Papers

Drawing Large Graphs by Low-Rank Stress Majorization

Tue, 27 Mar 2012 21:02:27 -0400

Marc Khoury, Yifan Hu, Shankar Krishnan, Carlos Scheidegger. Eurovis 2012, to appear.

Optimizing a stress model is a natural technique for drawing graphs: one seeks an embedding into $R^d$ which best preserves the induced graph metric. Current approaches to solving the stress model for a graph with $|V|$ nodes and $|E|$ edges require the full all-pairs shortest paths (APSP) matrix, which takes $O(|V|^2 \log|E| + |V||E|)$ time and $O(|V|^2)$ space. We propose a novel algorithm based on a low-rank approximation to the required matrices. The crux of our technique is an observation that it is possible to approximate the full APSP matrix, even when only a small subset of its entries are known. Our algorithm takes time $O(k |V| + |V| \log |V| + |E|)$ per iteration with a preprocessing time of $O(k^3+k(|E|+|V|\log|V|)+k^2 |V|)$ and memory usage of $O(k|V|)$, where a user-defined parameter $k$ trades off quality of approximation with running time and space. We give experimental results which show, to the best of our knowledge, the largest (albeit approximate) full stress model based layouts to date.

Get the paper preprint as a PDF file (12MB).

Topology Verification for Isosurface Extraction

Wed, 2 Nov 2011 16:19:03 -0400

Tiago Etiene, Luis Gustavo Nonato, Carlos Scheidegger, Julien Tierny, Thomas Peters, Valerio Pascucci, Mike Kirby, Claudio Silva. IEEE TVCG, Accepted.

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly-available isosurface codes.

Get the paper in PDF version (9.9MB).

Multilevel Agglomerative Edge Bundling for Visualizing Large Graphs

Tue, 1 Feb 2011 19:41:51 -0500

Emden Gansner, Yifan Hu, Carlos Scheidegger, Stephen North. Pacific Vis, 2011.

Graphs are often used to encapsulate relationships between objects. Node-link diagrams, commonly used to visualize graphs, suffer from visual clutter on large graphs. Edge bundling is an effective technique for alleviating clutter and revealing high-level edge patterns. Previous methods for general graph layouts either require a control mesh to guide the bundling process, which can introduce high variation in curvature along the bundles, or all-to-all force and compatibility calculations, which is not scalable. We propose a multilevel agglomerative edge bundling method based on a principled approach of minimizing ink needed to represent edges, with additional constraints on the curvature of the resulting splines. The proposed method is much faster than previous ones, able to bundle hundreds of thousands of edges in seconds, and one million edges in a few minutes.

Get the paper in PDF version (3.0MB). There are many additional examples on the paper webpage.

The Provenance of Workflow Upgrades

Sat, 4 Dec 2010 16:28:42 -0500

David Koop, Carlos E. Scheidegger, Juliana Freire, Claudio Silva. IPAW 2010.

Provenance has become an increasingly important part of documenting, verifying, and reproducing scientific research, but as users seek to extend or share results, it may be impractical to start from the exact original steps due to system configuration differ- ences, library updates, or new algorithms. Although there have been several approaches for capturing workflow provenance, the problem of managing upgrades of the underly- ing tools and libraries orchestrated by workflows has been largely overlooked. In this paper we consider the problem of maintaining and re-using the provenance of work- flow upgrades. We propose different kinds of upgrades that can be applied, including automatic mechanisms, developer-specified, and user-defined. We show how to cap- ture provenance from such upgrades and suggest how this provenance might be used to influence future upgrades. We also describe our implementation of these upgrade techniques.

You can get the paper in PDF version (1.3MB).

Verifiable Visualization for Isosurface Extraction

Fri, 3 Dec 2010 19:04:31 -0500

Tiago Etiene, Carlos Scheidegger, L. Gustavo Nonato, Robert M. Kirby, Claudio Silva. IEEE TVCG, 15(6):1227–1234, 2009.

Visual representations of isosurfaces are ubiquitous in the scientific and engineering literature. In this paper, we present techniques to assess the behavior of isosurface extraction codes. Where applicable, these techniques allow us to distinguish whether anomalies in isosurface features can be attributed to the underlying physical process or to artifacts from the extraction process. Such scientific scrutiny is at the heart of verifiable visualization - subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. More concretely, we derive formulas for the expected order of accuracy (or convergence rate) of several isosurface features, and compare them to experimentally observed results in the selected codes. This technique is practical: in two cases, it exposed actual problems in implementations. We provide the reader with the range of responses they can expect to encounter with isosurface techniques, both under “normal operating conditions” and also under adverse conditions. With the results of the verification process, practitioners can judiciously select the isosurface extraction technique appropriate for their problem of interest, and have confidence in its behavior.

Get the PDF version of the paper (27.4MB). Tiago’s presentation slides are also available.

Bandwidth Selection and Reconstruction Quality in Point-Based Surfaces

Wed, 1 Dec 2010 00:56:04 -0500

Hao Wang, Carlos Scheidegger, Claudio Silva. IEEE TVCG, 15(4):572–582, 2009.

We investigate the influence of bandwidth selection in the reconstruction quality of point-based surfaces. While the problem has received relatively little attention in the literature, we show that appropriate selection plays a significant role in the quality of reconstructed surfaces. We show how to compute optimal bandwidths for one class of moving-least squares surfaces by formulating the polynomial fitting step as a kernel regression problem for both noiseless and noisy data. In the context of Levin’s projection, we also discuss the implications of the two-step projection for bandwidth selection. We show experimental comparisons of our method, which outperforms heuristically chosen functions and weights previously proposed. We also show the influence of bandwidth on the reconstruction quality of different formulations of point-based surfaces. We provide, to the best of our knowledge, the first quantitative comparisons between different MLS surface formulations and their optimal bandwidths. Using these experiments, we investigate the choice of effective bandwidths for these alternative formulations. We conclude with a discussion of how to effectively compare the different MLS formulations in the literature.

Get the PDF version of the paper (3.8MB).

Edge Transformations for Improving Mesh Quality of Marching Cubes

Wed, 1 Dec 2010 00:25:00 -0500

Carlos A. Dietrich, Carlos Scheidegger, John Schreiner, Joao L. D. Comba, Luciana Nedel, Claudio Silva. IEEE TVCG, 15(1):150–159, 2009.

Marching Cubes is a popular choice for isosurface extraction from regular grids due to its simplicity, robustness, and efficiency. One of the key shortcomings of this approach is the quality of the resulting meshes, which tend to have many poorly shaped and degenerate triangles. This issue is often addressed through post processing operations such as smoothing. Rather than modifying the resulting mesh, we propose a method to modify the grid on which Marching Cubes operates. This modification greatly increases the quality of the extracted mesh. Our method incurs minimal computational overhead, can be readily integrated in existing Marching Cubes implementations, and is orthogonal to many Marching Cubes enhancements (particularly, performance enhancements such as out-of-core and acceleration structures).

Get the PDF version of the paper (30MB).

The source code is also available.

Revisiting Histograms and Isosurface Statistics

Sat, 27 Nov 2010 16:47:49 -0500

Carlos Scheidegger, John Schreiner, Brian Duffy, Hamish Carr, Claudio Silva. IEEE TVCG, 14(6):1659-1666, 2008. (Vis 2008)

Recent results have shown a link between geometric properties of isosurfaces and statistical properties of the underlying sampled data. However, this has two defects: not all of the properties described converge to the same solution, and the statistics computed are not always invariant under isosurface-preserving transformations. We apply Federer’s Coarea Formula from geometric measure theory to explain these discrepancies. We describe an improved substitute for histograms based on weighting with the inverse gradient magnitude, develop a statistical model that is invariant under isosurface-preserving transformations, and argue that this provides a consistent method for algorithm evaluation across multiple datasets based on histogram equalization. We use our corrected formulation to reevaluate recent results on average isosurface complexity, and show evidence that noise is one cause of the discrepancy between the expected figure and the observed one.

Get the paper in PDF format (7MB).

Dataset

We are publishing the set of volumes we collected to compute the histograms and isosurface statistics. Note that this is a fairly large dataset (~1GB). The files are in NRRD format. We have tried to give attribution to the people who originally made the data available in the NRRD header, as a comment. We couldn’t find the authors for a few of those files, so if you see your file here and it is incorrectly attributed, do not hesitate to let me know.

VisComplete: Automating Suggestions for Visualization Pipelines

Mon, 22 Nov 2010 22:17:27 -0500

David Koop, Carlos E. Scheidegger, Steven P. Callahan, Juliana Freire, Claudio T. Silva. IEEE TVCG 14(6):1691-1698, 2008 (Vis 2008).

Building visualization and analysis pipelines is a large hurdle in the adoption of visualization and workflow systems by domain scientists. In this paper, we propose techniques to help users construct pipelines by consensus, automatically suggesting completions based on a database of previously created pipelines. In particular, we compute correspondences between existing pipeline subgraphs from the database, and use these to predict sets of likely pipeline additions to a given partial pipeline. By presenting these predictions in a carefully designed interface, users can create visualizations and other data products more efficiently because they can augment their normal work patterns with the suggested completions. We present an implementation of our technique in a publicly-available, open-source scientific workflow system and demonstrate efficiency gains in real-world situations.

Get the paper in PDF Format (1.9MB).

Edge Groups: An Approach to Understanding the Mesh Quality of Marching Methods

Mon, 22 Nov 2010 22:09:13 -0500

Carlos A. Dietrich, Carlos Scheidegger, Joao Comba, Luciana Nedel, Claudio T. Silva. IEEE TVCG 14(6):1651-1658, 2008.

Marching Cubes is the most popular isosurface extraction algorithm due to its simplicity, efficiency and robustness. It has been widely studied, improved, and extended. While a lot of early work was concerned with efficiency and correctness issues, lately there is a push to improve the quality of Marching Cubes meshes so that they can be used for computational experiments. In this work we present a new classification of MC cases that we call Edge Groups, which helps elucidate the issues that impact the triangle quality of the meshes that the method generates. This formulation allows a more systematic way to bound the triangle quality, and is general enough to extend to other polyhedral cell shapes used in other polygonization algorithms. Using this analysis, we also discuss ways to improve the quality of the resulting triangle mesh, including some that require only minor modifications of the original algorithm.

Paper in PDF format (16MB).

Regenerating figures

Edge group datasets

Archive with all the volumes used to generate the volume renderings of triangle quality per case, in VTK format.

quality_volumes_float.zip, 32 bit floats (~150MB)
quality_volumes_float.tar.gz, 32 bit floats (~150MB)
quality_volumes_char.zip, 8-bit quantized (~8 MB) – recommended.
quality_volumes_char.tar.gz, 8-bit quantized (~8 MB) – recommended.

Regenerate Volume Renderings

The volume renderings in Tables 1 and 5 were generated with VisTrails. Download the software and get the vistrail here. This vistrail actually downloads the 8-bit zip file above from the web and unzips a particular file inside it. Change the Unzip module to pick a different case. The available lattices are cubic, BCC and CFK, each with as many cases as described on the paper.

Cubic Lattice

BCC Lattice

CFK Lattice

Code, Scripts

The quality volumes were generated with a set of Python scripts. These scripts can also generate SVG files of parallel coordinate plots. You will need:

Python 2.5 with a reasonably new version of numpy (we are currently running Ubuntu 8.04 (Hardy Heron)’s version on Linux, and the MacPorts version on Macs).
teem, compiled with VTK support.
The teem python bindings.

Download the scripts into a new directory and run them according to the instructions in the files. The main files are parallel_coordinates_svg.py, quality_histogram.py and quality_volume.py.

Regenerate parallel coordinate plots

This visualization didn’t make it into the final paper - we include it here for completeness. The script will generate an SVG file. Notice that most SVG renderers are slow, so if you want a nice parallel coordinate plot, expect Firefox to take a few seconds to render. Run the script as follows:

./parallel_coordinates_svg.py lattice case number_of_lines > output_svg_file

Parallel Coordinate Plots

These illustrations are meant to highlight the worst-case edge configurations for each case. We only show the bottom 5% quality of each case - anything above that is fully transparent.

Cubic Lattice

Note: The colorbar for cases 4, 5 and 7 is slightly wrong. The numbers in the colorbar are actual indicators of minimum and maximum quality, but the color scale is closer to what the other cases show. In these cases, black is around 0.7, while no lines with quality above 0.77 are shown.

BCC Lattice

CFK Lattice

Datasets

These datasets are stored in NRRD format.

Silicium - Courtesy VolVis SUNY Stony Brook.
Engine - Courtesy General Electric
Lobster - Courtesy VolVis SUNY Stony Brook.
Bonsai - Courtesy Bernd Tomandl and Stefan Roettger

Talk slides

PDF file with slides of talk (7.7MB)

Source code

2009-02-08: Tarball of source code with Makefiles for Linux and OSX: here. This version incorporates recent changes we made to the code, including a few tricks to remove edge group 2 entirely from the table (see talk slides for more details), and our CiSE article. Macet is GPL v2.