From 74ae33c26721688149520c9cf3b404ac540f9e2f Mon Sep 17 00:00:00 2001
From: Lukas Heiligenbrunner <lukas.heiligenbrunner@gmail.com>
Date: Sun, 23 Nov 2025 15:29:42 +0100
Subject: [PATCH] reorder some slides

---
 presentation/main.tex | 91 +++++++++++++++++++++++++------------------
 1 file changed, 53 insertions(+), 38 deletions(-)

diff --git a/presentation/main.tex b/presentation/main.tex
index b75232c..09f4b8b 100644
--- a/presentation/main.tex
+++ b/presentation/main.tex
@@ -61,38 +61,23 @@
 %	 SECTION 1: INTRODUCTION
 %----------------------------------------------------------------------------------------
 
-    \section{Introduction}
-
-    \begin{frame}{Goal of the Paper}
-        \begin{itemize}
-            \item Scatterplots are fundamental for exploring multidimensional data
-            \item But: with large datasets they suffer from \textbf{overplotting}
-            \item Dense regions obscure structure, samples become inaccessible
-            \item Goal:
-            \begin{itemize}
-                \item Reduce clutter
-                \item Preserve neighborhood relations
-                \item Achieve uniform sample distribution
-                \item Maintain interpretability
-            \end{itemize}
-        \end{itemize}
-    \end{frame}
-
 %----------------------------------------------------------------------------------------
 %	SECTION 2: PROBLEM
 %----------------------------------------------------------------------------------------
 
-    \section{Problem: Overplotting}
+    \section{Introduction}
 
-    \begin{frame}{Why Scatterplots Clutter}
+    \begin{frame}{Problem: Scatterplots Clutter}
         \begin{itemize}
+            \item Scatterplots are fundamental for exploring multidimensional data
             \item Modern datasets: millions of samples
             \item Pixel resolution fixed → many samples map to the same pixel
+            \item This results in \textbf{overplotting}
             \item Consequences:
             \begin{itemize}
-                \item Occlusion of clusters + outliers
+                \item Occlusion of clusters
                 \item Loss of density information
-                \item Hard to select individual items
+                \item Hard to select and see individual items
                 %\item Misleading visual perception
             \end{itemize}
             \item A method is needed to \textbf{declutter} without losing structure
@@ -105,6 +90,18 @@
         \footnotesize\text{Source: \cite{statisticsglobe_overplotting_r}}
     \end{frame}
 
+    \begin{frame}{Goal of the Paper}
+        \begin{itemize}
+            \item Goal:
+            \begin{itemize}
+                \item Reduce clutter
+                \item Preserve neighborhood relations
+                \item Achieve uniform sample distribution
+                \item Maintain interpretability
+            \end{itemize}
+        \end{itemize}
+    \end{frame}
+
     \begin{frame}{Limitations of Traditional Approaches}
         \begin{itemize}
             \item Transparency-based methods
@@ -124,12 +121,11 @@
             \item Need a \textbf{global}, \textbf{smooth}, \textbf{monotonic}, \textbf{collision-free} method
         \end{itemize}
     \end{frame}
-
     %----------------------------------------------------------------------------------------
 %	SECTION 3: BACKGROUND
 %----------------------------------------------------------------------------------------
 
-    \section{Background: Density Fields \& Integral Images}
+    \section{Background:\\Density Fields \& Integral Images}
 
     \begin{frame}{Density Estimation}
         \begin{itemize}
@@ -400,21 +396,6 @@
         \includegraphics[scale=0.4]{rsc/img}
     \end{frame}
 
-
-    % ---  THE END
-
-    \begin{frame}[focus]
-        Thanks for your Attention!
-    \end{frame}
-
-%----------------------------------------------------------------------------------------
-%	 CLOSING/SUPPLEMENTARY SLIDES
-%----------------------------------------------------------------------------------------
-
-    \appendix
-
-    \section{Backup}\label{sec:backup}
-
     \begin{frame}{Example I}
         \centering
         \includegraphics[scale=0.1]{rsc/2408.06513v1_page_8_1}\\
@@ -451,6 +432,40 @@
         \footnotesize\text{Source: \cite{Rave_2025}}
     \end{frame}
 
+    % ---  THE END
+
+    \begin{frame}[focus]
+        Thanks for your Attention!
+    \end{frame}
+
+%----------------------------------------------------------------------------------------
+%	 CLOSING/SUPPLEMENTARY SLIDES
+%----------------------------------------------------------------------------------------
+
+    \appendix
+
+    \section{Backup}\label{sec:backup}
+
+    \begin{frame}{Domain Transformation (Molchanov \& Linsen)}
+        \begin{itemize}
+            \item Integral Images $\rightarrow$ Transformation mapping
+            \item Definition:
+            \[
+                t(x,y; d) = \frac{
+                    \alpha q_1 + \beta q_2 + \gamma q_3 + \delta q_4
+                    + \alpha_t (x,1) + \beta_t (1,y) + \gamma_t (x,0) + \delta_t (0,y)
+                }{2C}
+            \]
+            \item Problems:
+            \begin{itemize}
+                \item Not identity for uniform density
+                \item Iteration unstable
+                \item Does not converge to equalized distribution
+            \end{itemize}
+        \end{itemize}
+    \end{frame}
+
+
     \begin{frame}{Sources}
         \nocite{*} % Display all references regardless of if they were cited
         \bibliography{sources}