diff --git a/bv/uebung2.tex b/bv/uebung2.tex new file mode 100644 index 0000000..ecef6ed --- /dev/null +++ b/bv/uebung2.tex @@ -0,0 +1,81 @@ +\documentclass[10pt,a4paper,oneside,ngerman,numbers=noenddot]{scrartcl} +\usepackage[T1]{fontenc} +\usepackage[utf8]{inputenc} +\usepackage[ngerman]{babel} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{bytefield} +\usepackage{paralist} +\usepackage{gauss} +\usepackage{pgfplots} +\usepackage{textcomp} +\usepackage[locale=DE,exponent-product=\cdot,detect-all]{siunitx} +\usepackage{tikz} +\usepackage{algpseudocode} +\usepackage{algorithm} +\usepackage{mathtools} +\usepackage{hyperref} +\usepackage[german=quotes]{csquotes} +%\usepackage{algorithmic} +%\usepackage{minted} +\usetikzlibrary{automata,matrix,fadings,calc,positioning,decorations.pathreplacing,arrows,decorations.markings} +\usepackage{polynom} +\polyset{style=C, div=:,vars=x} +\pgfplotsset{compat=1.8} +\pagenumbering{arabic} +%\def\thesection{\arabic{section})} +%\def\thesubsection{(\alph{subsection})} +%\def\thesubsubsection{(\roman{subsubsection})} +\makeatletter +\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{% + \hskip -\arraycolsep + \let\@ifnextchar\new@ifnextchar + \array{#1}} +\makeatother +\parskip 12pt plus 1pt minus 1pt +\parindent 0pt +\MakeOuterQuote{"} + +\DeclarePairedDelimiter\abs{\lvert}{\rvert}% +\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil} + +\newenvironment{myitemize}{\begin{itemize}\itemsep -9pt}{\end{itemize}} % Zeilenabstand in Aufzählungen geringer + +\def\thesection{\arabic{section}.} + +%switch starred and non-starred (auto-size) +\makeatletter +\let\oldabs\abs +\def\abs{\@ifstar{\oldabs}{\oldabs*}} +\makeatother + +\hypersetup{ + colorlinks, + citecolor=black, + filecolor=black, + linkcolor=black, + urlcolor=black +} + +\begin{document} +\author{Jim Martens (6420323)} +\title{Computer Vision/Image Processing} +\subtitle{Assignment 2} +\date{2nd Novembre 2016} + +\maketitle + +\section{} + +\begin{alignat*}{1} + \sigma^2 &= \frac{1}{N_{cols}N_{rows}-1} \sum\limits_{x=1}^{N_{cols}} \sum\limits_{y=1}^{N_{rows}} \left( I(y,x) - \mu_{n-1}\right) \cdot \left(I(y,x) - \mu_{n}\right) \\ + \intertext{Constraints} + n_0 &= 0 \\ + n_n &= n_{n-1} + 1 \\ + n_i & \{i \in [0, N_{cols}N_{rows}]\} \\ + \mu_0 &= 0 \\ + \mu_n &= \mu_{n-1} + \frac{I(y,x) - \mu_{n-1}}{n_n} +\end{alignat*} + +\end{document} \ No newline at end of file