diff --git a/presentation/main.tex b/presentation/main.tex index 9a25090..b75232c 100644 --- a/presentation/main.tex +++ b/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: - \[ - t(x,y; d) = \frac{ - \alpha q_1 + \beta q_2 + \gamma q_3 + \delta q_4 - + \alpha_t (x,1) + \beta_t (1,y) + \gamma_t (x,0) + \delta_t (0,y) - }{2C} - \] - \item But: + \item We want to transform the scatterplot domain so that: \begin{itemize} - \item Not identity for uniform density - \item Iteration unstable - \item Does not converge to equalized distribution + \item dense regions expand + \item sparse regions contract + \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 Compute deformation for constant density $d_0$ - \item Subtract: - \[ - t(x,y) = (x,y) + t(x,y; d) - t(x,y; d_0) - \] - \item This ensures: - \begin{itemize} - \item Identity for uniform density - \item Smooth monotonic deformation - \item Progressive convergence to equalization - \item No overlap of regions - \end{itemize} + \item Let $t(x,y; d)$ be the deformation computed from the + \textbf{actual density field} $d(x,y)$. + \item This deformation is built from cumulative sums of density + through the integral images. + \item Problem: even for \textbf{constant density}, $t(x,y; d_0)$ + is \emph{not} zero (due to construction of the integral tables). + \item Therefore:\\ + We subtract the deformation caused by constant density. + \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 Gaussian smoothing - \item Integral image computation + \item Density accumulation $\rightarrow$ vertex + fragment shader + \item Gaussian smoothing $\rightarrow$ 2 compute-shader passes + \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 Overplotting fraction also decreases monotonically + %\item Standard deviation of samples/bin 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} diff --git a/presentation/rsc/2408.06513v1_page_6_5.png b/presentation/rsc/2408.06513v1_page_6_5.png new file mode 100644 index 0000000..f394598 Binary files /dev/null and b/presentation/rsc/2408.06513v1_page_6_5.png differ diff --git a/presentation/rsc/2408.06513v1_page_6_6.png b/presentation/rsc/2408.06513v1_page_6_6.png new file mode 100644 index 0000000..1785f34 Binary files /dev/null and b/presentation/rsc/2408.06513v1_page_6_6.png differ diff --git a/presentation/rsc/2408.06513v1_page_6_7.png b/presentation/rsc/2408.06513v1_page_6_7.png new file mode 100644 index 0000000..67ae2ae Binary files /dev/null and b/presentation/rsc/2408.06513v1_page_6_7.png differ diff --git a/presentation/rsc/2408.06513v1_page_8_1.png b/presentation/rsc/2408.06513v1_page_8_1.png new file mode 100644 index 0000000..4be71b3 Binary files /dev/null and b/presentation/rsc/2408.06513v1_page_8_1.png differ diff --git a/presentation/rsc/2408.06513v1_page_8_2.png b/presentation/rsc/2408.06513v1_page_8_2.png new file mode 100644 index 0000000..7444304 Binary files /dev/null and b/presentation/rsc/2408.06513v1_page_8_2.png differ diff --git a/presentation/rsc/2408.06513v1_page_8_3.png b/presentation/rsc/2408.06513v1_page_8_3.png new file mode 100644 index 0000000..5a3a51e Binary files /dev/null and b/presentation/rsc/2408.06513v1_page_8_3.png differ diff --git a/presentation/rsc/2408.06513v1_page_8_4.png b/presentation/rsc/2408.06513v1_page_8_4.png new file mode 100644 index 0000000..db830d4 Binary files /dev/null and b/presentation/rsc/2408.06513v1_page_8_4.png differ diff --git a/presentation/rsc/2408.06513v1_page_8_5.png b/presentation/rsc/2408.06513v1_page_8_5.png new file mode 100644 index 0000000..d497556 Binary files /dev/null and b/presentation/rsc/2408.06513v1_page_8_5.png differ diff --git a/presentation/rsc/2408.06513v1_page_8_6.png b/presentation/rsc/2408.06513v1_page_8_6.png new file mode 100644 index 0000000..3034b4b Binary files /dev/null and b/presentation/rsc/2408.06513v1_page_8_6.png differ diff --git a/presentation/rsc/img.png b/presentation/rsc/img.png new file mode 100644 index 0000000..a3ec2c3 Binary files /dev/null and b/presentation/rsc/img.png differ diff --git a/presentation/sources.bib b/presentation/sources.bib index 0791896..c61edb3 100644 --- a/presentation/sources.bib +++ b/presentation/sources.bib @@ -1,16 +1,20 @@ -@InProceedings{Xu_2022_CVPR, - 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 = {Cross-Model Pseudo-Labeling for Semi-Supervised Action Recognition}, - booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}, - month = {June}, - year = {2022}, - pages = {2959-2968} -} +@article{Rave_2025, + title={De-Cluttering Scatterplots With Integral Images}, + volume={31}, + ISSN={2160-9306}, + url={http://dx.doi.org/10.1109/TVCG.2024.3381453}, + DOI={10.1109/tvcg.2024.3381453}, + 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, - author = "Kihyuk Sohn, David Berthelot, Chun-Liang Li", - title = "FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence", - url = "https://arxiv.org/abs/2001.07685", - addendum = "(accessed: 20.03.2023)", - keywords = "FixMatch, semi-supervised" +@online{statisticsglobe_overplotting_r, + author = {Statistics Globe}, + title = {Avoid Overplotting in R (4 Examples) | Point Size, Opacity \& Color}, + year = {2025}, + url = {https://statisticsglobe.com/avoid-overplotting-r}, + note = {Accessed: 2025-11-23} }