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This commit is contained in:
Nguyễn Anh Khoa
964
resource/Sources/ImageDerivatives/IPCV_ImageDerivatives.tex
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resource/Sources/ImageDerivatives/IPCV_ImageDerivatives.tex
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\documentclass[english,11pt,table,handout]{beamer}
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\input{dsa-style.tex}
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\usepackage{pgf}
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\usepackage{url}
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\usepackage{qtree}
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\usepackage{datetime}
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\usepackage{amsfonts}
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\usepackage{mathtools}
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\usepackage{fancybox}
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\usepackage[linesnumbered]{algorithm2e}
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\usepackage{ragged2e}
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\usepackage{verbatim}
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\lecture[3]{Image Derivatives}{lecture-text}
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% \subtitle{Sequence Control}
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\date{09 September 2015}
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\newcounter{saveenumi}
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\usepackage{wrapfig}
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\usetikzlibrary{automata,arrows,positioning, chains, shapes.callouts, calc}
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\tikzstyle{mnode}=[circle, draw, fill=black, inner sep=0pt, minimum width=4pt]
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\tikzstyle{thinking} = [draw=blue, very thick]
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\edef\sizetape{1cm}
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\tikzstyle{tmtape}=[draw,minimum size=\sizetape]
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\tikzstyle{tmhead}=[arrow box,draw,minimum size=.5cm,arrow box
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arrows={east:.25cm, west:0.25cm}]
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\tikzset{
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level/.style = { ultra thick, blue },
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connect/.style = { dashed, red },
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notice/.style = { draw, rectangle callout, callout relative pointer={#1} },
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label/.style = { text width=4cm }
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}
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\begin{document}
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\begin{frame}
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\selectlanguage{english}
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\maketitle
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\end{frame}
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\begin{frame}\frametitle<presentation>{Overview}
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\tableofcontents
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\frame
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%{
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% \Huge
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% \begin{center}
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% \textcolor{blue}{\textbf{What is local processing?}}
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% \end{center}
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%}
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\section{Image model}
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\frame
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{
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\frametitle{Image Model}
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\selectlanguage{english}
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\begin{block}{Image model}
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\begin{itemize}
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\item Image is a function of two variables $x$ and $y$: $f(x,y)$
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\item It can seen as a surface on 2D-space.
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\end{itemize}
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\end{block}
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\begin{figure}[!h]
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\begin{tabular}{cc}
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\includegraphics[scale=0.5]{char.png} &
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\includegraphics[scale=0.25]{char_mesh.png} \\
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An gray image & Mesh model of the image
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\end{tabular}
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\end{figure}
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}
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\section{First-order derivative}
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\frame
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{
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\frametitle{Derivative of one variable function}
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\selectlanguage{english}
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Taylor expansion for $f(x + \Delta x)$:
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\begin{align}
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\label{taylor_right}
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f(x + \Delta x) &= f(x) + \Delta x \times f^{'}(x) +\frac{{\Delta x}^2}{2!} \times f^{''}(x) + O({\Delta x}^3)
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\end{align}
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\begin{block}{First-order derivative from Eq. (\ref{taylor_right})}
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\alert{\textbf{Forward Approximation:}}
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\begin{equation*}
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\begin{split}
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f^{'}(x) &\cong \frac{f(x+ \Delta x) - f(x)}{\Delta x}\\
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&\cong f(x+1) - f(x) \quad \text{\alert{\textbf{in discrete domain}}}
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\end{split}
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\end{equation*}
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\begin{itemize}
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\item This approximation has error $O({\Delta x})$
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\end{itemize}
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\end{block}
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|
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}
|
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\frame
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{
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\frametitle{Derivative of one variable function}
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\selectlanguage{english}
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Taylor expansion for $f(x - \Delta x)$:
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|
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|
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\begin{align}
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\label{taylor_left}
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f(x - \Delta x) &= f(x) - \Delta x \times f^{'}(x) +\frac{{\Delta x}^2}{2!} \times f^{''}(x) - O({\Delta x}^3)
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\end{align}
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\begin{block}{First-order derivative from Eq. (\ref{taylor_left})}
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\alert{\textbf{Backward Approximation:}}
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\begin{equation*}
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\begin{split}
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f^{'}(x) &\cong \frac{f(x) - f(x- \Delta x)}{\Delta x}\\
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&\cong f(x) - f(x-1) \quad \text{\alert{\textbf{in discrete domain}}}
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\end{split}
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\end{equation*}
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\begin{itemize}
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\item This approximation has error $O({\Delta x})$
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\end{itemize}
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\end{block}
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|
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}
|
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\frame
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{
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\frametitle{Derivative of one variable function}
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\selectlanguage{english}
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Eq. (\ref{taylor_right}) - Eq. (\ref{taylor_left})
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\begin{align}
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\nonumber
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f(x + \Delta x) &= f(x) + \Delta x \times f^{'}(x) +\frac{{\Delta x}^2}{2!} \times f^{''}(x) + O({\Delta x}^3) \\
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\nonumber
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f(x - \Delta x) &= f(x) - \Delta x \times f^{'}(x) +\frac{{\Delta x}^2}{2!} \times f^{''}(x) - O({\Delta x}^3)
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\end{align}
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\begin{block}{First-order derivative from Eq. (\ref{taylor_right}) - Eq. (\ref{taylor_left}) }
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\alert{\textbf{Central Approximation:}}
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\begin{align}
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\nonumber
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f^{'}(x) &\cong \frac{f(x+ \Delta) - f(x- \Delta x)}{2\Delta x} &&\\
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\nonumber
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&\cong \frac{f(x+1) - f(x-1)}{2} &\text{\alert{\textbf{in discrete domain}}} \\
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\nonumber
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&\cong f(x+1) - f(x-1) &\text{\alert{\textbf{in discrete domain}}}
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\end{align}
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\begin{itemize}
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\item This approximation has error $O({\Delta x}^2)$
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\end{itemize}
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\end{block}
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}
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\frame
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{
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\frametitle{Derivative of one variable function}
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\selectlanguage{english}
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\begin{alertblock}{Notation}
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\begin{align}
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\nonumber
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f_x &\equiv \frac{\partial f(x,y)}{\partial x}\\
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\nonumber
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& \\
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\nonumber
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f_y &\equiv \frac{\partial f(x,y)}{\partial y}
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\end{align}
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\end{alertblock}
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}
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\frame
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{
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\frametitle{First-Order derivative of image}
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\selectlanguage{english}
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\renewcommand{\arraystretch}{3}
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\begin{tabular}{|*2{>{\renewcommand{\arraystretch}{1}}l|}}
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\hline
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\textbf{Derivatives} & \textbf{Kernel of filters}\\
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\hline
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$f_x \cong f(x+1, y) - f(x,y)$ &
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$H_{x} = $ $\left[ \begin{array}{cc} 1 & -1 \end{array}\right]$\\
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\hline
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$f_x \cong f(x, y) - f(x-1,y)$ &
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$H_{x} = $ $ \left[ \begin{array}{cc} 1 & -1 \end{array}\right]$\\
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\hline
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$f_x \cong f(x+1, y) - f(x-1,y)$ &
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$H_{x} =$ $ \left[ \begin{array}{ccc} 1 & 0 & -1 \end{array}\right]$\\
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\hline
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\end{tabular}
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}
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\frame
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{
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\frametitle{First-Order derivative of image}
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\selectlanguage{english}
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In general, fist-order derivatives can be computed by linear filters with the following kernels
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\newline
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\centering
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\begin{tabular}{|l||l|}
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\hline
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Derivative on x & Derivative on y \\
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\hline
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& \\
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$H_{x} = \left[ \begin{array}{cc} 1 & -1 \end{array}\right]^T$ &
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$H_{y} = \left[ \begin{array}{cc} 1 & -1 \end{array}\right]^T$\\
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&\\
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\hline
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& \\
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$H_{x} = \left[ \begin{array}{cc} -1 & 1 \end{array}\right]^T$ &
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$H_{y} = \left[ \begin{array}{cc} -1 & 1 \end{array}\right]^T$\\
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&\\
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\hline
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& \\
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$H_{x} = \left[ \begin{array}{ccc} -1 & 0 & 1 \end{array}\right]^T$ &
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$H_{y} = \left[ \begin{array}{ccc} -1 & 0 & 1 \end{array}\right]^T$\\
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&\\
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\hline
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& \\
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$H_{x} = \left[ \begin{array}{ccc} 1 & 0 & -1 \end{array}\right]^T$ &
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$H_{y} = \left[ \begin{array}{ccc} 1 & 0 & -1 \end{array}\right]^T$\\
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&\\
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\hline
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||||
\end{tabular}
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|
||||
}
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\frame
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||||
{
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\frametitle{First-Order derivative of image}
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\selectlanguage{english}
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||||
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Other kernels for computing first-order derivatives
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\renewcommand{\arraystretch}{1}
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\centering
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\begin{tabular}{|*3{>{\renewcommand{\arraystretch}{2}}l|}}
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\hline
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\textbf{Name} & \textbf{Derivative on x} & \textbf{Derivative on y}\\
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\hline
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||||
\textbf{Prewitt} &
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$H_{x} = $ $\left[ \begin{array}{rrr}
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-1 & 0 & 1 \\
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-1 & 0 & 1 \\
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-1 & 0 & 1 \\
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||||
\end{array}\right]$ &
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$H_{y} = $ $\left[ \begin{array}{rrr}
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-1 & -1 & -1 \\
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0 & 0 & 0 \\
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1 & 1 & 1 \\
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\end{array}\right]$\\
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\hline
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\textbf{Sobel} &
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$H_{x} = $ $\left[ \begin{array}{rrr}
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-1 & 0 & 1 \\
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-2 & 0 & 2 \\
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-1 & 0 & 1 \\
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\end{array}\right]$ &
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$H_{y} = $ $\left[ \begin{array}{rrr}
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-1 & -2 & -1 \\
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0 & 0 & 0 \\
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1 & 2 & 1 \\
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\end{array}\right]$\\
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\hline
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\textbf{Robert} &
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$H_{x} = $ $\left[ \begin{array}{rr}
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-1 & 0\\
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0 & 1 \\
|
||||
\end{array}\right]$ &
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||||
$H_{y} = $ $\left[ \begin{array}{rr}
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0 & -1\\
|
||||
1 & 0 \\
|
||||
\end{array}\right]$\\
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||||
\hline
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||||
\end{tabular}
|
||||
}
|
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\frame
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||||
{
|
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\frametitle{First-Order derivative of image}
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\selectlanguage{english}
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\begin{alertblock}{Properties}
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\begin{enumerate}
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\item First-order derivatives are operators that can be used to obtain the \alert{\textbf{variation of intensities}} on x and y axis.
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\item First-order derivatives can be either \alert{\textbf{positive}} or \alert{\textbf{negative}}.
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\item A large variation of intensities $\equiv$ \alert{\textbf{strong edge}} $\equiv$ large value in the absolute of derivatives.
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\item In order to display derivatives, we need to scale derivative images.
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\end{enumerate}
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\end{alertblock}
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}
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\begin{frame}[fragile]
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\frametitle{First-Order derivative of image}
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\selectlanguage{english}
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\begin{example}
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\lstset{language=Matlab}
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\begin{lstlisting}
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clear; close all; clc;
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im = checkerboard(50, 5, 5);
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im = uint8(255*(im > 0.5));
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H_1st_x = [1 0 -1];
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H_1st_y = [1 0 -1]';
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im_1st_x = abs(imfilter(double(im), H_1st_x));
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im_1st_y = abs(imfilter(double(im), H_1st_y));
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figure, imshow(im), title('Input Image');
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figure, imshow(gscale(im_1st_x)),
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title('1st derivative on x');
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figure, imshow(gscale(im_1st_y)),
|
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title('1st derivative on y');
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||||
\end{lstlisting}
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||||
\end{example}
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||||
|
||||
\end{frame}
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\begin{frame}[fragile]
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\frametitle{First-Order derivative of image}
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\selectlanguage{english}
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\begin{exercise}
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||||
\begin{figure}[!h]
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\includegraphics[scale=0.35]{checkboard.png}
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\caption{a chessboard shown by \alert{imshow(gscale(im))}}
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||||
\end{figure}
|
||||
|
||||
\begin{itemize}
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||||
\item What is the image obtained from the filtering with derivatives kernels?
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||||
\end{itemize}
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\end{exercise}
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||||
|
||||
\end{frame}
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||||
|
||||
\begin{frame}[fragile]
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||||
|
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\frametitle{First-Order derivative of image}
|
||||
\selectlanguage{english}
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||||
\begin{itemize}
|
||||
\item Sobel and Prewitt kernel can be obtained by function \alert{\textbf{fspecial}} in Matab
|
||||
\item In Matlab, the input image should be casted to \alert{\textbf{float}} or \alert{\textbf{double}} before filtering with function \alert{\textbf{imfilter}}
|
||||
\end{itemize}
|
||||
\begin{example}
|
||||
\lstset{language=Matlab}
|
||||
\begin{lstlisting}
|
||||
clear; close all; clc;
|
||||
im = imread('cameraman.tif');
|
||||
|
||||
H_1st_x = fspecial('Sobel');
|
||||
H_1st_y = fspecial('Sobel')'; %' = transpose
|
||||
|
||||
im_1st_x = abs(imfilter(double(im), H_1st_x));
|
||||
im_1st_y = abs(imfilter(double(im), H_1st_y));
|
||||
|
||||
figure, imshow(im), title('Input Image');
|
||||
figure, imshow(gscale(im_1st_x)),
|
||||
title('1st derivative on x');
|
||||
figure, imshow(gscale(im_1st_y)),
|
||||
title('1st derivative on y');
|
||||
\end{lstlisting}
|
||||
\end{example}
|
||||
|
||||
\end{frame}
|
||||
|
||||
\section{Gradient}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Gradient}
|
||||
\selectlanguage{english}
|
||||
|
||||
\begin{alertblock}{Definition}
|
||||
Gradient at a pixel in a image $f(x,y)$ is a vector $\nabla f$. It is defined as
|
||||
|
||||
\centering
|
||||
|
||||
$\nabla f = $
|
||||
$\left[ \begin{array}{r}
|
||||
f_x \\
|
||||
f_y
|
||||
\end{array}\right]$
|
||||
|
||||
\end{alertblock}
|
||||
|
||||
|
||||
}
|
||||
|
||||
\frame
|
||||
{
|
||||
\frametitle{Gradient}
|
||||
\selectlanguage{english}
|
||||
|
||||
\begin{block}{Magnitude and angle of gradient vectors}
|
||||
|
||||
\textbf{Magnitude} of gradient is computed by:
|
||||
|
||||
$|\nabla f|= \sqrt{f_{x}^{2} + f_{y}^{2}}$
|
||||
|
||||
or, approximated by
|
||||
|
||||
$|\nabla f|= |f_{x}| + |f_{y}|$
|
||||
|
||||
\begin{itemize}
|
||||
\item Magnitude of a gradient at pixel $(u,v)$ tells us the rate of change of intensities at $(u,v)$
|
||||
\item In other words, it tells us the edge passing $(u,v)$ is strong or not.
|
||||
\end{itemize}
|
||||
|
||||
|
||||
\end{block}
|
||||
|
||||
}
|
||||
|
||||
|
||||
\frame
|
||||
{
|
||||
\frametitle{Gradient}
|
||||
\selectlanguage{english}
|
||||
|
||||
\begin{block}{Magnitude and angle of gradient vectors}
|
||||
\textbf{Angle} of gradient is computed by:
|
||||
|
||||
$\theta(\nabla f)= $
|
||||
$tan^{-1}(\frac{f_{y}}{f_{x}})$
|
||||
|
||||
\begin{itemize}
|
||||
\item Angle of a gradient at pixel $(u,v)$ tells us the orientation of edge passing $(u,v)$
|
||||
|
||||
\item Gradient vector is perpendicular to the local edge passing $(u,v)$
|
||||
\end{itemize}
|
||||
|
||||
\end{block}
|
||||
|
||||
}
|
||||
\begin{frame}[fragile]
|
||||
|
||||
\frametitle{First-Order derivative of image}
|
||||
\selectlanguage{english}
|
||||
\begin{exercise}
|
||||
\begin{figure}[!h]
|
||||
\includegraphics[scale=0.25]{checkboard.png}
|
||||
\caption{a chessboard}
|
||||
\end{figure}
|
||||
|
||||
\begin{itemize}
|
||||
\item How do we create an image emphasizing both of horizontal and vertical edges the above chessboard?
|
||||
\item Which is the direction of gradient vectors at strong edge points?
|
||||
\end{itemize}
|
||||
\end{exercise}
|
||||
|
||||
\end{frame}
|
||||
|
||||
\section{Second-order derivative}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Second-order Derivative of one variable function}
|
||||
\selectlanguage{english}
|
||||
Second-order differential can be approximated by
|
||||
|
||||
|
||||
\begin{align}
|
||||
\nonumber
|
||||
f^{''}(x) \cong f^{'}(x) - f^{'}(x+1)
|
||||
\end{align}
|
||||
|
||||
|
||||
First-order derivatives can be approximated as
|
||||
\begin{align}
|
||||
\nonumber
|
||||
f^{'}(x) &\cong f(x) - f(x-1) \\
|
||||
\nonumber
|
||||
f^{'}(x+1) &\cong f(x+1) - f(x)
|
||||
\end{align}
|
||||
|
||||
\begin{alertblock}{Second-order derivative}
|
||||
\begin{align}
|
||||
\nonumber
|
||||
f^{''}(x) \cong -f^{'}(x-1) + 2f^{'}(x) - f(x+1)
|
||||
\end{align}
|
||||
\end{alertblock}
|
||||
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Second-Order derivative of image}
|
||||
\selectlanguage{english}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Second-order derivative on x
|
||||
\begin{itemize}
|
||||
\item Math:
|
||||
\begin{align}
|
||||
\nonumber
|
||||
\frac{\partial^{2} f(x,y)}{\partial x^2} = -f(x-1, y) + 2f(x,y) - f(x+1,y)
|
||||
\end{align}
|
||||
|
||||
|
||||
\item Kernel: $H_{conv} = $ $\left[ \begin{array}{rrr} -1 & 2 & -1 \end{array}\right] $
|
||||
|
||||
\end{itemize}
|
||||
\item Second-order derivative on y
|
||||
\begin{itemize}
|
||||
\item Math:
|
||||
\begin{align}
|
||||
\nonumber
|
||||
\frac{\partial^{2} f(x,y)}{\partial y^2} = -f(x, y-1) + 2f(x,y) - f(x,y+1)
|
||||
\end{align}
|
||||
|
||||
|
||||
\item Kernel: $H_{conv} = $ $\left[ \begin{array}{r} -1 \\ 2 \\ -1 \end{array}\right]$
|
||||
|
||||
\end{itemize}
|
||||
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Second-Order derivative of image}
|
||||
\selectlanguage{english}
|
||||
In general, second-order derivatives can be approximated by using the following kernels.
|
||||
\newline
|
||||
|
||||
\centering
|
||||
\small
|
||||
\begin{tabular}{|l|l|l|}
|
||||
\hline
|
||||
&Derivative on x & Derivative on y \\
|
||||
\hline
|
||||
& & \\
|
||||
|
||||
Positive at center: &
|
||||
$H_{x} = $ $\left[ \begin{array}{rrr} -1 & 2 & -1 \end{array}\right] $ &
|
||||
$H_{y} = $ $\left[ \begin{array}{r} -1 \\ 2 \\ -1 \end{array}\right]$\\
|
||||
|
||||
& & \\
|
||||
\hline
|
||||
& & \\
|
||||
|
||||
Negative at center: &
|
||||
$H_{x} = $ $\left[ \begin{array}{rrr} 1 & -2 & 1 \end{array}\right] $ &
|
||||
$H_{y} = $ $\left[ \begin{array}{r} 1 \\ -2 \\ 1 \end{array}\right]$\\
|
||||
& & \\
|
||||
|
||||
\hline
|
||||
\end{tabular}
|
||||
}
|
||||
|
||||
\frame
|
||||
{
|
||||
\frametitle{First-order and Second-order derivative}
|
||||
\selectlanguage{english}
|
||||
\begin{figure}[!h]
|
||||
\includegraphics[scale=0.6]{derivatives.png}
|
||||
\caption{Example of First-order and Second-order derivatives }
|
||||
\end{figure}
|
||||
}
|
||||
|
||||
\frame
|
||||
{
|
||||
\frametitle{First-order and Second-order derivative}
|
||||
\selectlanguage{english}
|
||||
\begin{alertblock}{First-order derivative's properties}
|
||||
\begin{enumerate}
|
||||
\item First-order derivatives produce \alert{\textbf{thicker edge}} in an image.
|
||||
\item First-order derivatives produce \alert{\textbf{strong response}} to a gray-level step.
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
\end{alertblock}
|
||||
|
||||
\begin{alertblock}{Second-order derivative's properties}
|
||||
\begin{enumerate}
|
||||
\item Second-order derivatives produce \alert{\textbf{stronger response}} to fine detail, such as thin lines or isolated points (noise).
|
||||
\item Second-order derivatives produce \alert{\textbf{double response}} (a \alert{\textbf{positive}} and a \alert{\textbf{negative}}) at step change in in gray level.
|
||||
\item \alert{\textbf{Zero-crossing}} at a point in second-order derivatives indicates that there is an edge passing that point.
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
\end{alertblock}
|
||||
}
|
||||
|
||||
\section{Laplacian}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Second-Order derivative of image}
|
||||
\selectlanguage{english}
|
||||
|
||||
\alert{\textbf{Second-order derivative on x and y}}
|
||||
|
||||
Laplacian operator:
|
||||
\begin{align}
|
||||
\nonumber
|
||||
\nabla^{2}f = \frac{\partial^{2} f(x,y)}{\partial x^2} + \frac{\partial^{2} f(x,y)}{\partial y^2}
|
||||
\end{align}
|
||||
|
||||
\begin{itemize}
|
||||
\item Math:
|
||||
\begin{align}
|
||||
\nonumber
|
||||
\nabla^{2}f & = &-f(x-1, y) + 2f(x,y) - f(x+1,y) \\
|
||||
\nonumber
|
||||
&&-f(x, y-1) + 2f(x,y) - f(x,y+1)
|
||||
\end{align}
|
||||
|
||||
|
||||
\item Kernel: $H_{lap} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
0 & -1 & 0 \\
|
||||
-1 & 4 & -1\\
|
||||
0 & -1 & 0
|
||||
\end{array}\right] $
|
||||
|
||||
\end{itemize}
|
||||
|
||||
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Second-Order derivative of image}
|
||||
\selectlanguage{english}
|
||||
|
||||
\alert{\textbf{Second-order derivative on x, y, and diagonals:}}
|
||||
|
||||
Extended Laplacian operator:
|
||||
|
||||
\begin{itemize}
|
||||
\item Math:
|
||||
\begin{align}
|
||||
\nonumber
|
||||
\nabla^{2}f & = &-f(x-1, y) + 2f(x,y) - f(x+1,y) \\
|
||||
\nonumber
|
||||
&&-f(x, y-1) + 2f(x,y) - f(x,y+1)
|
||||
\end{align}
|
||||
|
||||
|
||||
\item Kernel: $H_{lap} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
-1 & -1 & -1 \\
|
||||
-1 & 8 & -1\\
|
||||
-1 & -1 & -1
|
||||
\end{array}\right] $
|
||||
|
||||
\end{itemize}
|
||||
}
|
||||
|
||||
\frame
|
||||
{
|
||||
\frametitle{Second-Order derivative of image}
|
||||
\selectlanguage{english}
|
||||
|
||||
In general, Laplician can be computed by using the following kernels. The center coefficients maybe positive or negative.
|
||||
\newline
|
||||
|
||||
\centering
|
||||
\begin{tabular}{|l||l|}
|
||||
\hline
|
||||
& \\
|
||||
$H_{lap} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
0 & -1 & 0 \\
|
||||
-1 & 4 & -1\\
|
||||
0 & -1 & 0
|
||||
\end{array}\right] $
|
||||
&
|
||||
$H_{lap} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
-1 & -1 & -1 \\
|
||||
-1 & 8 & -1\\
|
||||
-1 & -1 & -1
|
||||
\end{array}\right] $ \\
|
||||
& \\
|
||||
\hline
|
||||
& \\
|
||||
$H_{lap} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
0 & 1 & 0 \\
|
||||
1 & -4 & 1\\
|
||||
0 & 1 & 0
|
||||
\end{array}\right] $
|
||||
&
|
||||
$H_{lap} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
1 & 1 & 1 \\
|
||||
1 & -8 & 1\\
|
||||
1 & 1 & 1
|
||||
\end{array}\right] $ \\
|
||||
& \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
|
||||
|
||||
|
||||
}
|
||||
\section{Applications of Laplacican}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Applications of Laplacican operator}
|
||||
\begin{alertblock}{Properties of Laplacican operators}
|
||||
\begin{enumerate}
|
||||
\item \textbf{Highlight} gray-level discontinues in images, i.e., edges on images
|
||||
\item \textbf{De-emphasize} regions with slowly varying gray-levels
|
||||
\end{enumerate}
|
||||
|
||||
Therefore, adding (or subtracting) the original image with Laplacian image (the image obtained by filtering the original with Laplacian kernel) $\Rightarrow$ \alert{\textbf{Sharpened images}}
|
||||
\end{alertblock}
|
||||
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Applications of Laplacican operator}
|
||||
Method for sharpening image $f(x,y)$:
|
||||
\flushleft
|
||||
$$
|
||||
g(x,y) =
|
||||
\begin{cases}
|
||||
f(x,y) - \nabla^2f(x,y)& \text{if the center coefficient of the}\\
|
||||
& \text{Laplacian mask is negative }\\
|
||||
f(x,y) + \nabla^2f(x,y)& \text{if the center coefficient of the} \\
|
||||
& \text{Laplacian mask is positive }
|
||||
\end{cases}
|
||||
$$
|
||||
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Second-Order derivative of image}
|
||||
\selectlanguage{english}
|
||||
Method for sharpening image $f(x,y)$ by using linear filters. Kernels are as follows:
|
||||
\newline
|
||||
|
||||
\begin{tabular}{|l|l|}
|
||||
\hline
|
||||
\textbf{Positive central coefficient} & \textbf{Positive central coefficient} \\
|
||||
\hline
|
||||
& \\
|
||||
$H_{Lap} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
-1 & -1 & -1 \\
|
||||
-1 & 9 & -1\\
|
||||
-1 & -1 & -1
|
||||
\end{array}\right] $ &
|
||||
$H_{Lap} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
1 & 1 & 1 \\
|
||||
1 & -9 & 1\\
|
||||
1 & -1 & 1
|
||||
\end{array}\right] $ \\
|
||||
& \\
|
||||
\hline
|
||||
& \\
|
||||
$H_{Lap} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
0 & -1 & 0 \\
|
||||
-1 & 5 & -1\\
|
||||
0 & -1 & 0
|
||||
\end{array}\right] $ &
|
||||
$H_{Lap} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
0 & 1 & 0 \\
|
||||
1 & -5 & 1\\
|
||||
0 & -1 & 0
|
||||
\end{array}\right] $ \\
|
||||
& \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
|
||||
|
||||
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Applications of Laplacican operator: Examples}
|
||||
\selectlanguage{english}
|
||||
\begin{figure}[!h]
|
||||
\includegraphics[scale=0.4]{north_pole.jpg}
|
||||
\caption{Input image: North pole of moon}
|
||||
\end{figure}
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Applications of Laplacican operator: Examples}
|
||||
\selectlanguage{english}
|
||||
\begin{figure}[!h]
|
||||
\begin{tabular}{cc}
|
||||
\includegraphics[scale=0.5]{north_pole_laplacian_unscaled.png} &
|
||||
\includegraphics[scale=0.5]{north_pole_laplacian_scaled.png} \\
|
||||
(a) & (b)
|
||||
\end{tabular}
|
||||
\centering
|
||||
\caption{Laplacian images = images obtained by filtering with Laplacian operator: (a) without scaling, (b) with scaling for display purpose}
|
||||
\end{figure}
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Applications of Laplacican operator: Exercises}
|
||||
\selectlanguage{english}
|
||||
\begin{exercise}
|
||||
\begin{enumerate}
|
||||
\item How can you sharpen images, e.g., north pole of moon, with Laplacian by using Matlab and OpenCV?
|
||||
\item Create blurred version and then sharpen the blurred version
|
||||
\begin{itemize}
|
||||
\item Read checkboard image from file
|
||||
\item Blur it with Box or Gaussian filter
|
||||
\item Sharpen the resulting blurred version with Laplacian
|
||||
\item Show the original, blurred version and sharpened version.
|
||||
\end{itemize}
|
||||
\end{enumerate}
|
||||
|
||||
\end{exercise}
|
||||
}
|
||||
|
||||
\frame
|
||||
{
|
||||
\frametitle{Unsharp masking and High-boost filtering}
|
||||
\selectlanguage{english}
|
||||
\textbf{Unsharp masking:} image obtained from subtracting a blurred version of an image from the image itself.
|
||||
|
||||
\begin{align}
|
||||
\nonumber
|
||||
f_s(x,y) &= f(x,y) - \bar{f}(x,y)
|
||||
\end{align}
|
||||
\begin{itemize}
|
||||
\item $\bar{f}(x,y)$ : blurred version of $f(x,y)$, e.g., using box filter
|
||||
\item $f_s(x,y)$: sharpened image
|
||||
\end{itemize}
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Unsharp masking and High-boost filtering}
|
||||
\selectlanguage{english}
|
||||
\begin{exercise}
|
||||
\begin{enumerate}
|
||||
\item How can you implement unsharp masking with Matlab and OpenCV?
|
||||
\item Create blurred version and then sharpen the blurred version
|
||||
\begin{itemize}
|
||||
\item Read checkboard image from file
|
||||
\item Blur it with Box or Gaussian filter
|
||||
\item Sharpen the resulting blurred version with Unsharp masking
|
||||
\item Show the original, blurred version and sharpened version.
|
||||
\end{itemize}
|
||||
\end{enumerate}
|
||||
|
||||
\end{exercise}
|
||||
}
|
||||
|
||||
\frame
|
||||
{
|
||||
\frametitle{Unsharp masking and High-boost filtering}
|
||||
\selectlanguage{english}
|
||||
\textbf{High-boost filtering:} a generalized unsharpened image.
|
||||
|
||||
\begin{align}
|
||||
\nonumber
|
||||
f_{hb}(x,y) &= Af(x,y) - \bar{f}(x,y)
|
||||
\end{align}
|
||||
\begin{itemize}
|
||||
\item $A$ : a parameter, $A \ge 1$. $A=1$, hight-boost filtering $\rightarrow$ unsharp masking
|
||||
\item $f_s(x,y)$: sharpened image
|
||||
\end{itemize}
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Unsharp masking and High-boost filtering}
|
||||
\selectlanguage{english}
|
||||
\textbf{High-boost filtering:} Other representations.
|
||||
|
||||
\begin{align}
|
||||
\nonumber
|
||||
f_{hb}(x,y) &= Af(x,y) - \bar{f}(x,y)\\
|
||||
\nonumber
|
||||
&= (A-1)f(x,y) + f(x,y) - \bar{f}(x,y)\\
|
||||
&= (A-1)f(x,y) + f_s(x,y) \label{eq:hb_filter}
|
||||
\end{align}
|
||||
Replace Eq. (\ref{eq:hb_filter}) with Laplacian sharpening filter:
|
||||
\small
|
||||
$$
|
||||
f_{hb}(x,y) =
|
||||
\begin{cases}
|
||||
Af(x,y) - \nabla^2f(x,y)& \text{if the center coefficient of the}\\
|
||||
& \text{Laplacian mask is negative }\\
|
||||
Af(x,y) + \nabla^2f(x,y)& \text{if the center coefficient of the} \\
|
||||
& \text{Laplacian mask is positive }
|
||||
\end{cases}
|
||||
$$
|
||||
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Unsharp masking and High-boost filtering}
|
||||
\selectlanguage{english}
|
||||
\textbf{High-boost filtering:} can be implemented as a linear filter, with one of the following kernels.
|
||||
\newline
|
||||
\newline
|
||||
\centering
|
||||
\begin{tabular}{l||l}
|
||||
\\
|
||||
$H_{hb8} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
-1 & -1 & -1 \\
|
||||
-1 & A+8 & -1\\
|
||||
-1 & -1 & -1
|
||||
\end{array}\right] $ &
|
||||
$H_{hb4} = $ $\left[
|
||||
\begin{array}{rrr}
|
||||
0 & -1 & 0 \\
|
||||
-1 & A+4 & -1\\
|
||||
0 & -1 & 0
|
||||
\end{array}\right] $ \\
|
||||
\\
|
||||
\end{tabular}
|
||||
\flushleft
|
||||
\textbf{$A$ is a parameter:}
|
||||
\begin{enumerate}
|
||||
\item $A=0$, hight-boost filter becomes standard \alert{Laplacian filter}
|
||||
\item $A=1$, hight-boost filter becomes standard \alert{Laplacian sharpening filter}
|
||||
\item $A$ increases pass $1$ the contribution of sharpening process becomes less and less important
|
||||
\end{enumerate}
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Unsharp masking and High-boost filtering}
|
||||
\selectlanguage{english}
|
||||
\begin{alertblock}{Applications of High-boost filtering:}
|
||||
\begin{itemize}
|
||||
\item High-boost filtering can sharpen images
|
||||
\item High-boost filtering can brighten dark images
|
||||
\end{itemize}
|
||||
|
||||
\end{alertblock}
|
||||
}
|
||||
\frame
|
||||
{
|
||||
\frametitle{Unsharp masking and High-boost filtering: Examples}
|
||||
\selectlanguage{english}
|
||||
\begin{figure}[!h]
|
||||
\includegraphics[scale=0.75]{highboost.png}
|
||||
\end{figure}
|
||||
}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
\end{document}
|
||||
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resource/Sources/ImageDerivatives/TeachingNote.pptx
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resource/Sources/ImageDerivatives/_DS_Store
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resource/Sources/ImageDerivatives/_DS_Store
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resource/Sources/ImageDerivatives/char.png
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resource/Sources/ImageDerivatives/char.png
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|
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resource/Sources/ImageDerivatives/char_mesh.png
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|
After Width: | Height: | Size: 78 KiB |
BIN
resource/Sources/ImageDerivatives/checkboard.png
Normal file
BIN
resource/Sources/ImageDerivatives/checkboard.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 1.0 KiB |
BIN
resource/Sources/ImageDerivatives/derivatives.png
Normal file
BIN
resource/Sources/ImageDerivatives/derivatives.png
Normal file
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|
After Width: | Height: | Size: 99 KiB |
236
resource/Sources/ImageDerivatives/dsa-style.tex
Normal file
236
resource/Sources/ImageDerivatives/dsa-style.tex
Normal file
@ -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}
|
||||
BIN
resource/Sources/ImageDerivatives/hcmut.png
Normal file
BIN
resource/Sources/ImageDerivatives/hcmut.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 15 KiB |
BIN
resource/Sources/ImageDerivatives/highboost.png
Normal file
BIN
resource/Sources/ImageDerivatives/highboost.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 219 KiB |
446
resource/Sources/ImageDerivatives/mathpartir.sty
Normal file
446
resource/Sources/ImageDerivatives/mathpartir.sty
Normal file
@ -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
|
||||
1108
resource/Sources/ImageDerivatives/mathtools.sty
Normal file
1108
resource/Sources/ImageDerivatives/mathtools.sty
Normal file
File diff suppressed because it is too large
Load Diff
166
resource/Sources/ImageDerivatives/mhsetup.sty
Normal file
166
resource/Sources/ImageDerivatives/mhsetup.sty
Normal file
@ -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'.
|
||||
BIN
resource/Sources/ImageDerivatives/north_pole.jpg
Normal file
BIN
resource/Sources/ImageDerivatives/north_pole.jpg
Normal file
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|
After Width: | Height: | Size: 54 KiB |
BIN
resource/Sources/ImageDerivatives/north_pole_laplacian.png
Normal file
BIN
resource/Sources/ImageDerivatives/north_pole_laplacian.png
Normal file
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|
After Width: | Height: | Size: 423 KiB |
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|
After Width: | Height: | Size: 197 KiB |
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|
After Width: | Height: | Size: 226 KiB |
BIN
resource/Sources/ImageDerivatives/north_pole_sharpened.png
Normal file
BIN
resource/Sources/ImageDerivatives/north_pole_sharpened.png
Normal file
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|
After Width: | Height: | Size: 268 KiB |
Reference in New Issue
Block a user