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resource/Sources/PointProcessing/IPCV_PointProcessing.tex

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+\documentclass[english,11pt,table,handout]{beamer}
+
+\input{ipcv-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}
+\usepackage{verbatim}
+
+
+
+\usepackage{pgfplots}
+
+
+\lecture[2]{Point Processing and Histogram}{lecture-text}
+
+% \subtitle{Sequence Control}
+
+\date{August 15, 2018}
+\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}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%\frame
+%{
+%	\Huge
+%	\begin{center}
+%	\textcolor{blue}{\textbf{What is local processing?}}
+%	\end{center}
+%}
+
+\section{Point processing}
+\frame
+{
+	\frametitle{Point processing}
+	\selectlanguage{english}
+	\begin{block}{Concepts}
+		\begin{itemize}
+			\item Image: $f(x,y)$
+			\begin{enumerate}
+				\item $x$: discrete variable, in $[0,1, .., N]$
+				\item $y$: discrete variable, in $[0,1, .., M]$
+				\item $f(x,y)$: discrete value, in $[0,1, .., 255]$
+			\end{enumerate}
+			\item point $\equiv$ pixel
+			\item $f(x,y)$: has $M \times N$ points (or pixels)
+		\end{itemize}
+	\end{block}
+
+	
+}
+\frame
+{
+	\frametitle{Point processing}
+	\selectlanguage{english}
+	\begin{block}{Definition and Notation}
+		\begin{itemize}
+			\item \textbf{Point processing}: Process each point by a function that depends ONLY the pixel's value and that does not depend on the point's neighbors.	
+			\item Pixel processing function:
+			\begin{itemize}
+				\item referred to as \textbf{transfer function}
+				\item denoted as $T[.]$
+			\end{itemize} 
+		\end{itemize}
+	\end{block}
+
+	\begin{figure}[!h]
+		\begin{tabular}{cc}
+			\includegraphics[scale=0.4]{point_process_model.png} &
+		\end{tabular}
+		
+	\end{figure}
+	\begin{itemize}
+		\item $f(x,y)$: input image
+		\item $g(x,y) = T[f(x,y)]$: output image
+	\end{itemize}
+	
+}
+
+\subsection{Linear transformation}
+\begin{frame}[fragile]
+	\frametitle{Point processing}
+	\selectlanguage{english}
+	\begin{block}{Linear transformation: Math}
+		\begin{itemize}
+			\item  $g(x,y) = a \times f(x,y) + b$
+			\item Where, $a$ and $b$: pre-defined parameters
+		\end{itemize}
+	\end{block}
+
+	\begin{block}{Linear transformation: Applications}
+		\begin{itemize}
+			\item General: Change the image's intensity, cause the input bighter or darker
+			\begin{itemize}
+				\item Users have to choose appropriate $a$ and $b$ (manually)
+			\end{itemize}
+			\item Specific:
+			\begin{itemize}
+				\item Create negative images
+				\item Convert to back-white image
+			\end{itemize}
+		\end{itemize}
+	\end{block}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+\begin{block}{Linear transformation: with Matlab}
+	\lstset{language=Matlab, basicstyle=\small, escapeinside={\%*}{*)}}
+	\begin{lstlisting}
+	%read input image
+	im = imread('cameraman.tif');
+	%set parameters
+	a1 = 1.5; b1 = 20;
+	a2 = 1.5; b2 = 50;
+	a3 = 0.5; b3 = 0;
+	%transform the input
+	im1 = a1 * im  + b1; %clipped to [0,255] auto
+	im2 = a2 * im  + b2; %clipped to [0,255] auto
+	im3 = a3 * im  + b3; %clipped to [0,255] auto
+	
+	
+	\end{lstlisting}
+\end{block}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+\begin{block}{Linear transformation: with Matlab(continued)}
+	\lstset{language=Matlab, basicstyle=\tiny, escapeinside={\%*}{*)}}
+	\begin{lstlisting}
+	%show output image
+	figure;
+	subplot(2,2,1); imshow(im); title('input image')
+	subplot(2,2,2); imshow(im1); 
+	t1 = sprintf('output image [a =%5.2f, b = %5.2f]',
+	              a1, b1); 
+	title(t1)
+	subplot(2,2,3); imshow(im2); 
+	t2 = sprintf('output image [a =%5.2f, b = %5.2f]', 
+	              a2, b2); 
+	title(t2)
+	subplot(2,2,4); imshow(im3); 
+	t3 = sprintf('output image [a =%5.2f, b = %5.2f]', 
+	              a3, b3); 
+	title(t3)
+	suptitle('Linear Transformation: output =  a*input + b');	
+	\end{lstlisting}
+\end{block}
+\end{frame}
+
+\begin{frame}[fragile]
+	\frametitle{Point processing}
+	\selectlanguage{english}
+	\begin{block}{Linear transformation: Illustration}
+	\begin{figure}[!h]
+		\begin{table}
+		\begin{tabular}{cc}
+			\includegraphics[width=2.3cm]{./images/cameraman.png} & \includegraphics[width=2.3cm]{./images/cameraman1.png} \\
+			Input image & Output Image \\
+			 & $[a=1.5, b=20]$ \\
+			\includegraphics[width=2.3cm]{./images/cameraman2.png} &
+			 \includegraphics[width=2.3cm]{./images/cameraman3.png} \\
+			 Output Image  & Output Image \\
+			 $[a=1.5, b=50]$ & $[a=0.5, b=0]$ 
+			 
+		\end{tabular}
+		\caption{Linear Transformation: \textbf{output} = a * \textbf{input} + b}
+		\end{table}
+	\end{figure}	
+	\end{block}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+\begin{block}{Linear transformation: Illustration}
+	\begin{figure}[!h]
+		\begin{table}
+			\begin{tabular}{c}
+				\includegraphics[width=7cm]{./images/linear_negative.png}
+				
+			\end{tabular}
+			\caption{Creating negative image: \textbf{output} = a * \textbf{input} + b; where, $\mathbf{a=-1, b = 255}$}
+		\end{table}
+	\end{figure}	
+\end{block}
+\end{frame}
+
+
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+\begin{block}{Linear transformation: Illustration}
+	\begin{figure}[!h]
+		\begin{table}
+			\begin{tabular}{c}
+				\includegraphics[height=6.5cm]{./images/negative_demo.png}
+				
+			\end{tabular}
+			\caption{Creating negative image: \textbf{output} = a * \textbf{input} + b; where, $\mathbf{a=-1, b = 255}$}
+		\end{table}
+	\end{figure}	
+\end{block}
+\end{frame}
+
+\subsection{Logarithmic transformation}
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+\begin{block}{Logarithmic transformation: Math}
+	\begin{itemize}
+		\item  $g(x,y) = a \times \log[{1 + f(x,y)] + b}$
+		\item Where, $a$: a pre-defined parameter
+	\end{itemize}
+\end{block}
+
+\begin{block}{Logarithm function}
+	\begin{tikzpicture}[scale=0.4,domain=1:16]
+	\draw[very thin,color=gray] (0,0) grid (15,6);
+	% Draw axes
+	\draw [<->] (0,7) node (yaxis) [above] {$\log_2(x)$}
+	|- (17,0) node (xaxis) [right] {$x$};
+	
+	\draw[color=blue, thick] plot (\x,{log2(\x)})
+	node[above] {$f(x) = \log_2(x)$};
+	
+	%\draw[color=blue, dashed] (0,0) -- (15,15) node[above] {$f(n)=n$};
+	%\draw[color=blue, dashed] (0,0) -- (16, 8) node[above] {$f(n)=n/2$};
+	\end{tikzpicture}
+	
+	\begin{itemize}
+		\item a large value $(x)$ $\rightarrow$ mapped to a smaller value $(\log_2 x)$
+		\item a large distance between two intensities in the input image $\rightarrow$ mapped to a smaller distance in the output image
+	\end{itemize}
+\end{block}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+
+\begin{block}{Logarithmic transformation: Applications}
+	\begin{itemize}
+		\item Input image: 
+		\begin{itemize}
+			\item have some regions with too dark intensities (\textbf{near 0})
+			\item have some regions with too bright intensities (\textbf{near 255})
+		\end{itemize}
+	
+		\item Requirement:
+		\begin{itemize}
+			\item Make dark regions brighter while keeping the intensity in bright regions lower than 255.
+			\item Or, make bright regions darker while keeping the intensity in dark regions lower than 0.
+		\end{itemize}
+		\item Solution: use logarithmic transformation
+		\item Often case:
+		\begin{itemize}
+			\item Should use logarithmic transformation to enhance the result of FFT before displaying
+		\end{itemize}
+			
+	\end{itemize}
+\end{block}
+\end{frame}
+
+
+
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+\begin{block}{Logarithmic transformation: Illustration}
+	\begin{figure}[!h]
+		\begin{table}
+			\begin{tabular}{c}
+				\includegraphics[height=6.5cm]{./images/log_trans.png}
+				
+			\end{tabular}
+			\caption{Samples}
+		\end{table}
+	\end{figure}	
+\end{block}
+\end{frame}
+
+
+
+\subsection{Exponential transformation}
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+\begin{block}{(Inverse-log) Exponential transformation: Math}
+	\begin{itemize}
+		\item  $g(x,y) = a \times e^{f(x,y)} + b$
+		\item Where, $a$  and $b$: pre-defined parameters
+	\end{itemize}
+\end{block}
+
+\begin{block}{Exponential function}
+	\begin{tikzpicture}[scale=0.5]
+		\begin{axis}[grid=both,
+				xmax=4,ymax=10,
+				axis lines=middle,
+				restrict y to domain=-1:10,
+				enlargelimits]
+		\addplot[blue]  {pow(e,x)} node[above]{$y=e^x$};
+		\end{axis}
+	\end{tikzpicture}
+	
+	\begin{itemize}
+		\item a small value $(x)$ $\rightarrow$ mapped to a larger value $e^x$
+		\item a small distance between two intensities in the input $\rightarrow$ mapped to a larger distance in the output image
+	\end{itemize}
+\end{block}
+\end{frame}
+
+
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+
+\begin{block}{Exponential transformation: Applications}
+	\begin{itemize}
+		\item map small differences between two intensities in the input to a larger differences in the output image (\textbf{contrast input images	})
+	\end{itemize}
+\end{block}
+
+\begin{block}{Exponential transformation: with Matlab}
+	\lstset{language=Matlab, basicstyle=\small, escapeinside={\%*}{*)}}
+	\begin{lstlisting}
+	%read input image
+	path = 'coffebean.png'
+	im = imread(path); %range [0->255]
+	%convert double image: [0->1]
+	im = im2double(im);
+	%set parameters
+	a = 1; b = -1;
+	%transform input image
+	im1 = a * exp(im) + b;
+	%normalize the output, to [0->1]
+	im1 = im1./max(im1(:));
+	\end{lstlisting}
+\end{block}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+
+\begin{block}{Exponential transformation: with Matlab (continued)}
+	\lstset{language=Matlab, basicstyle=\small, escapeinside={\%*}{*)}}
+	\begin{lstlisting}
+	%show image
+	figure; imshow(im); title('input image');
+	figure; imshow(im1); title('output image');
+	\end{lstlisting}
+\end{block}
+\begin{figure}[!h]
+	\begin{table}
+		\begin{tabular}{cc}
+			\includegraphics[height=4cm]{./images/coffeebean.png} &
+			\includegraphics[height=4cm]{./images/coffeebean1.png} \\
+			Input image & output image
+			
+		\end{tabular}
+		\caption{$g(x,y) = a \times e^{f(x,y)} + b$; where, $a = 1, b = -1$}
+	\end{table}
+\end{figure}
+
+\end{frame}
+
+
+\subsection{Power-law transformation}
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+\begin{block}{Power-law transformation: Math}
+	\begin{itemize}
+		\item  $g(x,y) = a \times f(x,y)^{\gamma} + b$
+		\item Where, $a$  and $b$: pre-defined parameters
+	\end{itemize}
+\end{block}
+
+\begin{block}{Power function}
+	\begin{figure}[!h]
+		\begin{table}
+			\begin{tabular}{c}
+				\includegraphics[height=5cm]{./images/gamma_func.png} 
+			\end{tabular}
+			%\caption{$f(x)= x^{\gamma}$}
+		\end{table}
+	\end{figure}
+\end{block}
+\end{frame}
+
+
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+\begin{block}{Power-law function: characteristics}
+	\begin{itemize}
+		\item Depend on $\gamma$, power-law transformation can be either
+		\begin{enumerate}
+			\item \textbf{linear transformation}: for $\gamma = 1$
+			\item \textbf{log transformation}: for $\gamma < 1$
+			\item \textbf{inverse-log transformation}: for $\gamma > 1$
+		\end{enumerate}
+		
+		
+	\end{itemize}
+\end{block}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Point processing}
+\selectlanguage{english}
+\begin{block}{Power-law transformation: Illustration}
+	\begin{figure}[!h]
+		\begin{table}
+			\begin{tabular}{c}
+				\includegraphics[width=9.5cm]{./images/power_law_trans.png} 
+			\end{tabular}
+			%\caption{$f(x)= x^{\gamma}$}
+		\end{table}
+	\end{figure}
+\end{block}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{Histogram}
+\subsection{Definition}
+\begin{frame}[fragile]
+\frametitle{Histogram}
+\selectlanguage{english}
+\begin{block}{Definition}
+	\textbf{Histogram} computed for image I is a \textbf{statistical quantity}, contains the following information
+	\begin{itemize}
+		\item number of pixels in I for each intensity (for each value in [0,255]). This kind of histogram is referred to as \textbf{unnormalized histogram}.
+		\begin{itemize}
+			\item Sum of all values in this kind of histogram  = total number of pixels in I
+		\end{itemize}
+		\item \textcolor{red}{probability distribution of intensities in image I}. This kind of histogram is referred to as \textbf{normalized histogram}.
+		\begin{itemize}
+			\item Sum of all values in this kind of histogram  = 1
+		\end{itemize}
+		
+	\end{itemize}
+\end{block}
+\end{frame}
+
+
+\begin{frame}[fragile]
+\frametitle{Histogram}
+\selectlanguage{english}
+\begin{figure}[!h]
+	\begin{table}
+		\begin{tabular}{cc}
+			\includegraphics[height=4cm]{./images/bean1.jpg} &
+			\includegraphics[height=4cm]{./images/histogram1.png} \\
+			(a) An image & (b) Its Histogram
+		\end{tabular}
+		%\caption{Image and Its histogram}
+	\end{table}
+\end{figure}
+\begin{itemize}
+	\item From histogram (b): almost of pixels in the image have the intensity near $0$. Therefore, the image is too dark, confirmed by image (a).
+\end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Histogram}
+\selectlanguage{english}
+\begin{figure}[!h]
+	\begin{table}
+		\begin{tabular}{cc}
+			\includegraphics[height=4cm]{./images/bean2.jpg} &
+			\includegraphics[height=4cm]{./images/histogram2.png} \\
+			(a) An image & (b) Its Histogram
+		\end{tabular}
+		%\caption{Image and Its histogram}
+	\end{table}
+\end{figure}
+\begin{itemize}
+	\item From histogram (b): almost of pixels in the image have the intensity near $255$. Therefore, the image is too bright, confirmed by image (a).
+\end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Histogram}
+\selectlanguage{english}
+\begin{figure}[!h]
+	\begin{table}
+		\begin{tabular}{cc}
+			\includegraphics[height=4cm]{./images/bean3.jpg} &
+			\includegraphics[height=4cm]{./images/histogram3.png} \\
+			(a) An image & (b) Its Histogram
+		\end{tabular}
+		%\caption{Image and Its histogram}
+	\end{table}
+\end{figure}
+\begin{itemize}
+	\item From histogram (b): almost of pixels in the image have the intensity compacted in short range $[100, 130]$. Therefore, the image has very low contrast, confirmed by image (a).
+\end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Histogram}
+\selectlanguage{english}
+\begin{figure}[!h]
+	\begin{table}
+		\begin{tabular}{cc}
+			\includegraphics[height=4cm]{./images/bean4.jpg} &
+			\includegraphics[height=4cm]{./images/histogram4.png} \\
+			(a) An image & (b) Its Histogram
+		\end{tabular}
+		%\caption{Image and Its histogram}
+	\end{table}
+\end{figure}
+\begin{itemize}
+	\item From histogram (b): the pixels in the image are distributed in a full range $[0,255]$. Therefore, the image is balanced (not to dark, not to bright) and has a high contrast (\textbf{preferred}).
+\end{itemize}
+\end{frame}
+
+\subsection{Computation}
+\begin{frame}[fragile]
+\frametitle{Histogram}
+\selectlanguage{english}
+\begin{block}{Histogram: with C/C++/Java}
+	Excercise:
+	\begin{itemize}
+		\item Write a function for computing the histogram (unnormalized and normalized) of the input image passed to the function.
+		
+	\end{itemize}
+\end{block}
+\end{frame}
+
+
+\begin{frame}[fragile]
+\frametitle{Histogram}
+\selectlanguage{english}
+\begin{block}{Histogram: with Matlab}
+	\begin{itemize}
+		\item use functions: \textbf{imhist}
+	\end{itemize}
+	\lstset{language=Matlab, basicstyle=\small, escapeinside={\%*}{*)}}
+	\begin{lstlisting}
+	%read input images
+	path1 = 'Fig3.15(a)1.jpg';
+	path2 = 'Fig3.15(a)2.jpg';
+	path3 = 'Fig3.15(a)3.jpg';
+	path4 = 'Fig3.15(a)4.jpg';
+	im1 = imread(path1); 
+	im2 = imread(path2); 
+	im3 = imread(path3); 
+	im4 = imread(path4); 
+	
+	%Compute histogram
+	[count1, x1] = imhist(im1);
+	[count2, x2] = imhist(im2);
+	[count3, x3] = imhist(im3);
+	[count4, x4] = imhist(im4);
+	\end{lstlisting}
+\end{block}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Histogram}
+\selectlanguage{english}
+\begin{block}{Histogram: with Matlab (continued)}
+	\lstset{language=Matlab, basicstyle=\small, escapeinside={\%*}{*)}}
+	\begin{lstlisting}
+	%show input images
+	figure; imshow(im1); title('input image 1');
+	figure; imshow(im2); title('input image 2');
+	figure; imshow(im3); title('input image 3');
+	figure; imshow(im4); title('input image 4');
+	
+	%draw histograms
+	figure; stem(x1, count1, '.'); 
+	xlim([0,255]); title('histogram 1');
+	figure; stem(x2, count2, '.'); 
+	xlim([0,255]); title('histogram 2');
+	figure; stem(x3, count3, '.'); 
+	xlim([0,255]); title('histogram 3');
+	figure; stem(x4, count4, '.'); 
+	xlim([0,255]); title('histogram 4');
+	\end{lstlisting}
+\end{block}
+\end{frame}
+
+\subsection{Equalization}
+\begin{frame}[fragile]
+\frametitle{Histogram: Equalization}
+\selectlanguage{english}
+\begin{block}{Histogram Equalization: What?}
+	\textbf{Histogram Equalization} is an operation to create an image (from a given image) whose pixels's value distributed uniformly in $[0,255]$
+	\begin{itemize}
+		\item Purpose of histogram equalization: to create image not too dark, not too bright, and high contrast
+	\end{itemize}
+\end{block}
+\begin{figure}[!h]
+	\begin{table}
+		\begin{tabular}{cc}
+			\includegraphics[height=4cm]{./images/bean1.jpg} &
+			\includegraphics[height=3.5cm]{./images/histogram1_norm.png} \\
+			(a) An image  & (b) Its normalized histogram \\
+			(\textcolor{red}{not preferred}) & (\textcolor{red}{not preferred})
+		\end{tabular}
+		%\caption{Image and Its histogram}
+	\end{table}
+\end{figure}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Histogram: Equalization}
+\selectlanguage{english}
+\begin{block}{Histogram Equalization: What?}
+	\textbf{Histogram Equalization} is an operation to create an image (from a given image) whose pixels's value distributed uniformly in $[0,255]$
+	\begin{itemize}
+		\item Purpose of histogram equalization: to create image not too dark, not too bright, and high contrast
+	\end{itemize}
+\end{block}
+\begin{figure}[!h]
+	\begin{table}
+		\begin{tabular}{cc}
+			\includegraphics[height=4cm]{./images/bean1_eq.png} &
+			\includegraphics[height=3.5cm]{./images/histogram1_eq_norm.png} \\
+			(a) Image, \textcolor{red}{ preferred} & (b) Histogram, \textcolor{red}{ preferred} \\
+			(after equalization)  &  (after equalization)
+			
+		\end{tabular}
+		%\caption{Image and Its histogram}
+	\end{table}
+\end{figure}
+\end{frame}
+
+
+\subsection{Specification}
+\begin{frame}[fragile]
+	\frametitle{Histogram: Equalization}
+	\selectlanguage{english}
+	
+	\begin{block}{Histogram Equalization: How?}
+		Input:
+		\begin{enumerate}
+			\item Input image I
+			\begin{itemize}
+				\item So, compute the \textbf{normalized-histogram} of image I, to obtain: $p_x(x)$: 
+			\end{itemize}
+			\item Expected \textbf{normalized-histogram} of the output image: $p_z(z)$
+			\begin{itemize}
+				\item with histogram equalization: $p_z(z)$ is a uniform distribution over $[0,255]$
+				\item with histogram specification: $p_z(z)$ is specified by users (interactively)
+			\end{itemize}
+		\end{enumerate} 
+	\end{block}
+\end{frame}
+
+\begin{frame}[fragile]
+\frametitle{Histogram: Equalization}
+\selectlanguage{english}
+
+\begin{block}{Histogram Equalization: How?}
+	We can determine $z$ (e.g., pixel value of the output image), if we know:
+	\begin{enumerate}
+		\item $x$: pixel value of the input image
+		\item $p_x(x)$: pdf of $x$
+		\item $p_z(z)$:  pdf of $z$
+	\end{enumerate} 
+
+	Assume that $z = f(x)$ has been determined, the output image $g(u,v)$ can be produced from the input $f(u,v)$ as follows:
+	\begin{itemize}
+		\item \textbf{foreach} point $(u,v)$ in $f(u,v)$:
+		\begin{itemize}
+			\item $x = f(u,v)$ (get the value of the input pixel)
+			\item $z = f(x)$  (map to the output value)
+			\item $g(u,v) = z$  (assign to the output pixel)
+		\end{itemize}
+	\end{itemize}
+\end{block}
+\end{frame}
+
+
+\begin{frame}[fragile]
+	\frametitle{Histogram: Equalization}
+	\selectlanguage{english}
+	
+	\begin{block}{Determination of $z = f(x)$ }
+		Let $c_x(x)$ and $c_z(z)$ be cumulative density functions of $x$ and $z$. 
+		
+		\begin{align}
+		\nonumber
+		c_x(x) &= \sum_{i=0}^{x}{p_x(i)}\\
+		\nonumber
+		c_z(z) &= \sum_{i=0}^{z}{p_z(i)}
+		\end{align}
+	\end{block}
+\end{frame}
+
+
+\begin{frame}[fragile]
+	\frametitle{Histogram: Equalization}
+	\selectlanguage{english}
+	
+	$z = f(x)$ be a function that map one-to-one between $x$ and $z$.
+	\begin{block}{Determination of $z = f(x)$ }
+		\begin{itemize}
+			\item Assume that we have $z_1 = f(x_1)$ 
+			\item Then, $c_z(z_1) = c_x(x_1)$. This is because of one-one mapping
+			\begin{itemize}
+				\item A value $x < x_1$ will be mapped into $z < z_1$
+			\end{itemize}
+			\item Define $w \equiv c_x(x_1)$, i.e., $w \equiv c_z(z_1) \equiv c_x(x_1)$
+		\end{itemize}
+		
+		Therefore,
+		\begin{itemize}
+			\item $z_1 = c_z^{-1}(w) \equiv   c_z^{-1}(c_x(x_1))$
+		\end{itemize}
+	\end{block}
+	\begin{alertblock}{Mapping function $f(x)$}
+		\centering
+		$z = f(x) =  c_z^{-1}(c_x(x))$
+		
+	\end{alertblock}
+	
+\end{frame}
+
+
+\begin{frame}[fragile]
+\frametitle{Histogram: Equalization}
+	\selectlanguage{english}
+	
+	\begin{block}{Implemtation of $z = f(x) =  c_z^{-1}(c_x(x))$}
+		\begin{enumerate}
+			\item If we have closed-form of $z = c_z^{-1}(w)$ then can use this function to determine $z$.
+			\item If we do not have closed-form of $c_z^{-1}(z)$
+			\begin{itemize}
+				\item Create a lookup table at the beginning for mapping $z \rightarrow c_z^{-1}(p)$, for discrete values $p$. We can do this because we know $c_z(z)$ in advance. This task is equal to rasterize $p = c_z(z)$ and store pairs into lookup table
+				\item Determine $z$ according to the lookup table.
+			\end{itemize} 
+			
+		\end{enumerate}
+		
+	\end{block}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\end{document}

resource/Sources/PointProcessing/ipcv-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/PointProcessing/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/PointProcessing/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'.