2012

J.A. Levine, S. Jadhav, H. Bhatia, V. Pascucci, P.-T. Bremer.
**“A Quantized Boundary Representation of 2D Flows,”** In *Computer Graphics Forum*, Vol. 31, No. 3 Pt. 1, pp. 945--954. June, 2012.

DOI: 10.1111/j.1467-8659.2012.03087.x

Analysis and visualization of complex vector fields remain major challenges when studying large scale simulation of physical phenomena. The primary reason is the gap between the concepts of smooth vector field theory and their computational realization. In practice, researchers must choose between either numerical techniques, with limited or no guarantees on how they preserve fundamental invariants, or discrete techniques which limit the precision at which the vector field can be represented. We propose a new representation of vector fields that combines the advantages of both approaches. In particular, we represent a subset of possible streamlines by storing their paths as they traverse the edges of a triangulation. Using only a finite set of streamlines creates a fully discrete version of a vector field that nevertheless approximates the smooth flow up to a user controlled error bound. The discrete nature of our representation enables us to directly compute and classify analogues of critical points, closed orbits, and other common topological structures. Further, by varying the number of divisions (quantizations) used per edge, we vary the resolution used to represent the field, allowing for controlled precision. This representation is compact in memory and supports standard vector field operations.

S. Liu, J.A. Levine, P.-T. Bremer, V. Pascucci.
**“Gaussian Mixture Model Based Volume Visualization,”** In *Proceedings of the IEEE Large-Scale Data Analysis and Visualization Symposium 2012*, Note: *Received Best Paper Award*, pp. 73--77. 2012.

DOI: 10.1109/LDAV.2012.6378978

Representing uncertainty when creating visualizations is becoming more indispensable to understand and analyze scientific data. Uncertainty may come from different sources, such as, ensembles of experiments or unavoidable information loss when performing data reduction. One natural model to represent uncertainty is to assume that each position in space instead of a single value may take on a distribution of values. In this paper we present a new volume rendering method using per voxel Gaussian mixture models (GMMs) as the input data representation. GMMs are an elegant and compact way to drastically reduce the amount of data stored while still enabling realtime data access and rendering on the GPU. Our renderer offers efficient sampling of the data distribution, generating renderings of the data that flicker at each frame to indicate high variance. We can accumulate samples as well to generate still frames of the data, which preserve additional details in the data as compared to either traditional scalar indicators (such as a mean or a single nearest neighbor down sample) or to fitting the data with only a single Gaussian per voxel. We demonstrate the effectiveness of our method using ensembles of climate simulations and MRI scans as well as the down sampling of large scalar fields as examples.

**Keywords:** Uncertainty Visualization, Volume Rendering, Gaussian Mixture Model, Ensemble Visualization

V. Pascucci, G. Scorzelli, B. Summa, P.-T. Bremer, A. Gyulassy, C. Christensen, S. Philip, S. Kumar.
**“The ViSUS Visualization Framework,”** In *High Performance Visualization: Enabling Extreme-Scale Scientific Insight*, Chapman and Hall/CRC Computational Science, Ch. 19, Edited by E. Wes Bethel and Hank Childs (LBNL) and Charles Hansen (UofU), Chapman and Hall/CRC, 2012.

The ViSUS software framework was designed with the primary philosophy that the visualization of massive data need not be tied to specialized hardware or infrastructure. In other words, a visualization environment for large data can be designed to be lightweight, highly scalable and run on a variety of plat- forms or hardware. Moreover, if designed generally such an infrastructure can have a wide variety of applications, all from the same code base. Figure 19.1 details example applications and the major components of the ViSUS infrastructure. The components can be grouped into three major categories. First, a lightweight and fast out-of-core data management framework using multi- resolution space filling curves. This allows the organization of information in an order that exploits the cache hierarchies of any modern data storage architectures. Second, a data flow framework that allows data to be processed during movement. Processing massive datasets in their entirety would be a long and expensive operation which hinders interactive exploration. By designing new algorithms to fit within this framework, data can be processed as it moves. Third, a portable visualization layer which was designed to scale from mobile devices to powerwall displays with same code base. In this chapter we will describe the ViSUS infrastructure, as well as give practical examples of its use in real world applications.

B. Summa, J. Tierny, V. Pascucci.
**“Panorama weaving: fast and flexible seam processing,”** In *ACM Trans. Graph.*, Vol. 31, No. 4, Note: *ACM ID:2335434*, ACM, New York, NY, USA pp. 83:1--83:11. July, 2012.

ISSN: 0730-0301

DOI: 10.1145/2185520.2185579

A fundamental step in stitching several pictures to form a larger mosaic is the computation of boundary seams that minimize the visual artifacts in the transition between images. Current seam computation algorithms use optimization methods that may be slow, sequential, memory intensive, and prone to finding suboptimal solutions related to local minima of the chosen energy function. Moreover, even when these techniques perform well, their solution may not be perceptually ideal (or even good). Such an inflexible approach does not allow the possibility of user-based improvement. This paper introduces the

**Keywords:** digital panoramas, interactive image boundaries, panorama editing, panorama seams

J. Tierny, V. Pascucci.
**“Generalized Topological Simplification of Scalar Fields on Surfaces,”** In *IEEE Transactions on Visualization and Computer Graphics (TVCG)*, Vol. 18, No. 12, pp. 2005--2013. Dec, 2012.

DOI: 10.1109/TVCG.2012.228

We present a combinatorial algorithm for the general topological simplification of scalar fields on surfaces. Given a scalar field f, our algorithm generates a simplified field g that provably admits only critical points from a constrained subset of the singularities of f, while guaranteeing a small distance ||f - g||

W. Widanagamaachchi, C. Christensen, P.-T. Bremer, V. Pascucci.
**“Interactive Exploration of Large-scale Time-varying Data using Dynamic Tracking Graphs,”** In *2012 IEEE Symposium on Large Data Analysis and Visualization (LDAV)*, pp. 9--17. 2012.

DOI: 10.1109/LDAV.2012.6378962

Exploring and analyzing the temporal evolution of features in large-scale time-varying datasets is a common problem in many areas of science and engineering. One natural representation of such data is tracking graphs, i.e., constrained graph layouts that use one spatial dimension to indicate time and show the “tracks” of each feature as it evolves, merges or disappears. However, for practical data sets creating the corresponding optimal graph layouts that minimize the number of intersections can take hours to compute with existing techniques. Furthermore, the resulting graphs are often unmanageably large and complex even with an ideal layout. Finally, due to the cost of the layout, changing the feature definition, e.g. by changing an iso-value, or analyzing properly adjusted sub-graphs is infeasible. To address these challenges, this paper presents a new framework that couples hierarchical feature definitions with progressive graph layout algorithms to provide an interactive exploration of dynamically constructed tracking graphs. Our system enables users to change feature definitions on-the-fly and filter features using arbitrary attributes while providing an interactive view of the resulting tracking graphs. Furthermore, the graph display is integrated into a linked view system that provides a traditional 3D view of the current set of features and allows a cross-linked selection to enable a fully flexible spatio-temporal exploration of data. We demonstrate the utility of our approach with several large-scale scientific simulations from combustion science.

P.C. Wong, H. Shen, V. Pascucci.
**“Extreme-Scale Visual Analytics,”** In *IEEE Computer Graphics and Applications*, Vol. 32, No. 4, pp. 23--25. 2012.

DOI: 10.1109/MCG.2012.73

Extreme-scale visual analytics (VA) is about applying VA to extreme-scale data. The articles in this special issue examine advances related to extreme-scale VA problems, their analytical and computational challenges, and their real-world applications.

2011

S. Ahern, A. Shoshani, K.L. Ma, A. Choudhary, T. Critchlow, S. Klasky, V. Pascucci.
**“Scientific Discovery at the Exascale: Report from the (DOE) (ASCR) 2011 Workshop on Exascale Data Management, Analysis, and Visualization,”** Note: *Office of Scientific and Technical Information (OSTI)*, January, 2011.

DOI: 10.2172/1011053

J.C. Bennett, V. Krishnamoorthy, S. Liu, R.W. Grout, E.R. Hawkes, J.H. Chen, J. Shepherd, V. Pascucci, P.-T. Bremer.
**“Feature-Based Statistical Analysis of Combustion Simulation Data,”** In *IEEE Transactions on Visualization and Computer Graphics, Proceedings of the 2011 IEEE Visualization Conference*, Vol. 17, No. 12, pp. 1822--1831. 2011.

H. Bhatia, S. Jadhav, P.-T. Bremer, G. Chen, J.A. Levine, L.G. Nonato, V. Pascucci.
**“Edge Maps: Representing Flow with Bounded Error,”** In *Proceedings of IEEE Pacific Visualization Symposium 2011*, Hong Kong, China, Note: *Won Best Paper Award!*, pp. 75--82. March, 2011.

DOI: 10.1109/PACIFICVIS.2011.5742375

H. Bhatia, S. Jadhav, P.-T. Bremer, G. Chen, J.A. Levine, L.G. Nonato, V. Pascucci.
**“Flow Visualization with Quantified Spatial and Temporal Errors using Edge Maps,”** In *IEEE Transactions on Visualization and Computer Graphics (TVCG)*, Vol. 18, No. 9, IEEE Society, pp. 1383--1396. 2011.

DOI: 10.1109/TVCG.2011.265

A. Cuadros-Vargas, L.G. Nonato, V. Pascucci.
**“Combinatorial Laplacian Image Cloning,”** In *Proceedings of XXIV Sibgrapi – Conference on Graphics, Patterns and Images*, pp. 236--241. 2011.

DOI: 10.1109/SIBGRAPI.2011.7

Seamless image cloning has become one of the most important editing operation for photomontage. Recent coordinate-based methods have lessened considerably the computational cost of image cloning, thus enabling interactive applications. However, those techniques still bear severe limitations as to concavities and dynamic shape deformation. In this paper we present novel methodology for image cloning that turns out to be highly efficient in terms of computational times while still being more flexible than existing techniques. Our approach builds on combinatorial Laplacian and fast Cholesky factorization to ensure interactive image manipulation, handling holes, concavities, and dynamic deformations during the cloning process. The provided experimental results show that the proposed technique outperforms existing methods in requisites such as accuracy and flexibility.

T. Etiene, L.G. Nonato, C. Scheidegger, J. Tierny, T.J. Peters, V. Pascucci, R.M. Kirby, C.T. Silva.
**“Topology Verfication for Isosurface Extraction,”** In *IEEE Transactions on Visualization and Computer Graphics*, pp. (accepted). 2011.

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.

Attila Gyulassy, J.A. Levine, V. Pascucci.
**“Visualization of Discrete Gradient Construction (Multimedia submission),”** In *Proceedings of the 27th Symposium on Computational Geometry*, Paris, France, ACM, pp. 289--290. June, 2011.

DOI: 10.1145/1998196.1998241

This video presents a visualization of a recent algorithm to compute discrete gradient fields on regular cell complexes [3]. Discrete gradient fields are used in practical methods that robustly translate smooth Morse theory to combinatorial domains. We describe the stages of the algorithm, highlighting both its simplicity and generality.

S. Jadhav, H. Bhatia, P.-T. Bremer, J.A. Levine, L.G. Nonato, V. Pascucci.
**“Consistent Approximation of Local Flow Behavior for 2D Vector Fields,”** In *Mathematics and Visualization*, Springer, pp. 141--159. Nov, 2011.

DOI: 10.1007/978-3-642-23175-9 10

Typically, vector fields are stored as a set of sample vectors at discrete locations. Vector values at unsampled points are defined by interpolating some subset of the known sample values. In this work, we consider two-dimensional domains represented as triangular meshes with samples at all vertices, and vector values on the interior of each triangle are computed by piecewise linear interpolation.

Many of the commonly used techniques for studying properties of the vector field require integration techniques that are prone to inconsistent results. Analysis based on such inconsistent results may lead to incorrect conclusions about the data. For example, vector field visualization techniques integrate the paths of massless particles (streamlines) in the flow or advect a texture using line integral convolution (LIC). Techniques like computation of the topological skeleton of a vector field, require integrating separatrices, which are streamlines that asymptotically bound regions where the flow behaves differently. Since these integrations may lead to compound numerical errors, the computed streamlines may intersect, violating some of their fundamental properties such as being pairwise disjoint. Detecting these computational artifacts to allow further analysis to proceed normally remains a significant challenge.

S. Kumar, V. Vishwanath, P. Carns, B. Summa, G. Scorzelli, V. Pascucci, R. Ross, J. Chen, H. Kolla, R. Grout.
**“PIDX: Efficient Parallel I/O for Multi-resolution Multi-dimensional Scientific Datasets,”** In *Proceedings of The IEEE International Conference on Cluster Computing*, pp. 103--111. September, 2011.

Valerio Pascucci, Xavier Tricoche, Hans Hagen, Julien Tierny.
**“Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications (Mathematics and Visualization),”** Springer, 2011.

ISBN: 978-3642150135

T. Peterka, R. Ross, A. Gyulassy, V. Pascucci, W. Kendall, H.-W. Shen, T.-Y. Lee, A. Chaudhuri.
**“Scalable Parallel Building Blocks for Custom Data Analysis,”** In *Proceedings of the 2011 IEEE Symposium on Large-Scale Data Analysis and Visualization (LDAV)*, pp. 105--112. October, 2011.

DOI: 10.1109/LDAV.2011.6092324

We present a set of building blocks that provide scalable data movement capability to computational scientists and visualization researchers for writing their own parallel analysis. The set includes scalable tools for domain decomposition, process assignment, parallel I/O, global reduction, and local neighborhood communicationtasks that are common across many analysis applications. The global reduction is performed with a new algorithm, described in this paper, that efficiently merges blocks of analysis results into a smaller number of larger blocks. The merging is configurable in the number of blocks that are reduced in each round, the number of rounds, and the total number of resulting blocks. We highlight the use of our library in two analysis applications: parallel streamline generation and parallel Morse-Smale topological analysis. The first case uses an existing local neighborhood communication algorithm, whereas the latter uses the new merge algorithm.

S. Philip, B. Summa, P.-T. Bremer, and V. Pascucci.
**“Parallel Gradient Domain Processing of Massive Images,”** In *Proceedings of the 2011 Eurographics Symposium on Parallel Graphics and Visualization*, pp. 11--19. 2011.

Gradient domain processing remains a particularly computationally expensive technique even for relatively small images. When images become massive in size, giga or terapixel, these problems become particularly troublesome and the best serial techniques take on the order of hours or days to compute a solution. In this paper, we provide a simple framework for the parallel gradient domain processing. Specifically, we provide a parallel out-of-core method for the seamless stitching of gigapixel panoramas in a parallel MPI environment. Unlike existing techniques, the framework provides both a straightforward implementation, maintains strict control over the required/allocated resources, and makes no assumptions on the speed of convergence to an acceptable image. Furthermore, the approach shows good weak/strong scaling from several to hundreds of cores and runs on a variety of hardware.

S. Philip, B. Summa, P-T Bremer, V. Pascucci.
**“Hybrid CPU-GPU Solver for Gradient Domain Processing of Massive Images,”** In *Proceedings of 2011 International Conference on Parallel and Distributed Systems (ICPADS)*, pp. 244--251. 2011.

Gradient domain processing is a computationally expensive image processing technique. Its use for processing massive images, giga or terapixels in size, can take several hours with serial techniques. To address this challenge, parallel algorithms are being developed to make this class of techniques applicable to the largest images available with running times that are more acceptable to the users. To this end we target the most ubiquitous form of computing power available today, which is small or medium scale clusters of commodity hardware. Such clusters are continuously increasing in scale, not only in the number of nodes, but also in the amount of parallelism available within each node in the form of multicore CPUs and GPUs. In this paper we present a hybrid parallel implementation of gradient domain processing for seamless stitching of gigapixel panoramas that utilizes MPI, threading and a CUDA based GPU component. We demonstrate the performance and scalability of our implementation by presenting results from two GPU clusters processing two large data sets.