\section{Problems}
\begin{frame}
    \centering
    \Huge
    Problems
\end{frame}
\subsection{Why differentiable rendering is hard}
\begin{frame}{Why differentiable rendering is hard}
    \begin{itemize}
        \item Geometry term
        \item Causes dirac delta terms\\
        $\implies$ Have 0 probability of being sampled correctly [\cite{ACM:diracdelta},\cite{ACM:diffable_raytracing}]
        %\item Differentiation with respect to certain scene parameters possible but we need to differentiate with respect to any scene parameter
        \item Need to differentiate with respect to any scene parameter
    \end{itemize}   
\end{frame}
\begin{frame}{primary occlusion}
    \centering
    \input{presentation/diagrams/diagramm_occlusion.tex}
\end{frame}
\begin{frame}{Angle change $\leftrightarrow$ visibility change}
    \centering
    \input{presentation/diagrams/geometry_term_diff.tex}
\end{frame}
\subsection{Former methods}
\begin{frame}{Former methods}
    \begin{block}{Previous differentiable renderers considered by this paper}
        \begin{itemize}
            \item OpenDR [\cite{DBLP:OpenDR}]
            \item Neural 3D Mesh Renderer [\cite{DBLP:Neural3DKatoetal}]
            \item Both rasterization based %(first render the image using rasterization, then approximate the gradients using the resulting color buffer)
            \item Focused on speed $\rightarrow$ impercise
        \end{itemize}
    \end{block}
\end{frame}
\begin{frame}{Former methods - visualization}
    \begin{figure}
        \begin{minipage}{0.12\linewidth}
            \begin{figure}
                \centering
                \includegraphics[width=\linewidth]{presentation/img/comparisons/plane.png}
                \caption{planar scene}
                \label{fig:planar-scene}
            \end{figure}
        \end{minipage}
        \hspace{2mm}
        \begin{minipage}{0.12\linewidth}
            \begin{figure}
                \centering
                \includegraphics[width=\linewidth]{presentation/img/comparisons/opendr.png}
                \caption{OpenDR}
                \label{fig:grad-OpenDR}
            \end{figure}
        \end{minipage}
        \hspace{2mm}
        \begin{minipage}{0.12\linewidth}
            \begin{figure}
                \centering
                \includegraphics[width=\linewidth]{presentation/img/comparisons/Neural.png}
                \caption{Neural}
                \label{fig:grad-Neural3DMesh}
            \end{figure}
        \end{minipage}
        \hspace{2mm}
        \begin{minipage}{0.12\linewidth}
            \begin{figure}
                \centering
                \includegraphics[width=\linewidth]{presentation/img/comparisons/ours.png}
                \caption{this paper}
                \label{fig:grad-this}
            \end{figure}
        \end{minipage}
        \hspace{4mm}
        \begin{minipage}{0.3\linewidth}
            \caption{
                %A plane lit by a point light source. Images visualize a gradient with respect to the plane moving right. Since the light source remains static the gradient should only be $\ne 0$ at the boundaries. OpenDR and Neural are not able to correctly calculate the gradients as they are based on color buffer differences.\\
                Visualizations of gradients calculated by different differentiable renderers.\\
                Images: \cite{ACM:diffable_raytracing}
            }
            \label{fig:grad-explanation}
        \end{minipage}
    \end{figure}
    \pause
    $\implies$ Problems are caused at the edges and by approximation using color buffers
\end{frame}