131 lines
5.0 KiB
TeX
131 lines
5.0 KiB
TeX
%! TeX program = lualatex
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\documentclass[a4paper]{article}
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% packages
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\usepackage{microtype} % Slightly tweak font spacing for aesthetics
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\usepackage[english]{babel} % Language hyphenation and typographical rules
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\usepackage[final, colorlinks = true, urlcolor = black, linkcolor = black]{hyperref}
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\usepackage{changepage} % adjust margins on the fly
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\usepackage{fontspec}
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\setmainfont{EB Garamond}
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\setmonofont[Scale=MatchLowercase]{Deja Vu Sans Mono}
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\usepackage{minted}
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\usemintedstyle{algol_nu}
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\usepackage{xcolor}
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\usepackage{pgfplots}
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\pgfplotsset{width=\textwidth,compat=1.9}
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\usepackage{caption}
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\newenvironment{code}{\captionsetup{type=listing}}{}
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\captionsetup[listing]{skip=0pt}
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\setlength{\abovecaptionskip}{5pt}
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\setlength{\belowcaptionskip}{5pt}
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\usepackage[yyyymmdd]{datetime}
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\renewcommand{\dateseparator}{--}
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\usepackage{titlesec}
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% \titleformat{\section}{\LARGE\bfseries}{}{}{}[\titlerule]
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% \titleformat{\subsection}{\Large\bfseries}{}{0em}{}
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% \titlespacing{\subsection}{0em}{-0.7em}{0em}
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%
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% \titleformat{\subsubsection}{\large\bfseries}{}{0em}{$\bullet$ }
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% \titlespacing{\subsubsection}{1em}{-0.7em}{0em}
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% margins
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\addtolength{\hoffset}{-2.25cm}
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\addtolength{\textwidth}{4.5cm}
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\addtolength{\voffset}{-3.25cm}
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\addtolength{\textheight}{5cm}
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\setlength{\parskip}{0pt}
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\setlength{\parindent}{0in}
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% \setcounter{secnumdepth}{0}
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\begin{document}
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\hrule \medskip
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\begin{minipage}{0.295\textwidth}
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\raggedright
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\footnotesize
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\begin{tabular}{@{}l l} % Define a two-column table with left alignment
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Name: & Andrew Hayes \\
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Student ID: & 21321503 \\
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\end{tabular}
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\end{minipage}
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\begin{minipage}{0.4\textwidth}
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\centering
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\vspace{0.4em}
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\LARGE
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\textsc{ct404} \\
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\end{minipage}
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\begin{minipage}{0.295\textwidth}
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\raggedleft
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\footnotesize
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\begin{tabular}{@{}l l} % Define a two-column table with left alignment
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Name: & Maxwell Maia \\
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Student ID: & 21236277 \\
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\end{tabular}
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\end{minipage}
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\smallskip
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\hrule
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\begin{center}
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\normalsize
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Lab Assignment 1: Camera Callibration
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\end{center}
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\hrule
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\section{\textit{P}-Matrix Estimation Using Provided Code}
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\begin{figure}[H]
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\centering
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\includegraphics[width=\textwidth]{./images/1.1.png}
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\caption{ Command window output showing he computed camera matrix $P$, the intrinsic matrix $K$, \& the rotation matrix $R$ }
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\end{figure}
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\begin{figure}[H]
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\centering
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\includegraphics[width=\textwidth]{./images/1.2.png}
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\caption{ The 3D plot showing the camera center, the world points, \& the principal axis }
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\end{figure}
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\begin{figure}[H]
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\centering
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\includegraphics[width=\textwidth]{./images/1.3.png}
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\caption{ The image with projected 3D points \& vanishing lines }
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\end{figure}
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\section{Using Your Own Image from Your Camera for \textit{P}-Matrix Estimation}
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\begin{figure}[H]
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\centering
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\includegraphics[width=\textwidth]{./images/2.1.png}
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\caption{ Command window output showing he computed camera matrix $P$, the intrinsic matrix $K$, \& the rotation matrix $R$ }
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\end{figure}
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\begin{figure}[H]
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\centering
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\includegraphics[width=\textwidth]{./images/2.2.png}
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\caption{ The 3D plot showing the camera center, the world points, \& the principal axis }
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\end{figure}
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\begin{figure}[H]
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\centering
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\includegraphics[width=\textwidth]{./images/2.3.png}
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\caption{ The image with projected 3D points \& vanishing lines }
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\end{figure}
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\section{Experiment \& Reflect}
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\subsection{How does increasing the number of points affect the accuracy \& stability of the \textit{P}-matrix estimation?}
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As the number of control points increased, the accuracy and stability of the estimated P Matrix improved. With 12 points, we observed discrepancies in the back-projected 3D points, while results with 40 points were far more consistent. The intrinsic and rotation matrices derived from the P Matrix appeared less sensitive to noise with more points, enhancing the reliability of the calibration.
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\subsection{Is there a noticeable difference in the accuracy of the back-projection when using fewer points versus more points?}
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Using fewer points (e.g., 12) resulted in higher deviations in back-projected points compared to their actual image locations. With 40 points, the back-projection closely matched the real-world setup, minimizing errors.
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\subsection{What challenges did you encounter when manually selecting points \& entering 3D world coordinates?}
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The primary challenge that we faced when manually entering selecting the points was the precision: it was extremely difficult to precisely select the correct points due to the imprecision of the mouse as a selection device, human error, and a lack of fine-grain zoom control in the MATLAB UI.
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\\\\
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We also found the process of manually entering the points very time-consuming and error-prone.
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If we mis-clicked a point or accidentally entered in the wrong world coordinate, it would greatly damage the accuracy of the entire calibration and we would be forced to start over again.
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\end{document}
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