add sources and images, shrink text a bit

summary/main.tex

@@ -5,6 +5,8 @@
 \usepackage{mathtools}
 
 \usepackage[inline]{enumitem}
+\usepackage{graphicx}
+\usepackage{subcaption}
 
 \settopmatter{printacmref=false} % Removes citation information below abstract
 \renewcommand\footnotetextcopyrightpermission[1]{} % removes footnote with conference information in first column
@@ -38,7 +40,7 @@
 \affiliation{%
   \institution{Johannes Kepler University Linz}
   \city{Linz}
-  \state{Upperaustria}
+  \state{Upper Austria}
   \country{Austria}
   \postcode{4020}
 }
@@ -49,7 +51,7 @@
 %% other information printed in the page headers. This command allows
 %% the author to define a more concise list
 %% of authors' names for this purpose.
-\renewcommand{\shortauthors}{Lukas Heilgenbrunner}
+\renewcommand{\shortauthors}{Lukas Heiligenbrunner}
 
 %%
 %% The abstract is a short summary of the work to be presented in the
@@ -64,7 +66,7 @@
 %%
 %% Keywords. The author(s) should pick words that accurately describe
 %% the work being presented. Separate the keywords with commas.
-\keywords{Scatterplots, Overplotting, Integral Images, Density Equalization, Information Visualization}
+\keywords{Scatterplots, Overplotting, Integral Images, Density Equalization}
 
 %\received{20 February 2007}
 %\received[revised]{12 March 2009}
@@ -83,7 +85,7 @@ This visual clutter negatively impacts the data analysis process by making it di
 
 To alleviate these issues, visualization research has traditionally employed three main strategies: appearance modification, data reduction, and spatial transformation.
 Appearance modification, such as adjusting sample transparency (opacity), is a common technique to improve the visibility of local density.
-hile effective for density estimation, it does not resolve the overlap of interaction targets, leaving individual samples inaccessible.
+While effective for density estimation, it does not resolve the overlap of interaction targets, leaving individual samples inaccessible.
 Data reduction techniques, such as down-sampling, reduce the number of rendered elements but inevitably discard information, altering the representation of the underlying phenomenon.
 
 The third category, spatial transformation, involves distorting the visualization domain to utilize screen space more efficiently.
@@ -91,58 +93,86 @@ This paper focuses on this domain, specifically addressing the limitations of ex
 Many prior spatial distortion methods rely on local collision detection or force-directed layouts, which can be computationally expensive (often $\mathcal{O}(n^2)$ or $\mathcal{O}(n^3)$) and may fail to preserve essential neighborhood relations.
 Furthermore, previous attempts to use Integral Images (InIms) for smooth deformation, such as the work by Molchanov and Linsen, lacked stability and failed to converge to a uniform distribution in general cases.
 
+The following summary examines the methodologies and contributions detailed in `De-cluttering Scatterplots with Integral Images` by Hennes Rave, Vladimir Molchanov, and Lars Linsen.
 This work proposes a novel, deterministic algorithm for de-cluttering scatterplots using a corrected, stable regularization mapping based on Integral Images.
 Unlike methods that rely on local collision handling, this approach evaluates the global density distribution to compute a smooth transformation.
 This ensures that sample neighborhood relations are preserved without the need for expensive collision checks, enabling the processing of large datasets at interactive rates.
-The authors present a parallel GPU-based implementation for fast computation and introduce visual encodings—such as deformed grids and density textures—to help users interpret the spatial distortions applied to the data.
+The authors present a parallel GPU-based implementation for fast computation and introduce visual encodings—such as deformed grids and density textures—to help users interpret the spatial distortions applied to the data~\cite{Rave_2025}.
 
 \section{Method}
-The core of the proposed summarization technique is a deterministic, iterative algorithm that uses global density information to redistribute data samples.
+The core of the de-cluttering technique is a deterministic, iterative algorithm that uses global density information to redistribute data samples.
 The method consists of three primary stages: constructing a density field, applying a smooth global deformation, and optimizing the process for real-time performance on a GPU.
 
 \subsection{Density Field Construction}
-To represent the distribution of n data samples zi within the scatterplot domain, the algorithm first generates a smooth scalar-valued density function dr(x,y).
+To represent the distribution of $n$ data samples $z_i$ within the scatterplot domain, the algorithm first generates a smooth scalar-valued density function $d_r(x,y)$.
-This is achieved by summing contributions from individual samples using a smooth radial basis function, such as a 2D Gaussian kernel with a dilation parameter r.
+This is achieved by summing contributions from individual samples using a smooth radial basis function, such as a 2D Gaussian kernel with a dilation parameter $r$.
-To ensure numerical stability—particularly in `empty` regions where the mapping might otherwise become singular—a global constant d0 is added to the density field:
+To ensure numerical stability, particularly in `empty` regions where the mapping might otherwise become singular, a global constant $d_0$ is added to the density field:
 
 \begin{equation}
   \label{eq:dfc}
   d(i,j) = d_r(i,j) + D_{0}
 \end{equation}
 
-This constant d0 is typically set to the average number of samples per pixel, representing the theoretical density of a perfectly uniform distribution.
+This constant $d_0$ is typically set to the average number of samples per pixel, representing the theoretical density of a perfectly uniform distribution~\cite{Rave_2025}.
 
 \subsection{Smooth Global Deformation}
 The transformation utilizes Integral Images (InIms), which provide a pixel-centered description of the global density distribution.
-While prior work by Molchanov and Linsen proposed a global mapping t(x,y;d), it failed to remain an identity transformation for constant density textures, making it unsuitable for iterative equalization.
+While prior work by Molchanov and Linsen proposed a global mapping $t(x,y;d)$, it failed to remain an identity transformation for constant density textures, making it unsuitable for iterative equalization.
 
-This work introduces a corrected transformation t(x,y) that subtracts the `defect` mapping of a constant texture d0 from the original formula:
+This work introduces a corrected transformation $t(x,y)$ that subtracts the `defect` mapping of a constant texture $d_0$ from the original formula:
 
 \begin{equation}
   \label{eq:sgd}
   t(x,y) = (x,y) + t(x,y; d) - t(x,y; d_0)
 \end{equation}
 
-By ensuring that t(x,y)=(x,y) when the density is already uniform (d=d0), the algorithm can be applied iteratively to converge toward a nearly uniform state.
+By ensuring that $t(x,y)=(x,y)$ when the density is already uniform $(d=d0)$, the algorithm can be applied iteratively to converge toward a nearly uniform state.
-This smooth deformation preserves essential neighborhood relations and the local ordering of data points without requiring expensive collision detection.
+This smooth deformation preserves essential neighborhood relations and the local ordering of data points without requiring expensive collision detection~\cite{Rave_2025}.
 
-\subsection{Efficient GPU Implementation}
+\subsection{Implementation and Visual Encodings}
-To maintain interactivity with datasets containing millions of points, the authors developed a parallel GPU-based scheme for computing InIms.
+To maintain interactivity with datasets containing millions of points, the authors developed a parallel GPU-based scheme using compute shaders to calculate InIms in linear O(n) time.
-The implementation uses a multi-pass approach in compute shaders:
+This multi-pass approach computes column and full integrals to determine new sample positions via bi-linear interpolation.
-
+Because this spatial distortion alters original distances, the method incorporates critical visual cues to help users maintain context.
-\begin{enumerate}
+These include deformed regular grids to show area expansion, density background textures to highlight original cluster locations, and contour lines to define the boundaries of the original data structures~\cite{Rave_2025}.
-\item \textbf{Column Integrals:} Computes upper- and lower-column sums using a progressive 2D reduction technique.
-\item \textbf{Full InIms:} Accumulates these column integrals horizontally to generate the standard and tilted InIms.
-\item \textbf{Sample Mapping:} The final deformation is calculated at each pixel, and new sample positions are determined via bi-linear interpolation.
-\end{enumerate}
-
-\subsection{Visual Encodings}
-Since spatial distortion alters original distances, the method includes visual cues to help users interpret the transformation.
-These include \textbf{deformed regular grids} to show area expansion/contraction, \textbf{density background textures} to highlight the original cluster locations, and \textbf{contour lines} to define the boundaries of the original data structures.
 
 \section{Results}
 The effectiveness of the proposed density-equalization method was evaluated through a combination of algorithmic performance benchmarks, quantitative metrics for structure preservation, and a controlled user study.
 
+\begin{figure}[htbp]
+  \centering
+  % First Row
+  \begin{subfigure}[b]{0.2\textwidth}
+    \centering
+    \includegraphics[width=\textwidth]{../presentation/rsc/2408.06513v1_page_7_1}
+    \caption{Original Scatterplot}
+    \label{fig:original}
+  \end{subfigure}
+  \hfill
+  \begin{subfigure}[b]{0.2\textwidth}
+    \centering
+    \includegraphics[width=\textwidth]{../presentation/rsc/2408.06513v1_page_7_2}
+    \caption{Density Estimation}
+    \label{fig:density}
+  \end{subfigure}
+
+  \begin{subfigure}[b]{0.2\textwidth}
+    \centering
+    \includegraphics[width=\textwidth]{../presentation/rsc/2408.06513v1_page_7_3}
+    \caption{Result with background texture}
+    \label{fig:grid}
+  \end{subfigure}
+  \hfill
+  \begin{subfigure}[b]{0.2\textwidth}
+    \centering
+    \includegraphics[width=\textwidth]{../presentation/rsc/2408.06513v1_page_7_4}
+    \caption{Result with contour lines}
+    \label{fig:final}
+  \end{subfigure}
+
+  \caption{MNIST Dataset with CMAP applied and then de-cluttered using InIms~\cite{Rave_2025}}\label{fig:figure}
+  \label{fig:2x2grid}
+\end{figure}
+
 \subsection{Performance and Scalability}
 A significant contribution of this work is the GPU-accelerated implementation of the integral image-based mapping.
 By leveraging parallel compute shaders, the algorithm achieves linear time complexity, O(n), relative to the number of data points.
@@ -154,19 +184,23 @@ The method was compared against `Hagrid`, a state-of-the-art grid-based de-clutt
 Using metrics such as the preservation of k-nearest neighbors (KNN) and spatial stress, the proposed integral image approach demonstrated superior stability.
 Unlike Hagrid, which can introduce artifacts due to its discrete grid-based nature, the continuous transformation provided by this method ensures that the relative ordering of points remains consistent.
 The results showed that while both methods successfully utilize screen space, the InIm-based approach maintains a higher correlation with the original local data structure.
+
 \subsection{User Study Findings}
-A user study involving 20 participants was conducted to evaluate the practical utility of the regularized scatterplots.
+%A user study involving 20 participants was conducted to evaluate the practical utility of the regularized scatterplots.
-The study focused on two primary tasks: estimating the relative size of clusters and analyzing class distributions within overlapping regions.
+%The study focused on two primary tasks: estimating the relative size of clusters and analyzing class distributions within overlapping regions.
 
-\begin{itemize}
+%\begin{enumerate}
-\item \textbf{Accuracy:} Participants were significantly more accurate at estimating the number of samples within dense clusters when using the regularized view compared to the original scatterplot (even with transparency).
+%\item \textbf{Accuracy:} Participants were significantly more accurate at estimating the number of samples within dense clusters when using the regularized view compared to the original scatterplot (even with transparency).
-\item \textbf{Confidence:} Users reported higher confidence levels when performing class-separation tasks in the equalized view, as the spatial expansion made individual color-coded classes more distinguishable.
+%\item \textbf{Confidence:} Users reported higher confidence levels when performing class-separation tasks in the equalized view, as the spatial expansion made individual color-coded classes more distinguishable.
-\item \textbf{Interpretation:} While the distorted view required the use of visual cues (like background textures and grids) to understand the original density, participants found these encodings intuitive and effective for maintaining context.
+%\item \textbf{Interpretation:} While the distorted view required the use of visual cues (like background textures and grids) to understand the original density, participants found these encodings intuitive and effective for maintaining context.
-\end{itemize}
+%\end{enumerate}
 
+A controlled study involving 20 participants demonstrated that the regularized view significantly improves accuracy in estimating sample counts within dense clusters compared to traditional scatterplots.
+Users reported higher confidence levels when performing class-separation tasks, as the spatial expansion made color-coded classes more distinguishable.
+Although the distortion requires the use of visual aids like background textures and grids to maintain context, participants found these encodings intuitive and effective for interpreting the original data distribution.
 
 \section{Conclusion}
-This paper presented a robust and scalable summarization technique for de-cluttering dense scatterplots using density-equalizing transformations.
+This paper presented a robust and scalable visualization technique for de-cluttering dense scatterplots using density-equalizing transformations.
 By correcting previous mapping formulas and utilizing GPU-accelerated integral images, the authors established a deterministic framework that transforms cluttered, overlapping data into a nearly uniform distribution while strictly preserving neighborhood relationships.
 
 The integration of visual aids, such as deformed grids and density contours, successfully bridges the gap between the equalized layout and the original data distribution, ensuring that analysts do not lose spatial context.

summary/sources.bib

@@ -1,16 +1,12 @@
-@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)},
-@online{fixmatch,
+    author={Rave, Hennes and Molchanov, Vladimir and Linsen, Lars},
-    author = "Kihyuk Sohn, David Berthelot, Chun-Liang Li",
+    year={2025},
-    title = "FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence",
+    month=apr, pages={2114–2126} }
-    url  = "https://arxiv.org/abs/2001.07685",
-    addendum = "(accessed: 20.03.2023)",
-    keywords = "FixMatch, semi-supervised"
-}