improve presentation

presentation/main.tex

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

presentation/sources.bib

@@ -1,16 +1,20 @@
-@InProceedings{Xu_2022_CVPR,
+@article{Rave_2025,
-    author    = {Xu, Yinghao and Wei, Fangyun and Sun, Xiao and Yang, Ceyuan and Shen, Yujun and Dai, Bo and Zhou, Bolei and Lin, Stephen},
+    title={De-Cluttering Scatterplots With Integral Images},
-    title     = {Cross-Model Pseudo-Labeling for Semi-Supervised Action Recognition},
+    volume={31},
-    booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
+    ISSN={2160-9306},
-    month     = {June},
+    url={http://dx.doi.org/10.1109/TVCG.2024.3381453},
-    year      = {2022},
+    DOI={10.1109/tvcg.2024.3381453},
-    pages     = {2959-2968}
+    number={4},
-}
+    journal={IEEE Transactions on Visualization and Computer Graphics},
+    publisher={Institute of Electrical and Electronics Engineers (IEEE)},
+    author={Rave, Hennes and Molchanov, Vladimir and Linsen, Lars},
+    year={2025},
+    month=apr, pages={2114–2126} }
 
-@online{knuthwebsite,
+@online{statisticsglobe_overplotting_r,
-    author = "Kihyuk Sohn, David Berthelot, Chun-Liang Li",
+    author       = {Statistics Globe},
-    title = "FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence",
+    title        = {Avoid Overplotting in R (4 Examples) | Point Size, Opacity \& Color},
-    url  = "https://arxiv.org/abs/2001.07685",
+    year         = {2025},
-    addendum = "(accessed: 20.03.2023)",
+    url          = {https://statisticsglobe.com/avoid-overplotting-r},
-    keywords = "FixMatch, semi-supervised"
+    note         = {Accessed: 2025-11-23}
 }