forked from lukas/Seminar_in_AI
improve presentation
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\documentclass[usenames,dvipsnames]{beamer}
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\documentclass[usenames,dvipsnames, aspectratio=169]{beamer}
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%----------------------------------------------------------------------------------------
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% Struktur und Pointer Referat
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% 20.04.2020
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@@ -93,7 +93,7 @@
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\item Occlusion of clusters + outliers
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\item Loss of density information
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\item Hard to select individual items
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\item Misleading visual perception
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%\item Misleading visual perception
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\end{itemize}
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\item A method is needed to \textbf{declutter} without losing structure
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\end{itemize}
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@@ -102,7 +102,7 @@
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\begin{frame}
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\centering
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\includegraphics[scale=0.8]{rsc/overplotting}
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\footnotesize\text{Source: https://statisticsglobe.com/avoid-overplotting-r}
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\footnotesize\text{Source: \cite{statisticsglobe_overplotting_r}}
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\end{frame}
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\begin{frame}{Limitations of Traditional Approaches}
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@@ -147,7 +147,7 @@
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\end{itemize}
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\end{frame}
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\begin{frame}{Integral Images (InIms)}
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\begin{frame}{Integral Images (InIms) I}
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\begin{itemize}
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\item Integral images compute cumulative sums over regions
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\item Four standard tables:
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@@ -167,48 +167,100 @@
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\end{itemize}
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\end{frame}
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\begin{frame}{Integral Images (InIms) II}
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\centering
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\includegraphics[scale=0.3]{rsc/2408.06513v1_page_6_5}\\
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\footnotesize\text{Source: \cite{Rave_2025}}
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\end{frame}
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\begin{frame}{Integral Images (InIms) III}
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\centering
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\includegraphics[scale=0.3]{rsc/2408.06513v1_page_6_6}\\
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\footnotesize\text{Source: \cite{Rave_2025}}
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\end{frame}
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\begin{frame}{Integral Images (InIms) IV}
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\centering
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\includegraphics[scale=0.3]{rsc/2408.06513v1_page_6_7}\\
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\footnotesize\text{Source: \cite{Rave_2025}}
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\end{frame}
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%----------------------------------------------------------------------------------------
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% SECTION 4: METHOD
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%----------------------------------------------------------------------------------------
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\section{Density-Equalizing Mapping}
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\begin{frame}{Original Mapping (Molchanov \& Linsen)}
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\begin{frame}{Goal of the Mapping}
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\begin{itemize}
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\item Prior work defined mapping:
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\[
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t(x,y; d) = \frac{
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\alpha q_1 + \beta q_2 + \gamma q_3 + \delta q_4
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+ \alpha_t (x,1) + \beta_t (1,y) + \gamma_t (x,0) + \delta_t (0,y)
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}{2C}
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\]
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\item But:
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\item We want to transform the scatterplot domain so that:
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\begin{itemize}
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\item Not identity for uniform density
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\item Iteration unstable
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\item Does not converge to equalized distribution
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\item dense regions expand
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\item sparse regions contract
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\item overall density becomes approximately uniform
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\end{itemize}
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\item The deformation must be:
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\begin{itemize}
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\item smooth
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\item globally consistent
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\item monotonic (no point order swaps)
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\item free of collisions
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\end{itemize}
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\item To achieve this, we compute a \textbf{density–driven displacement field}.
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\end{itemize}
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\end{frame}
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\begin{frame}{Corrected Mapping (This Paper)}
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\begin{frame}{Corrected Mapping: Key Idea}
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\begin{itemize}
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\item Compute deformation for true density $d$
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\item Compute deformation for constant density $d_0$
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\item Subtract:
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\[
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t(x,y) = (x,y) + t(x,y; d) - t(x,y; d_0)
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\]
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\item This ensures:
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\begin{itemize}
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\item Identity for uniform density
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\item Smooth monotonic deformation
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\item Progressive convergence to equalization
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\item No overlap of regions
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\end{itemize}
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\item Let $t(x,y; d)$ be the deformation computed from the
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\textbf{actual density field} $d(x,y)$.
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\item This deformation is built from cumulative sums of density
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through the integral images.
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\item Problem: even for \textbf{constant density}, $t(x,y; d_0)$
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is \emph{not} zero (due to construction of the integral tables).
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\item Therefore:\\
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We subtract the deformation caused by constant density.
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\end{itemize}
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\begin{align*}
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T(x,y) = (x,y) \;+\; t(x,y; d) \;-\; t(x,y; d_0) \;
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\end{align*}
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\begin{itemize}
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\item $T(x,y)$ is the \textbf{corrected mapping}.
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\item For uniform density: $t(x,y; d) = t(x,y; d_0)$ $\rightarrow$ identity mapping.
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\end{itemize}
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\end{frame}
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% \begin{frame}{Why the Corrected Mapping Works}
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% \begin{itemize}
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% \item \textbf{Identity on uniform density}
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% \begin{itemize}
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% \item Without correction: the old mapping distorted even uniform fields.
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% \item With correction: uniform density $\rightarrow$ no deformation.
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% \end{itemize}
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% \item \textbf{Monotonicity}
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% \begin{itemize}
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% \item The corrected mapping guarantees no coordinate inversions.
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% \item Order of points is preserved along both axes.
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% \end{itemize}
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% \item \textbf{Smoothness}
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% \begin{itemize}
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% \item The mapping is built from integral images (global cumulative fields),
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% \item yielding slow, continuous changes.
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% \end{itemize}
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% \item \textbf{Stability in iteration}
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% \begin{itemize}
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% \item As the density becomes more equalized, $t(x,y;d)$ approaches $t(x,y;d_0)$.
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% \item Mapping naturally converges toward identity.
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% \end{itemize}
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% \item \textbf{No collisions}
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% \begin{itemize}
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% \item Global, monotonic deformation prevents points from crossing paths.
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% \end{itemize}
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% \end{itemize}
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% \end{frame}
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\begin{frame}{Iterative Algorithm Overview}
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\begin{enumerate}
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\item Rasterize and smooth density
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@@ -232,7 +284,7 @@
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\includegraphics[width=\textwidth]{rsc/2408.06513v1_page_7_1}
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\vspace{4pt}
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\footnotesize MNIST Dataset (UMAP)
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\footnotesize MNIST Dataset (UMAP)~\cite{Rave_2025}
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\end{minipage}
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\begin{minipage}{0.15\textwidth}
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\centering
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@@ -243,7 +295,7 @@
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\includegraphics[width=\textwidth]{rsc/2408.06513v1_page_7_2}
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\vspace{4pt}
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\footnotesize Visual encoding of the density-equalizing transform
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\footnotesize Visual encoding of the density-equalizing transform (32 Iterations)~\cite{Rave_2025}
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\end{minipage}
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\label{fig:figure}
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\end{figure}
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@@ -267,7 +319,7 @@
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\end{itemize}
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\end{frame}
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\begin{frame}{Three Proposed Encodings}
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\begin{frame}{Three Proposed Encodings I}
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\begin{itemize}
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\item \textbf{Deformed grid lines}
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\begin{itemize}
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@@ -293,21 +345,21 @@
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\includegraphics[width=\textwidth]{rsc/2408.06513v1_page_7_2}
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\vspace{4pt}
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\footnotesize Deformed grid lines
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\footnotesize Deformed grid lines~\cite{Rave_2025}
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\end{minipage}
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\begin{minipage}{0.3\textwidth}
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\centering
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\includegraphics[width=\textwidth]{rsc/2408.06513v1_page_7_3}
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\vspace{4pt}
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\footnotesize Background density texture
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\footnotesize Background density texture~\cite{Rave_2025}
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\end{minipage}
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\begin{minipage}{0.3\textwidth}
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\centering
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\includegraphics[width=\textwidth]{rsc/2408.06513v1_page_7_4}
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\vspace{4pt}
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\footnotesize Contour lines
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\footnotesize Contour lines~\cite{Rave_2025}
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\end{minipage}
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\label{fig:figure2}
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\end{figure}
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@@ -323,38 +375,29 @@
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\begin{itemize}
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\item All major steps implemented on GPU:
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\begin{itemize}
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\item Density accumulation
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\item Gaussian smoothing
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\item Integral image computation
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\item Density accumulation $\rightarrow$ vertex + fragment shader
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\item Gaussian smoothing $\rightarrow$ 2 compute-shader passes
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\item Integral image computation $\rightarrow$ fragment shader
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\end{itemize}
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\item Fast multi-pass reduction for InIms
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\item Complexity:
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\[
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O(n + m)
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\]
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where $m = 2^k \times 2^k$ is texture resolution
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\item Achieves interactive rates for millions of samples
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\end{itemize}
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\end{frame}
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%----------------------------------------------------------------------------------------
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% SECTION 7: RESULTS
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%----------------------------------------------------------------------------------------
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\section{Results}
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\begin{frame}{Performance}
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\begin{itemize}
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\item Runs at interactive frame rates:
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\begin{itemize}
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\item e.g. 4M samples in $\approx 28$ ms per iteration
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\item e.g. 4M samples in $\approx 3$ ms per iteration
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\end{itemize}
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\item Standard deviation of samples/bin decreases monotonically
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\item Overplotting fraction also decreases monotonically
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%\item Standard deviation of samples/bin decreases monotonically
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%\item Overplotting fraction also decreases monotonically
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\end{itemize}
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\centering
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\includegraphics[scale=0.4]{rsc/results}
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\includegraphics[scale=0.4]{rsc/img}
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\end{frame}
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@@ -370,33 +413,47 @@
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\appendix
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\section{Backup}\label{sec:backup}
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\begin{frame}{Example I}
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\centering
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\includegraphics[scale=0.1]{rsc/2408.06513v1_page_8_1}\\
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\footnotesize\text{Source: \cite{Rave_2025}}
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\end{frame}
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\begin{frame}{Example II}
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\centering
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\includegraphics[scale=0.1]{rsc/2408.06513v1_page_8_2}\\
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\footnotesize\text{Source: \cite{Rave_2025}}
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\end{frame}
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\begin{frame}{Example III}
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\centering
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\includegraphics[scale=0.1]{rsc/2408.06513v1_page_8_3}\\
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\footnotesize\text{Source: \cite{Rave_2025}}
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\end{frame}
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\begin{frame}{Example IV}
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\centering
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\includegraphics[scale=0.1]{rsc/2408.06513v1_page_8_4}\\
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\footnotesize\text{Source: \cite{Rave_2025}}
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\end{frame}
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\begin{frame}{Example V}
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\centering
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\includegraphics[scale=0.1]{rsc/2408.06513v1_page_8_5}\\
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\footnotesize\text{Source: \cite{Rave_2025}}
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\end{frame}
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\begin{frame}{Example VI}
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\centering
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\includegraphics[scale=0.1]{rsc/2408.06513v1_page_8_6}\\
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\footnotesize\text{Source: \cite{Rave_2025}}
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\end{frame}
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\begin{frame}{Sources}
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\nocite{*} % Display all references regardless of if they were cited
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\bibliography{sources}
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\bibliographystyle{plain}
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\end{frame}
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\section{Backup}\label{sec:backup}
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\begin{frame}{User Study}
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\begin{itemize}
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\item 25 participants, 3 tasks:
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\begin{enumerate}
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\item Estimate cluster size
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\item Sort clusters by size
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\item Select clusters (lasso)
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\end{enumerate}
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\item Findings:
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\begin{itemize}
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\item Size estimation (T1): regularized significantly better
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\item Sorting (T2): regularized significantly better
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\item Cluster selection (T3):
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\begin{itemize}
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\item Grid encoding: worst
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\item Background texture: better
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\item Original scatterplot: best
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\end{itemize}
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\end{itemize}
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\end{itemize}
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\end{frame}
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\end{document}
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