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@ -23,14 +23,21 @@
\makeatother
% END: DO NOT CHANGE HERE!
\title{The Title of Your Talk}
\author{Your Name}
\date{02.03.2023} % Put the date of your talk here
\title{Differentiable Monte Carlo Ray Tracing through Edge Sampling}
\author{Clemens Dautermann}
\date{\today} % Put the date of your talk here
% Bibliography setup
\usepackage[citestyle=numeric,bibstyle=numeric,hyperref,backend=biber]{biblatex}
\addbibresource{bibliography.bib}
\usepackage[english]{babel}
\usepackage{csquotes}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,patterns,angles,quotes,shapes,arrows, positioning,overlay-beamer-styles}
\usepackage{xcolor}
\usepackage{graphicx}
@ -41,152 +48,40 @@
\maketitle
\begin{abstract}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vivamus euismod varius diam, ut maximus neque efficitur quis. Etiam laoreet, nunc sed sagittis tristique, velit velit feugiat metus, id tincidunt tellus turpis ut neque. Pellentesque maximus ex quis massa pretium posuere. Phasellus lacus lacus, egestas laoreet tellus a, ornare egestas arcu. Aliquam at velit ut velit egestas pretium. In a ipsum volutpat, varius magna et, suscipit augue. Nulla eleifend magna quis condimentum dictum. \cite{DBLP:journals/ibmrd/RabinS59}
Differentiable Programming is a technique frequently used to solve optimization problems by minimizing some kind of error function. To do this though the error function needs to be differentiable with respect to the parameters that are to be optimized. This is usually not the case with ray tracing. This report will explain why this problem occurs and present the method to tackle it developed in \cite{ACM:diffable_raytracing}.
\end{abstract}
\section{Introduction}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Vivamus euismod varius
diam, ut maximus neque efficitur quis. Etiam laoreet, nunc sed sagittis
tristique, velit velit feugiat metus, id tincidunt tellus turpis ut neque.
Pellentesque maximus ex quis massa pretium posuere. Phasellus lacus lacus,
egestas laoreet tellus a, ornare egestas arcu. Aliquam at velit ut velit
egestas pretium. In a ipsum volutpat, varius magna et, suscipit augue. Nulla
eleifend magna quis condimentum dictum.
Nam et risus arcu. Nulla pulvinar nibh risus, eget dignissim ipsum condimentum
in. Quisque non felis ac sapien consectetur accumsan. Mauris in iaculis arcu.
Nullam sit amet ullamcorper leo, sit amet mattis tortor. Vestibulum molestie
justo non felis mattis semper. Curabitur ac justo nunc. Ut tempus odio est,
vitae fringilla risus eleifend id. Aliquam convallis ante orci, quis consequat
dolor finibus a.
One of the main tasks in Computer Graphics is image synthesis. This means ``given a 3D scene, output an image depicting the scene``. Often it is required for the image to be as realistic as possible, meaning as close to a picture of the scene as if it was set in the real world as possible. This is most commonly achieved using the ray tracing algorithm and is a well studied problem. Doing this in a differentiable way however is much less trivial. This stems from the fact that the rendering integral (equation \ref{eq:rendering_integral}) is not differentiable in certain well defined places. Because being able to ray trace an image differentiably has numerous applications a solution to this problem has been proposed in \cite{ACM:diffable_raytracing}. This report will go into how exactly this problem arises, how it can be mitigated and what some of the applications of differentiable ray tracing are.
\section{How to cite a reference}
\subsection{Add it to the bibliography}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec ac lobortis
nibh. Curabitur erat lectus, posuere sit amet dapibus eu, rutrum eget metus.
Maecenas aliquam dapibus sem eget scelerisque. Aliquam nec elementum elit.
Aliquam erat volutpat. Mauris a pretium ex. Proin non magna eget nibh elementum
euismod. Etiam nulla tellus, ullamcorper quis molestie eget, tincidunt eget
urna. Nulla suscipit eros quis ex fringilla iaculis. In mollis ante sed nisi
tincidunt tempor nec at ipsum. Duis mauris ligula, pretium sit amet risus in,
porttitor vestibulum tortor. Nulla ullamcorper ante quis massa semper, vitae
blandit risus rutrum. Sed sed eros velit.
\paragraph*{Duis} sed augue quis dolor vulputate aliquam. Donec ultrices egestas
felis, ac dignissim lacus ultricies at. Nunc fermentum porta mi, sit amet
mattis purus venenatis at. Etiam nec justo et nunc fermentum ullamcorper ac in
libero. Proin tempor turpis volutpat consequat posuere. Sed aliquam purus vel
mauris rhoncus, in interdum mauris tincidunt. Sed rhoncus eros id risus
convallis, et varius risus ultrices.
\begin{table}[htbp]
\caption{Table Type Styles}
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
\textbf{Table} & \multicolumn{3}{|c|}{\textbf{Table Column Head}} \\
\cline{2-4}
\textbf{Head} & \textbf{\textit{Table column subhead}} & \textbf{\textit{Subhead}} & \textbf{\textit{Subhead}} \\
\hline
copy & More table copy$^{\mathrm{a}}$ & & \\
\hline
\multicolumn{4}{l}{$^{\mathrm{a}}$Sample of a Table footnote.}
\end{tabular}
\label{tab1}
\end{center}
\end{table}
\textcolor{red}{We can refer to Table \ref{tab1}.}
Sed viverra sollicitudin tellus sit amet auctor. Sed ut convallis purus. Nulla
non quam vitae est egestas fermentum. Maecenas porta erat at mi luctus
vestibulum. Vestibulum volutpat efficitur augue a maximus. Vestibulum
imperdiet, mi eu facilisis ornare, urna massa dapibus enim, vel fringilla ipsum
tellus ut urna. Vestibulum ante ipsum primis in faucibus orci luctus et
ultrices posuere cubilia curae; Proin malesuada dictum dui, at ornare nisl
blandit a. Phasellus a mauris vitae enim auctor consectetur. Suspendisse
potenti. Morbi porttitor scelerisque hendrerit. Sed congue egestas tellus, eu
congue nulla pulvinar eget.
Nullam lobortis semper neque eget volutpat. In hac habitasse platea dictumst.
Maecenas rhoncus risus vitae pulvinar interdum. Suspendisse faucibus metus
velit, eget posuere elit elementum mollis. Ut dictum eleifend tortor ac
facilisis. Cras ultrices volutpat viverra. Nulla facilisi. Aenean et ornare
urna. Duis pulvinar justo ac nulla pretium porta. Vestibulum ante ipsum primis
in faucibus orci luctus et ultrices posuere cubilia curae; In molestie dapibus
rhoncus. Nam lacinia ex eget dui iaculis faucibus.
Proin lacus nisl, semper vitae ex sed, dignissim ullamcorper quam. Vivamus
volutpat feugiat odio et eleifend. Maecenas interdum, elit et facilisis
commodo, leo est pharetra quam, at elementum dolor risus ut est. Nam eleifend
est sit amet eleifend aliquet. Pellentesque egestas rutrum lectus, cursus
viverra lectus lacinia id. Nunc tincidunt eleifend urna id blandit. Mauris
vestibulum tincidunt augue. Sed feugiat, ante sit amet porttitor pretium, ante
enim rhoncus justo, sit amet suscipit sem tortor et quam. Praesent at sagittis
tortor, id aliquam tortor. Praesent iaculis purus ut dui ultricies ultricies.
Proin gravida pharetra tortor quis sagittis. Fusce gravida consequat ex, ac
sodales diam sodales sodales.
\subsection{Refer to it in the text}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec ac lobortis
nibh. Curabitur erat lectus, posuere sit amet dapibus eu, rutrum eget metus.
Maecenas aliquam dapibus sem eget scelerisque. Aliquam nec elementum elit.
Aliquam erat volutpat. Mauris a pretium ex. Proin non magna eget nibh elementum
euismod. Etiam nulla tellus, ullamcorper quis molestie eget, tincidunt eget
urna. Nulla suscipit eros quis ex fringilla iaculis. In mollis ante sed nisi
tincidunt tempor nec at ipsum. Duis mauris ligula, pretium sit amet risus in,
porttitor vestibulum tortor. Nulla ullamcorper ante quis massa semper, vitae
blandit risus rutrum. Sed sed eros velit.
\begin{figure}[htbp]
\centerline{\includegraphics[width=\columnwidth,keepaspectratio]{Logo_KIT.png}}
\caption{The KIT Logo}
\label{kitlogo}
\section{Ray Tracing}
To formalize the problem of photo realistic image synthesis, an equation has been proposed by Kajiya in 1986 \cite{ACM:rendering_equation}. This equation captures physical light transport for a scene and if solved yields the color for a given point in the scene accounting for most physical light transport phenomena.
\begin{figure}[h]
\centering
\begin{equation}
I(x,x^{\prime})=
g(x,x')
\left[
\epsilon(x,x')+\int_S \rho(x,x',x'')I(x',x'')dx''
\right]
\notag
\label{eq:rendering_integral}
\end{equation}
\caption{The rendering equation capturing physical light transport. It assigns a value to the the Intensity of light transported from a point $x$ to a point $x^\prime$. The geometry term $g$ will be discussed later. The term $\epsilon$ accounts for the emissivity of the point $x$. The integral term represents all light scattered from any other point in the scene towards the point $x$. The integral domain $S$ contains all points in the scene.}
\end{figure}
This equation (equation \ref{eq:rendering_integral}) is now widely recognized as ``the rendering integral``. It is not analytically solvable and is thus most commonly solved using Monte-Carlo integration - i.e. ray tracing. Ray tracing works by backtracking light rays from the light sources in the scene and thus simulate physically realistic lighting.\\
To do this, rays are cast from the camera, through each pixel in the camera frustum. The intersection point with the scene geometry $x$ is calculated for each ray and material properties (e.g. color, emissivity etc.) are taken into account to calculate the pixel color. From this point more rays are drawn towards each light source. If the light source is visible, its light contributes to the pixel color as well. To account for indirect lighting the ray ``bounces around``, yielding a color for some of the points scattering lights towards $x$. This approximates the integral term in equation \ref{eq:rendering_integral}.\\
Differentiable ray tracing is the task of calculating the gradient of this process with respect to \emph{any} scene parameter.
\textcolor{red}{Note} that the figure will float to the top of the column and is not necessarily
placed where it is included. We may refer to the KIT logo as Figure
\ref{kitlogo}.
Duis sed augue quis dolor vulputate aliquam. Donec ultrices egestas felis, ac
dignissim lacus ultricies at. Nunc fermentum porta mi, sit amet mattis purus
venenatis at. Etiam nec justo et nunc fermentum ullamcorper ac in libero. Proin
tempor turpis volutpat consequat posuere. Sed aliquam purus vel mauris rhoncus,
in interdum mauris tincidunt. Sed rhoncus eros id risus convallis, et varius
risus ultrices.
Sed viverra sollicitudin tellus sit amet auctor. Sed ut convallis purus. Nulla
non quam vitae est egestas fermentum. Maecenas porta erat at mi luctus
vestibulum. Vestibulum volutpat efficitur augue a maximus. Vestibulum
imperdiet, mi eu facilisis ornare, urna massa dapibus enim, vel fringilla ipsum
tellus ut urna. Vestibulum ante ipsum primis in faucibus orci luctus et
ultrices posuere cubilia curae; Proin malesuada dictum dui, at ornare nisl
blandit a. Phasellus a mauris vitae enim auctor consectetur. Suspendisse
potenti. Morbi porttitor scelerisque hendrerit. Sed congue egestas tellus, eu
congue nulla pulvinar eget.
\newpage
\textcolor{red}{\emph{Important} Move this newpage command between two pargraphs to approximately equalize the length of the columns on the last page.}
% Make sure that the right column is no longer than the left column.
Nullam lobortis semper neque eget volutpat. In hac habitasse platea dictumst.
Maecenas rhoncus risus vitae pulvinar interdum. Suspendisse faucibus metus
velit, eget posuere elit elementum mollis. Ut dictum eleifend tortor ac
facilisis. Cras ultrices volutpat viverra. Nulla facilisi. Aenean et ornare
urna. Duis pulvinar justo ac nulla pretium porta.
Proin lacus nisl, semper vitae ex sed, dignissim ullamcorper quam. Vivamus
volutpat feugiat odio et eleifend. Maecenas interdum, elit et facilisis
commodo, leo est pharetra quam, at elementum dolor risus ut est. Nam eleifend
est sit amet eleifend aliquet. Pellentesque egestas rutrum lectus, cursus
viverra lectus lacinia id. Nunc tincidunt eleifend urna id blandit. Mauris
vestibulum tincidunt augue. Sed feugiat, ante sit amet porttitor pretium, ante
enim rhoncus justo, sit amet suscipit sem tortor et quam. Praesent at sagittis
tortor, id aliquam tortor. Praesent iaculis purus ut dui ultricies ultricies.
Proin gravida pharetra tortor quis sagittis. Fusce gravida consequat ex, ac
sodales diam sodales sodales.
\section{Problems with differentiability}
The geometry term $g(x,x^\prime)$ in equation \ref{eq:rendering_integral} is the main problem when it comes do differentiating the rendering integral. This term is 1 iff $x$ is visible from $x^\prime$, 0 otherwise.
\begin{figure}
\centering
\include{presentation/diagrams/edge_sampling.tex}
\caption{Caption}
\label{fig:enter-label}
\end{figure}
% BIBLIOGRAPHY
\nocite{*} % List all entries of the .bib file, even those not cited in the main body