernel
+		\end{itemize}
+		$$
+		H = 
+		\begin{bmatrix}
+		0 & 0 & 0 & 0 & 1\\
+		0 & 0 & 0 & 0 & 0\\
+		0 & 0 & 0 & 0 & 0\\
+		0 & 0 & 0 & 0 & 0\\
+		0 & 0 & 0 & 0 & 0\\
+		\end{bmatrix}
+		$$
+		
+	\end{example}
+}
+
+\frame
+{
+	\frametitle{Popular Linear Filter: Shifting filter}
+	\selectlanguage{english}
+	\begin{figure}
+		\begin{tabular}{cc}
+			\includegraphics[scale=0.53]{char.png} &
+			\includegraphics[scale=0.53]{char_shifted_2_2.png} \\
+			Original image & Shifted with $d=[-2, 2]$ 
+		\end{tabular}
+	\end{figure}
+}
+
+\subsection{Convolution's Analysis}
+\frame
+{
+	\frametitle{Convolution's Complexity}
+	\selectlanguage{english}
+	\begin{block}{Computational Complexity}
+		\begin{itemize}
+			\item Input image $I$ has size $N \times M$
+			\item Kernel's size is $(2r+1) \times (2r+1)$
+			\item Then, the computational complexity is as follows:
+		\end{itemize}
+		\begin{equation*}
+			\begin{split}
+				O(MN(2r+1)(2r+1)) &= O(MNr^2)
+			\end{split}
+		\end{equation*}
+	\end{block}
+	
+}
+\frame
+{
+	\frametitle{Convolution's Properties}
+	\selectlanguage{english}
+	\begin{block}{Commutativity:}
+		\centering
+		$I * H = H * I$
+	\end{block}
+	\begin{alertblock}{Meaning}
+		\begin{enumerate}
+			\item This means that we can think of the image as the kernel and the kernel as the image and get the same result. 
+			
+			\item In other words, we can leave the image fixed and slide the kernel or leave the kernel fixed and slide the image.
+		\end{enumerate}		
+		
+	\end{alertblock}
+}
+
+\frame
+{
+	\frametitle{Convolution's Properties}
+	\selectlanguage{english}
+	\begin{block}{Associativity:}
+		\centering
+		$(I * H_{1})*H_{2} =I * (H_{1}*H_{2})$
+	\end{block}
+	\begin{alertblock}{Meaning}
+		\begin{enumerate}
+			\item This means that we can apply $H_{1}$ to $I$ followed by $H_{2}$, or we can convolve the kernel $H_{2} * H_{1}$  and then apply the resulting kernel to $I$.
+		\end{enumerate}		
+		
+	\end{alertblock}
+}
+\frame
+{
+	\frametitle{Convolution's Properties}
+	\selectlanguage{english}
+	\begin{block}{Linearity:}
+		\centering
+		$(\alpha .I)* H = \alpha. (I * H)$
+		
+		$(I_{1} + I_{2}) * H = I_{1} * H + I_{2}*H$
+		
+	\end{block}
+	\begin{alertblock}{Meaning}
+		\begin{enumerate}
+			\item This means that we can multiply an image by a constant before or after convolution, and we can add two images before or after convolution and get the same results. 
+		\end{enumerate}		
+		
+	\end{alertblock}
+}
+\frame
+{
+	\frametitle{Convolution's Properties}
+	\selectlanguage{english}
+	\begin{block}{Shift-Invariance}
+		Let $S$ be an operator that shifts an image I:
+		\centering
+		$S(I)(u,v) = I(u+a, v+b)$
+		
+		
+		\flushleft Then,
+		
+		\centering
+		$S(I*H) = S(I)*H$
+		
+	\end{block}
+	\begin{alertblock}{Meaning}
+		
+		\begin{enumerate}
+			\item This means that we can convolve $I$ and $H$ and then shift the result, or we can shift $I$ and then convolve it with $H$.
+		\end{enumerate}		
+		
+	\end{alertblock}
+}
+
+\frame
+{
+	\frametitle{Convolution's Properties}
+	\selectlanguage{english}
+	\begin{block}{Separability}
+		A kernel H is called separable if it can be broken down into the convolution of two kernels:
+		
+		\centering $H = H_{1} * H_{2}$
+		
+		\flushleft More generally, we might have:
+		
+		\centering $H = H_{1} * H_{2}* ... * H_{n}$
+	\end{block}
+}
+
+\frame
+{
+	\frametitle{Convolution's Properties}
+	\selectlanguage{english}
+	\begin{block}{Saving the computation with separability}
+		If we can separate a kernel H into two smaller kernels $H = H_{1} * H_{2}$, then it will often be cheaper to apply $H_{1}$ followed by $H_{2}$, rather than $H$.
+	\end{block}
+	Because, we have
+	
+	\begin{block}{Associativity:}
+		\centering
+		$(I * H_{1})*H_{2} =I * (H_{1}*H_{2})$
+	\end{block}
+}
+
+\frame
+{
+	\frametitle{Convolution's Properties}
+	\selectlanguage{english}
+	\begin{example}
+		$$
+		H_{x} = 
+		\begin{bmatrix}
+		1 & 1 & 1 & 1 & 1
+		\end{bmatrix}
+		\quad
+		H_{y} = 
+		\begin{bmatrix}
+		1 \\ 1 \\ 1
+		\end{bmatrix}
+		$$
+		
+		Then,
+		$$
+		H_{x}  = H_{x} * H_{y} = 
+		\begin{bmatrix}
+			1 & 1 & 1 & 1 & 1\\
+			1 & 1 & 1 & 1 & 1\\
+			1 & 1 & 1 & 1 & 1
+		\end{bmatrix}
+		$$
+		
+	\end{example}
+	
+}
+\frame
+{
+	\frametitle{Processing at the boundary of image}
+	\selectlanguage{english}
+	
+	\begin{figure}[!h]
+		\includegraphics[scale=0.57]{boundary_effect.png}
+		\caption{Without any special consideration, the processing is invalid at boundary pixels} 
+	\end{figure}
+
+}
+\frame
+{
+	\frametitle{Processing at the boundary of image}
+	\selectlanguage{english}
+	
+	\begin{block}{Methods for processing boundary pixels}
+		\begin{enumerate}
+			\item \textbf{Cropping}:do not process boundary pixels. Just obtain a smaller output image by cropping the output image.
+			\item \textbf{Padding}: pad a band of pixels (with zeros) to the boundary of input image. Perform the processing and the crop to get the output image.
+			\item \textbf{Extending}: copy pixels on the boundary to outside to get a new image. Perform the processing and the crop to get the output image.
+			\item \textbf{Wrapping}: reflect pixels on the boundary to outside to get a new image. Perform the processing and the crop to get the output image.
+			
+		\end{enumerate} 
+	\end{block}
+	
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\end{document}

resource/Sources/LocalProcessing/dsa-style.tex

@@ -0,0 +1,236 @@
+% Copyright 2007 by Till Tantau
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+%
+% See the file doc/licenses/LICENSE for more details.
+
+
+% Common packages
+\usepackage[utf8x]{inputenc}
+\usepackage[vietnam,english]{babel}
+\usepackage[utf8]{vietnam}
+%\usepackage{times}
+\usefonttheme[onlymath]{serif}
+\usecolortheme{default}
+\usepackage{booktabs}
+\usepackage{mathpartir}
+\usepackage{listings}
+\usepackage{listingsutf8}
+
+\usepackage{pbox}
+\mprset{flushleft}
+\mode<article>
+{
+  \usepackage{times}
+  \usepackage{mathptmx}
+  \usepackage[left=1.5cm,right=6cm,top=1.5cm,bottom=3cm]{geometry}
+}
+
+\usepackage{hyperref}
+\usepackage{tikz}
+\usetikzlibrary{arrows,backgrounds}
+%\tikzstyle{mnode}=[circle, draw, fill=black, inner sep=0pt, minimum width=4pt]
+\usepackage{colortbl}
+%\usepackage{yfonts}
+\usepackage{translator} % comment this, if not available
+
+
+% Common settings for all lectures in this course
+
+\def\lecturename{Image Processing and Computer Vision}
+
+\title{\insertlecture}
+
+\author{\textbf{LE Thanh Sach}}
+
+\institute
+{
+  \textit{Faculty of Computer Science and Engineering}\\
+  \textit{Ho Chi Minh University of Technology, VNU-HCM}
+}
+
+\subject{Lecturer \lecturename}
+
+% Beamer version theme settings
+
+\useoutertheme[height=0pt,width=2cm,right]{sidebar}
+\usecolortheme{rose,sidebartab}
+\useinnertheme{circles}
+\usefonttheme[only large]{structurebold}
+
+\setbeamercolor{sidebar right}{bg=black!15}
+\setbeamercolor{structure}{fg=blue}
+\setbeamercolor{author}{parent=structure}
+
+\setbeamerfont{title}{series=\normalfont,size=\LARGE}
+\setbeamerfont{title in sidebar}{series=\bfseries}
+\setbeamerfont{author in sidebar}{series=\bfseries}
+\setbeamerfont*{item}{series=}
+\setbeamerfont{frametitle}{size=}
+\setbeamerfont{block title}{size=\small}
+\setbeamerfont{subtitle}{size=\normalsize,series=\normalfont}
+
+\setbeamertemplate{navigation symbols}{}
+\setbeamertemplate{bibliography item}[book]
+\setbeamertemplate{sidebar right}
+{
+  {\usebeamerfont{title in sidebar}%
+    \vskip1.5em%
+    \hskip3pt%
+    \usebeamercolor[fg]{title in sidebar}%
+    \insertshorttitle[width=2cm,center,respectlinebreaks]\par%
+    \vskip1.25em%
+  }%
+  {%
+    \hskip3pt%
+    \usebeamercolor[fg]{author in sidebar}%
+    \usebeamerfont{author in sidebar}%
+    \insertshortauthor[width=2cm,center,respectlinebreaks]\par%
+    \vskip1.25em%
+  }%
+  \hbox to2cm{\hss\insertlogo\hss}
+  \vskip1.25em%
+  \insertverticalnavigation{2cm}%
+  \vfill
+  \hbox to 2cm{\hfill\usebeamerfont{subsection in
+      sidebar}\strut\usebeamercolor[fg]{subsection in
+      sidebar}\insertshortlecture.\insertframenumber\hskip5pt}%
+  \vskip3pt%
+}%
+
+\setbeamertemplate{title page}
+{
+  \vbox{}
+  \vskip1em
+  {\huge Chapter \insertshortlecture\par}
+  {\usebeamercolor[fg]{title}\usebeamerfont{title}\inserttitle\par}%
+  \ifx\insertsubtitle\@empty%
+  \else%
+    \vskip0.25em%
+    {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}%
+  \fi%     
+  \vskip1em\par
+  \emph{\lecturename}\ 
+  %on \insertdate\par
+  \vskip3em\par
+
+  \leftskip=0pt plus1fill\insertauthor\par
+  \insertinstitute\vskip1em
+}
+
+\logo{\includegraphics[width=1.5cm]{hcmut.png}}
+
+
+
+% Article version layout settings
+
+\mode<article>
+
+\makeatletter
+\def\@listI{\leftmargin\leftmargini
+  \parsep 0pt
+  \topsep 5\p@   \@plus3\p@ \@minus5\p@
+  \itemsep0pt}
+\let\@listi=\@listI
+
+
+\setbeamertemplate{frametitle}{\paragraph*{\insertframetitle\
+    \ \small\insertframesubtitle}\ \par
+}
+\setbeamertemplate{frame end}{%
+  \marginpar{\scriptsize\hbox to 1cm{\sffamily%
+      \hfill\strut\insertshortlecture.\insertframenumber}\hrule height .2pt}}
+\setlength{\marginparwidth}{1cm}
+\setlength{\marginparsep}{4.5cm}
+
+\def\@maketitle{\makechapter}
+
+\def\makechapter{
+  \newpage
+  \null
+  \vskip 2em%
+  {%
+    \parindent=0pt
+    \raggedright
+    \sffamily
+    \vskip8pt
+    {\fontsize{36pt}{36pt}\selectfont Chapter \insertshortlecture \par\vskip2pt}
+    {\fontsize{24pt}{28pt}\selectfont \color{blue!50!black} \insertlecture\par\vskip4pt}
+    {\Large\selectfont \color{blue!50!black} \insertsubtitle\par}
+    \vskip10pt
+
+    \normalsize\selectfont Print version of
+    Lecturer \emph{\lecturename} of \@date\par\vskip1.5em
+    %\hfill Le Thanh Sach and Luong The Nhan, Faculty of CSE, HCMC University of Technology
+  }
+  \par
+  \vskip 1.5em%
+}
+
+\let\origstartsection=\@startsection
+\def\@startsection#1#2#3#4#5#6{%
+  \origstartsection{#1}{#2}{#3}{#4}{#5}{#6\normalfont\sffamily\color{blue!50!black}\selectfont}}
+
+\makeatother
+
+\mode
+<all>
+
+
+
+
+% Typesetting Listings
+
+\usepackage{listings}
+\lstset{language=Java}
+
+\alt<presentation>
+{\lstset{%
+  basicstyle=\footnotesize\ttfamily,
+  commentstyle=\slshape\color{green!50!black},
+  keywordstyle=\bfseries\color{blue!50!black},
+  identifierstyle=\color{blue},
+  stringstyle=\color{orange},
+  escapechar=\#,
+  emphstyle=\color{red}}
+}
+{
+  \lstset{%
+    basicstyle=\ttfamily,
+    keywordstyle=\bfseries,
+    commentstyle=\itshape,
+    escapechar=\#,
+    emphstyle=\bfseries\color{red}
+  }
+}
+
+
+
+% Common theorem-like environments
+
+\theoremstyle{example}
+\newtheorem{exercise}[theorem]{\translate{Exercise}}
+
+
+% New useful definitions:
+
+\newbox\mytempbox
+\newdimen\mytempdimen
+
+\newcommand\includegraphicscopyright[3][]{%
+  \leavevmode\vbox{\vskip3pt\raggedright\setbox\mytempbox=\hbox{\includegraphics[#1]{#2}}%
+    \mytempdimen=\wd\mytempbox\box\mytempbox\par\vskip1pt%
+    \fontsize{3}{3.5}\selectfont{\color{black!25}{\vbox{\hsize=\mytempdimen#3}}}\vskip3pt%
+}}
+
+\newenvironment{colortabular}[1]{\medskip\rowcolors[]{1}{blue!20}{blue!10}\tabular{#1}\rowcolor{blue!40}}{\endtabular\medskip}
+
+\def\equad{\leavevmode\hbox{}\quad}
+
+\newenvironment{greencolortabular}[1]
+{\medskip\rowcolors[]{1}{green!50!black!20}{green!50!black!10}%
+  \tabular{#1}\rowcolor{green!50!black!40}}%
+{\endtabular\medskip}

resource/Sources/LocalProcessing/mathpartir.sty

@@ -0,0 +1,446 @@
+%  Mathpartir --- Math Paragraph for Typesetting Inference Rules
+%
+%  Copyright (C) 2001, 2002, 2003, 2004, 2005 Didier R<>my
+%
+%  Author         : Didier Remy 
+%  Version        : 1.2.0
+%  Bug Reports    : to author
+%  Web Site       : http://pauillac.inria.fr/~remy/latex/
+% 
+%  Mathpartir is free software; you can redistribute it and/or modify
+%  it under the terms of the GNU General Public License as published by
+%  the Free Software Foundation; either version 2, or (at your option)
+%  any later version.
+%  
+%  Mathpartir is distributed in the hope that it will be useful,
+%  but WITHOUT ANY WARRANTY; without even the implied warranty of
+%  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+%  GNU General Public License for more details 
+%  (http://pauillac.inria.fr/~remy/license/GPL).
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%  File mathpartir.sty (LaTeX macros)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{mathpartir}
+    [2005/12/20 version 1.2.0 Math Paragraph for Typesetting Inference Rules]
+
+%%
+
+%% Identification
+%% Preliminary declarations
+
+\RequirePackage {keyval}
+
+%% Options
+%% More declarations
+
+%% PART I: Typesetting maths in paragraphe mode
+
+%% \newdimen \mpr@tmpdim
+%% Dimens are a precious ressource. Uses seems to be local.
+\let \mpr@tmpdim \@tempdima
+
+% To ensure hevea \hva compatibility, \hva should expands to nothing 
+% in mathpar or in inferrule
+\let \mpr@hva \empty
+
+%% normal paragraph parametters, should rather be taken dynamically
+\def \mpr@savepar {%
+  \edef \MathparNormalpar
+     {\noexpand \lineskiplimit \the\lineskiplimit
+      \noexpand \lineskip \the\lineskip}%
+  }
+
+\def \mpr@rulelineskip {\lineskiplimit=0.3em\lineskip=0.2em plus 0.1em}
+\def \mpr@lesslineskip {\lineskiplimit=0.6em\lineskip=0.5em plus 0.2em}
+\def \mpr@lineskip  {\lineskiplimit=1.2em\lineskip=1.2em plus 0.2em}
+\let \MathparLineskip \mpr@lineskip
+\def \mpr@paroptions {\MathparLineskip}
+\let \mpr@prebindings \relax
+
+\newskip \mpr@andskip \mpr@andskip 2em plus 0.5fil minus 0.5em
+
+\def \mpr@goodbreakand
+   {\hskip -\mpr@andskip  \penalty -1000\hskip \mpr@andskip}
+\def \mpr@and {\hskip \mpr@andskip}
+\def \mpr@andcr {\penalty 50\mpr@and}
+\def \mpr@cr {\penalty -10000\mpr@and}
+\def \mpr@eqno #1{\mpr@andcr #1\hskip 0em plus -1fil \penalty 10}
+
+\def \mpr@bindings {%
+  \let \and \mpr@andcr
+  \let \par \mpr@andcr
+  \let \\\mpr@cr
+  \let \eqno \mpr@eqno
+  \let \hva \mpr@hva
+  } 
+\let \MathparBindings \mpr@bindings
+
+% \@ifundefined {ignorespacesafterend}
+%    {\def \ignorespacesafterend {\aftergroup \ignorespaces}
+
+\newenvironment{mathpar}[1][]
+  {$$\mpr@savepar \parskip 0em \hsize \linewidth \centering
+     \vbox \bgroup \mpr@prebindings \mpr@paroptions #1\ifmmode $\else
+     \noindent $\displaystyle\fi
+     \MathparBindings}
+  {\unskip \ifmmode $\fi\egroup $$\ignorespacesafterend}
+
+\newenvironment{mathparpagebreakable}[1][]
+  {\begingroup 
+   \par
+   \mpr@savepar \parskip 0em \hsize \linewidth \centering
+      \mpr@prebindings \mpr@paroptions #1%
+      \vskip \abovedisplayskip \vskip -\lineskip%
+     \ifmmode  \else  $\displaystyle\fi
+     \MathparBindings
+  }
+  {\unskip
+   \ifmmode $\fi \par\endgroup
+   \vskip \belowdisplayskip
+   \noindent
+  \ignorespacesafterend}
+
+% \def \math@mathpar #1{\setbox0 \hbox {$\displaystyle #1$}\ifnum
+%     \wd0 < \hsize  $$\box0$$\else \bmathpar #1\emathpar \fi}
+
+%%% HOV BOXES
+
+\def \mathvbox@ #1{\hbox \bgroup \mpr@normallineskip 
+  \vbox \bgroup \tabskip 0em \let \\ \cr
+  \halign \bgroup \hfil $##$\hfil\cr #1\crcr \egroup \egroup
+  \egroup}
+
+\def \mathhvbox@ #1{\setbox0 \hbox {\let \\\qquad $#1$}\ifnum \wd0 < \hsize
+      \box0\else \mathvbox {#1}\fi}
+
+
+%% Part II -- operations on lists
+
+\newtoks \mpr@lista
+\newtoks \mpr@listb
+
+\long \def\mpr@cons #1\mpr@to#2{\mpr@lista {\\{#1}}\mpr@listb \expandafter
+{#2}\edef #2{\the \mpr@lista \the \mpr@listb}}
+
+\long \def\mpr@snoc #1\mpr@to#2{\mpr@lista {\\{#1}}\mpr@listb \expandafter
+{#2}\edef #2{\the \mpr@listb\the\mpr@lista}}
+
+\long \def \mpr@concat#1=#2\mpr@to#3{\mpr@lista \expandafter {#2}\mpr@listb
+\expandafter {#3}\edef #1{\the \mpr@listb\the\mpr@lista}}
+
+\def \mpr@head #1\mpr@to #2{\expandafter \mpr@head@ #1\mpr@head@ #1#2}
+\long \def \mpr@head@ #1#2\mpr@head@ #3#4{\def #4{#1}\def#3{#2}}
+
+\def \mpr@flatten #1\mpr@to #2{\expandafter \mpr@flatten@ #1\mpr@flatten@ #1#2}
+\long \def \mpr@flatten@ \\#1\\#2\mpr@flatten@ #3#4{\def #4{#1}\def #3{\\#2}}
+
+\def \mpr@makelist #1\mpr@to #2{\def \mpr@all {#1}%
+   \mpr@lista {\\}\mpr@listb \expandafter {\mpr@all}\edef \mpr@all {\the
+   \mpr@lista \the \mpr@listb \the \mpr@lista}\let #2\empty 
+   \def \mpr@stripof ##1##2\mpr@stripend{\def \mpr@stripped{##2}}\loop
+     \mpr@flatten \mpr@all \mpr@to \mpr@one
+     \expandafter \mpr@snoc \mpr@one \mpr@to #2\expandafter \mpr@stripof
+     \mpr@all \mpr@stripend  
+     \ifx \mpr@stripped \empty \let \mpr@isempty 0\else \let \mpr@isempty 1\fi
+     \ifx 1\mpr@isempty
+   \repeat
+}
+
+\def \mpr@rev #1\mpr@to #2{\let \mpr@tmp \empty
+   \def \\##1{\mpr@cons ##1\mpr@to \mpr@tmp}#1\let #2\mpr@tmp}
+
+%% Part III -- Type inference rules
+
+\newif \if@premisse
+\newbox \mpr@hlist
+\newbox \mpr@vlist
+\newif \ifmpr@center \mpr@centertrue
+\def \mpr@htovlist {%
+   \setbox \mpr@hlist
+      \hbox {\strut
+             \ifmpr@center \hskip -0.5\wd\mpr@hlist\fi
+             \unhbox \mpr@hlist}%
+   \setbox \mpr@vlist
+      \vbox {\if@premisse  \box \mpr@hlist \unvbox \mpr@vlist
+             \else \unvbox \mpr@vlist \box \mpr@hlist
+             \fi}%
+}
+% OLD version
+% \def \mpr@htovlist {%
+%    \setbox \mpr@hlist
+%       \hbox {\strut \hskip -0.5\wd\mpr@hlist \unhbox \mpr@hlist}%
+%    \setbox \mpr@vlist
+%       \vbox {\if@premisse  \box \mpr@hlist \unvbox \mpr@vlist
+%              \else \unvbox \mpr@vlist \box \mpr@hlist
+%              \fi}%
+% }
+
+\def \mpr@item #1{$\displaystyle #1$}
+\def \mpr@sep{2em}
+\def \mpr@blank { }
+\def \mpr@hovbox #1#2{\hbox
+  \bgroup
+  \ifx #1T\@premissetrue
+  \else \ifx #1B\@premissefalse
+  \else
+     \PackageError{mathpartir}
+       {Premisse orientation should either be T or B}
+       {Fatal error in Package}%
+  \fi \fi
+  \def \@test {#2}\ifx \@test \mpr@blank\else
+  \setbox \mpr@hlist \hbox {}%
+  \setbox \mpr@vlist \vbox {}%
+  \if@premisse \let \snoc \mpr@cons \else \let \snoc \mpr@snoc \fi
+  \let \@hvlist \empty \let \@rev \empty
+  \mpr@tmpdim 0em
+  \expandafter \mpr@makelist #2\mpr@to \mpr@flat
+  \if@premisse \mpr@rev \mpr@flat \mpr@to \@rev \else \let \@rev \mpr@flat \fi
+  \def \\##1{%
+     \def \@test {##1}\ifx \@test \empty
+        \mpr@htovlist
+        \mpr@tmpdim 0em %%% last bug fix not extensively checked
+     \else
+      \setbox0 \hbox{\mpr@item {##1}}\relax
+      \advance \mpr@tmpdim by \wd0
+      %\mpr@tmpdim 1.02\mpr@tmpdim
+      \ifnum \mpr@tmpdim < \hsize
+         \ifnum \wd\mpr@hlist > 0
+           \if@premisse
+             \setbox \mpr@hlist 
+                \hbox {\unhbox0 \hskip \mpr@sep \unhbox \mpr@hlist}%
+           \else
+             \setbox \mpr@hlist
+                \hbox {\unhbox \mpr@hlist  \hskip \mpr@sep \unhbox0}%
+           \fi
+         \else 
+         \setbox \mpr@hlist \hbox {\unhbox0}%
+         \fi
+      \else
+         \ifnum \wd \mpr@hlist > 0
+            \mpr@htovlist 
+            \mpr@tmpdim \wd0
+         \fi
+         \setbox \mpr@hlist \hbox {\unhbox0}%
+      \fi
+      \advance \mpr@tmpdim by \mpr@sep
+   \fi
+   }%
+   \@rev
+   \mpr@htovlist
+   \ifmpr@center \hskip \wd\mpr@vlist\fi \box \mpr@vlist
+   \fi
+   \egroup
+}
+
+%%% INFERENCE RULES
+
+\@ifundefined{@@over}{%
+    \let\@@over\over % fallback if amsmath is not loaded
+    \let\@@overwithdelims\overwithdelims
+    \let\@@atop\atop \let\@@atopwithdelims\atopwithdelims
+    \let\@@above\above \let\@@abovewithdelims\abovewithdelims
+  }{}
+
+%% The default
+
+\def \mpr@@fraction #1#2{\hbox {\advance \hsize by -0.5em
+    $\displaystyle {#1\mpr@over #2}$}}
+\def \mpr@@nofraction #1#2{\hbox {\advance \hsize by -0.5em
+    $\displaystyle {#1\@@atop #2}$}}
+
+\let \mpr@fraction \mpr@@fraction
+
+%% A generic solution to arrow
+
+\def \mpr@make@fraction #1#2#3#4#5{\hbox {%
+     \def \mpr@tail{#1}%
+     \def \mpr@body{#2}%
+     \def \mpr@head{#3}%
+     \setbox1=\hbox{$#4$}\setbox2=\hbox{$#5$}%
+     \setbox3=\hbox{$\mkern -3mu\mpr@body\mkern -3mu$}%
+     \setbox3=\hbox{$\mkern -3mu \mpr@body\mkern -3mu$}%
+     \dimen0=\dp1\advance\dimen0 by \ht3\relax\dp1\dimen0\relax
+     \dimen0=\ht2\advance\dimen0 by \dp3\relax\ht2\dimen0\relax
+     \setbox0=\hbox {$\box1 \@@atop \box2$}%
+     \dimen0=\wd0\box0
+     \box0 \hskip -\dimen0\relax
+     \hbox to \dimen0 {$%
+       \mathrel{\mpr@tail}\joinrel
+       \xleaders\hbox{\copy3}\hfil\joinrel\mathrel{\mpr@head}%
+     $}}}
+
+%% Old stuff should be removed in next version
+\def \mpr@@nothing #1#2
+    {$\lower 0.01pt \mpr@@nofraction {#1}{#2}$}
+\def \mpr@@reduce #1#2{\hbox
+    {$\lower 0.01pt \mpr@@fraction {#1}{#2}\mkern -15mu\rightarrow$}}
+\def \mpr@@rewrite #1#2#3{\hbox
+    {$\lower 0.01pt \mpr@@fraction {#2}{#3}\mkern -8mu#1$}}
+\def \mpr@infercenter #1{\vcenter {\mpr@hovbox{T}{#1}}}
+
+\def \mpr@empty {}
+\def \mpr@inferrule
+  {\bgroup
+     \ifnum \linewidth<\hsize \hsize \linewidth\fi
+     \mpr@rulelineskip
+     \let \and \qquad
+     \let \hva \mpr@hva
+     \let \@rulename \mpr@empty
+     \let \@rule@options \mpr@empty
+     \let \mpr@over \@@over
+     \mpr@inferrule@}
+\newcommand {\mpr@inferrule@}[3][]
+  {\everymath={\displaystyle}%       
+   \def \@test {#2}\ifx \empty \@test
+      \setbox0 \hbox {$\vcenter {\mpr@hovbox{B}{#3}}$}%
+   \else 
+   \def \@test {#3}\ifx \empty \@test
+      \setbox0 \hbox {$\vcenter {\mpr@hovbox{T}{#2}}$}%
+   \else
+   \setbox0 \mpr@fraction {\mpr@hovbox{T}{#2}}{\mpr@hovbox{B}{#3}}%
+   \fi \fi
+   \def \@test {#1}\ifx \@test\empty \box0
+   \else \vbox 
+%%% Suggestion de Francois pour les etiquettes longues
+%%%   {\hbox to \wd0 {\RefTirName {#1}\hfil}\box0}\fi
+      {\hbox {\RefTirName {#1}}\box0}\fi
+   \egroup}
+
+\def \mpr@vdotfil #1{\vbox to #1{\leaders \hbox{$\cdot$} \vfil}}
+
+% They are two forms
+% \inferrule [label]{[premisses}{conclusions}
+% or
+% \inferrule* [options]{[premisses}{conclusions}
+%
+% Premisses and conclusions are lists of elements separated by \\
+% Each \\ produces a break, attempting horizontal breaks if possible, 
+% and  vertical breaks if needed. 
+% 
+% An empty element obtained by \\\\ produces a vertical break in all cases. 
+%
+% The former rule is aligned on the fraction bar. 
+% The optional label appears on top of the rule
+% The second form to be used in a derivation tree is aligned on the last
+% line of its conclusion
+% 
+% The second form can be parameterized, using the key=val interface. The
+% folloiwng keys are recognized:
+%       
+%  width                set the width of the rule to val
+%  narrower             set the width of the rule to val\hsize
+%  before               execute val at the beginning/left
+%  lab                  put a label [Val] on top of the rule
+%  lskip                add negative skip on the right
+%  left                 put a left label [Val]
+%  Left                 put a left label [Val],  ignoring its width 
+%  right                put a right label [Val]
+%  Right                put a right label [Val], ignoring its width
+%  leftskip             skip negative space on the left-hand side
+%  rightskip            skip negative space on the right-hand side
+%  vdots                lift the rule by val and fill vertical space with dots
+%  after                execute val at the end/right
+%  
+%  Note that most options must come in this order to avoid strange
+%  typesetting (in particular  leftskip must preceed left and Left and
+%  rightskip must follow Right or right; vdots must come last 
+%  or be only followed by rightskip. 
+%  
+
+%% Keys that make sence in all kinds of rules
+\def \mprset #1{\setkeys{mprset}{#1}}
+\define@key {mprset}{andskip}[]{\mpr@andskip=#1}
+\define@key {mprset}{lineskip}[]{\lineskip=#1}
+\define@key {mprset}{flushleft}[]{\mpr@centerfalse}
+\define@key {mprset}{center}[]{\mpr@centertrue}
+\define@key {mprset}{rewrite}[]{\let \mpr@fraction \mpr@@rewrite}
+\define@key {mprset}{atop}[]{\let \mpr@fraction \mpr@@nofraction}
+\define@key {mprset}{myfraction}[]{\let \mpr@fraction #1}
+\define@key {mprset}{fraction}[]{\def \mpr@fraction {\mpr@make@fraction #1}}
+\define@key {mprset}{sep}{\def\mpr@sep{#1}}
+
+\newbox \mpr@right
+\define@key {mpr}{flushleft}[]{\mpr@centerfalse}
+\define@key {mpr}{center}[]{\mpr@centertrue}
+\define@key {mpr}{rewrite}[]{\let \mpr@fraction \mpr@@rewrite}
+\define@key {mpr}{myfraction}[]{\let \mpr@fraction #1}
+\define@key {mpr}{fraction}[]{\def \mpr@fraction {\mpr@make@fraction #1}}
+\define@key {mpr}{left}{\setbox0 \hbox {$\TirName {#1}\;$}\relax
+     \advance \hsize by -\wd0\box0}
+\define@key {mpr}{width}{\hsize #1}
+\define@key {mpr}{sep}{\def\mpr@sep{#1}}
+\define@key {mpr}{before}{#1}
+\define@key {mpr}{lab}{\let \RefTirName \TirName \def \mpr@rulename {#1}}
+\define@key {mpr}{Lab}{\let \RefTirName \TirName \def \mpr@rulename {#1}}
+\define@key {mpr}{narrower}{\hsize #1\hsize}
+\define@key {mpr}{leftskip}{\hskip -#1}
+\define@key {mpr}{reduce}[]{\let \mpr@fraction \mpr@@reduce}
+\define@key {mpr}{rightskip}
+  {\setbox \mpr@right \hbox {\unhbox \mpr@right \hskip -#1}}
+\define@key {mpr}{LEFT}{\setbox0 \hbox {$#1$}\relax
+     \advance \hsize by -\wd0\box0}
+\define@key {mpr}{left}{\setbox0 \hbox {$\TirName {#1}\;$}\relax
+     \advance \hsize by -\wd0\box0}
+\define@key {mpr}{Left}{\llap{$\TirName {#1}\;$}}
+\define@key {mpr}{right}
+  {\setbox0 \hbox {$\;\TirName {#1}$}\relax \advance \hsize by -\wd0
+   \setbox \mpr@right \hbox {\unhbox \mpr@right \unhbox0}}
+\define@key {mpr}{RIGHT}
+  {\setbox0 \hbox {$#1$}\relax \advance \hsize by -\wd0
+   \setbox \mpr@right \hbox {\unhbox \mpr@right \unhbox0}}
+\define@key {mpr}{Right}
+  {\setbox \mpr@right \hbox {\unhbox \mpr@right \rlap {$\;\TirName {#1}$}}}
+\define@key {mpr}{vdots}{\def \mpr@vdots {\@@atop \mpr@vdotfil{#1}}}
+\define@key {mpr}{after}{\edef \mpr@after {\mpr@after #1}}
+
+\newcommand \mpr@inferstar@ [3][]{\setbox0
+  \hbox {\let \mpr@rulename \mpr@empty \let \mpr@vdots \relax
+         \setbox \mpr@right \hbox{}%
+         $\setkeys{mpr}{#1}%
+          \ifx \mpr@rulename \mpr@empty \mpr@inferrule {#2}{#3}\else
+          \mpr@inferrule [{\mpr@rulename}]{#2}{#3}\fi
+          \box \mpr@right \mpr@vdots$}
+  \setbox1 \hbox {\strut}
+  \@tempdima \dp0 \advance \@tempdima by -\dp1
+  \raise \@tempdima \box0}
+
+\def \mpr@infer {\@ifnextchar *{\mpr@inferstar}{\mpr@inferrule}}
+\newcommand \mpr@err@skipargs[3][]{}
+\def \mpr@inferstar*{\ifmmode 
+    \let \@do \mpr@inferstar@
+  \else 
+    \let \@do \mpr@err@skipargs
+    \PackageError {mathpartir}
+      {\string\inferrule* can only be used in math mode}{}%
+  \fi \@do}
+
+
+%%% Exports
+
+% Envirnonment mathpar
+
+\let \inferrule \mpr@infer
+
+% make a short name \infer is not already defined
+\@ifundefined {infer}{\let \infer \mpr@infer}{}
+
+\def \TirNameStyle #1{\small \textsc{#1}}
+\def \tir@name #1{\hbox {\small \TirNameStyle{#1}}}
+\let \TirName \tir@name
+\let \DefTirName \TirName
+\let \RefTirName \TirName
+
+%%% Other Exports
+
+% \let \listcons \mpr@cons
+% \let \listsnoc \mpr@snoc
+% \let \listhead \mpr@head
+% \let \listmake \mpr@makelist
+
+
+
+
+\endinput

resource/Sources/LocalProcessing/mhsetup.sty

@@ -0,0 +1,166 @@
+%%
+%% This is file `mhsetup.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% mhsetup.dtx  (with options: `package')
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%   http://www.latex-project.org/lppl.txt
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 2003/12/01 or later.
+%% 
+%% This work has the LPPL maintenance status "maintained".
+%% 
+%% The Current Maintainer of this work is Morten H\o gholm.
+%% 
+%% This work consists of the files mhsetup.dtx and mhsetup.ins and
+%% the derived file mhsetup.sty.
+%% 
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{mhsetup}
+  [2004/10/10 v1.0b programming setup (MH)]
+\def\MHInternalSyntaxOn{
+  \edef\MHInternalSyntaxOff{%
+  \catcode`\noexpand\~=\the\catcode`\~\relax
+  \catcode`\noexpand\ =\the\catcode`\ \relax
+  \catcode`\noexpand\^^I=\the\catcode`\^^I\relax
+  \catcode`\noexpand\@=\the\catcode`\@\relax
+  \catcode`\noexpand\:=\the\catcode`\:\relax
+  \catcode`\noexpand\_=\the\catcode`\_\relax
+  \endlinechar=\the\endlinechar\relax
+  }%
+  \catcode`\~=10\relax
+  \catcode`\ =9\relax
+  \catcode`\^^I=9\relax
+  \makeatletter
+  \catcode`\_=11\relax
+  \catcode`\:=11\relax
+  \endlinechar=` %
+  \relax
+}
+\MHInternalSyntaxOn
+\AtEndOfPackage{\MHInternalSyntaxOff}
+\let\MH_let:NwN \let
+\def\MH_let:cN #1#2{
+  \expandafter\MH_let:NwN \csname#1\endcsname#2}
+\def\MH_let:cc #1#2{
+  \expandafter\MH_let:NwN\csname#1\expandafter\endcsname
+  \csname#2\endcsname}
+\def\MH_new_boolean:n #1{
+  \expandafter\@ifdefinable\csname if_boolean_#1:\endcsname{
+    \@namedef{boolean_#1_true:}
+      {\MH_let:cN{if_boolean_#1:}\iftrue}
+    \@namedef{boolean_#1_false:}
+      {\MH_let:cN{if_boolean_#1:}\iffalse}
+    \@nameuse{boolean_#1_false:}%
+  }
+}
+\def\MH_set_boolean_F:n #1{ \@nameuse{boolean_#1_false:} }
+\def\MH_set_boolean_T:n #1{ \@nameuse{boolean_#1_true:} }
+\def\MH_if_boolean:nTF #1{
+  \@nameuse{if_boolean_#1:}
+    \expandafter\@firstoftwo
+  \else:
+    \expandafter\@secondoftwo
+  \fi:
+}
+\def\MH_if_boolean:nT #1{
+  \@nameuse{if_boolean_#1:}
+    \expandafter\@firstofone
+  \else:
+    \expandafter\@gobble
+  \fi:
+}
+\def\MH_if_boolean:nF #1{
+  \@nameuse{if_boolean_#1:}
+    \expandafter\@gobble
+  \else:
+    \expandafter\@firstofone
+  \fi:
+}
+\@ifundefined{if:w}{\MH_let:NwN \if:w =\if}{}
+\@ifundefined{if_meaning:NN}{\MH_let:NwN \if_meaning:NN =\ifx}{}
+\@ifundefined{else:}{\MH_let:NwN \else:=\else}{}
+\@ifundefined{fi:}{\MH_let:NwN \fi:=\fi}{}
+\@ifundefined{if_num:w}{\MH_let:NwN \if_num:w =\ifnum}{}
+\@ifundefined{if_dim:w}{\MH_let:NwN \if_dim:w =\ifdim}{}
+\@ifundefined{if_case:w}{\MH_let:NwN \if_case:w =\ifcase}{}
+\@ifundefined{or:}{\MH_let:NwN \or:=\or}{}
+\def\MH_cs_to_str:N {\expandafter\@gobble\string}
+\@ifundefined{eTeXversion}
+  {
+    \MH_let:NwN \MH_protected:\relax
+    \def\MH_setlength:dn{\setlength}
+    \def\MH_addtolength:dn{\addtolength}
+  }
+  {
+    \MH_let:NwN \MH_protected:\protected
+    \def\MH_setlength:dn #1#2{#1=\dimexpr#2\relax\relax}
+    \def\MH_addtolength:dn #1#2{\advance#1 \dimexpr#2\relax\relax}
+  }
+
+\def\MH_keyval_alias_with_addon:nnnn #1#2#3#4{
+  \@namedef{KV@#1@#2}{\@nameuse{KV@#1@#3}#4}
+  \@namedef{KV@#1@#2@default}{\@nameuse{KV@#1@#3@default}#4}}
+\def\MH_keyval_alias:nnn #1#2#3{
+  \MH_keyval_alias_with_addon:nnnn {#1}{#2}{#3}{}}
+\def\MH_use_choice_i:nnnn #1#2#3#4{#1}
+\def\MH_use_choice_ii:nnnn #1#2#3#4{#2}
+\def\MH_use_choice_iii:nnnn #1#2#3#4{#3}
+\def\MH_use_choice_iv:nnnn #1#2#3#4{#4}
+\long\def\MH_nospace_ifnextchar:Nnn #1#2#3{
+  \MH_let:NwN\reserved@d=~#1
+  \def\reserved@a{#2}
+  \def\reserved@b{#3}
+  \futurelet\@let@token\MH_nospace_nextchar:
+}
+\def\MH_nospace_nextchar:{
+  \if_meaning:NN \@let@token\reserved@d
+    \MH_let:NwN \reserved@b\reserved@a
+  \fi:
+  \reserved@b
+}
+\long\def\MH_nospace_testopt:nn #1#2{
+  \MH_nospace_ifnextchar:Nnn[
+    {#1}
+    {#1[{#2}]}
+}
+\def\MH_nospace_protected_testopt:n #1{
+  \if_meaning:NN \protect\@typeset@protect
+    \expandafter\MH_nospace_testopt:nn
+  \else:
+    \@x@protect#1
+  \fi:
+}
+\@ifundefined{kernel@ifnextchar}
+  {\MH_let:NwN \kernel@ifnextchar \@ifnextchar}
+  {}
+\MH_let:NwN \MH_kernel_xargdef:nwwn \@xargdef
+\long\def\MH_nospace_xargdef:nwwn #1[#2][#3]#4{
+  \@ifdefinable#1{
+     \expandafter\def\expandafter#1\expandafter{
+          \expandafter
+          \MH_nospace_protected_testopt:n
+          \expandafter
+          #1
+          \csname\string#1\endcsname
+          {#3}}
+       \expandafter\@yargdef
+          \csname\string#1\endcsname
+           \tw@
+           {#2}
+           {#4}}}
+\providecommand*\MHPrecedingSpacesOff{
+  \MH_let:NwN \@xargdef \MH_nospace_xargdef:nwwn
+}
+\providecommand*\MHPrecedingSpacesOn{
+  \MH_let:NwN \@xargdef \MH_kernel_xargdef:nwwn
+}
+\endinput
+%%
+%% End of file `mhsetup.sty'.