Tensor Field Visualization,
Topological Data Analysis
R.S. MacLeod, J.J.E. Blauer. In Multimodal Cardiovascular Imaging: Principles and Clinical Applications, Ch. 25, Edited by O. Pahlm and G. Wagner, McGraw Hill, 2011.
Atrial fibrillation (AF) is the most common form of cardiac arrhythmia so that a review of the role imaging in AF is a natural topic to include in this book. Further motivation comes from the fact that the treatment of AF probably includes more different forms of imaging, often merged or combined in a variety of ways, than perhaps any other clinical intervention. A typical clinical electrophysiology lab for the treatment of AF usually contains no less than 6 and often more than 8 individual monitors, each rendering some form of image based information about the patient undergoing therapy. There is naturally great motivation to merge different images and different imaging modalities in the setting of AF but also very challenging because of a host of factors related to the small size, extremely thin walls, the large natural variation in atrial shape, and the fact that fibrillation is occurring so that atrial shape is changing rapidly and irregularly. Thus, the use of multimodal imaging has recently become a very active and challenging area of image processing and analysis research and development, driven by an enormous clinical need to understand and treat a disease that affects some 5 million Americans alone, a number that is predicted to increase to almost 16 million by 2050.
In this chapter we attempt to provide an overview of the large variety of imaging modalities and uses in the management and understanding of atrial fibrillation, with special emphasis on the most novel applications of magnetic resonance imaging (MRI) technology. To provide clinical and biomedical motivation, we outline the basics of the disease together with some contemporary hypotheses about its etiology and management. We then describe briefly the imaging modalities in common use in the management and research of AF, then focus on the use or MRI for all phases of the management of patients with AF and indicate some of the major engineering challenges that can motivate further progress.
Keywords: ablation, carma, cvrti, 5P41-RR012553-10
Scientific Discovery at the Exascale: Report from the (DOE) (ASCR) 2011 Workshop on Exascale Data Management, Analysis, and Visualization|
S. Ahern, A. Shoshani, K.L. Ma, A. Choudhary, T. Critchlow, S. Klasky, V. Pascucci. Note: Office of Scientific and Technical Information (OSTI), January, 2011.
Cyber Science and Engineering: A Report of the National Science Foundation Advisory Committee for Cyberinfrastructure Task Force on Grand Challenges|
J.T. Oden, O. Ghattas, J.L. King, B.I. Schneider, K. Bartschat, F. Darema, J. Drake, T. Dunning, D. Estep, S. Glotzer, M. Gurnis, C.R. Johnson, D.S. Katz, D. Keyes, S. Kiesler, S. Kim, J. Kinter, G. Klimeck, C.W. McCurdy, R. Moser, C. Ott, A. Patra, L. Petzold, T. Schlick, K. Schulten, V. Stodden, J. Tromp, M. Wheeler, S.J. Winter, C. Wu, K. Yelick. Note: NSF Report, 2011.
This document contains the findings and recommendations of the NSF – Advisory Committee for Cyberinfrastructure Task Force on Grand Challenges addressed by advances in Cyber Science and Engineering. The term Cyber Science and Engineering (CS&E) is introduced to describe the intellectual discipline that brings together core areas of science and engineering, computer science, and computational and applied mathematics in a concerted effort to use the cyberinfrastructure (CI) for scientific discovery and engineering innovations; CS&E is computational and data-based science and engineering enabled by CI. The report examines a host of broad issues faced in addressing the Grand Challenges of science and technology and explores how those can be met by advances in CI. Included in the report are recommendations for new programs and initiatives that will expand the portfolio of the Office of Cyberinfrastructure and that will be critical to advances in all areas of science and engineering that rely on the CI.
Advisory Committee for CyberInfrastructure Task Force on Software for Science and Engineering|
D. Keyes, V. Taylor, T. Hey, S. Feldman, G. Allen, P. Colella, P. Cummings, F. Darema, J. Dongarra, T. Dunning, M. Ellisman, I. Foster, W. Gropp, C.R. Johnson, C. Kamath, R. Madduri, M. Mascagni, S.G. Parker, P. Raghavan, A. Trefethen, S. Valcourt, A. Patra, F. Choudhury, C. Cooper, P. McCartney, M. Parashar, T. Russell, B. Schneider, J. Schopf, N. Sharp. Note: NSF Report, 2011.
The Software for Science and Engineering (SSE) Task Force commenced in June 2009 with a charge that consisted of the following three elements:Identify specific needs and opportunities across the spectrum of scientific software infrastructure. Characterize the specific needs and analyze technical gaps and opportunities for NSF to meet those needs through individual and systemic approaches. Design responsive approaches. Develop initiatives and programs led (or co-led) by NSF to grow, develop, and sustain the software infrastructure needed to support NSF’s mission of transformative research and innovation leading to scientific leadership and technological competitiveness. Address issues of institutional barriers. Anticipate, analyze and address both institutional and exogenous barriers to NSF’s promotion of such an infrastructure.
The SSE Task Force members participated in bi-weekly telecons to address the given charge. The telecons often included additional distinguished members of the scientific community beyond the task force membership engaged in software issues, as well as personnel from federal agencies outside of NSF who manage software programs. It was quickly acknowledged that a number of reports loosely and tightly related to SSE existed and should be leveraged. By September 2009, the task formed had formed three subcommittees focused on the following topics: (1) compute-intensive science, (2) data-intensive science, and (3) software evolution.
Visualization of Covariance and Cross-covariance Field|
C. Yang, D. Xiu, R.M. Kirby. In International Journal for Uncertainty Quantification, Vol. 3, No. 1, pp. 25--38. 2011.
We present a numerical technique to visualize covariance and cross-covariance fields of a stochastic simulation. The method is local in the sense that it demonstrates the covariance structure of the solution at a point with its neighboring locations. When coupled with an efficient stochastic simulation solver, our framework allows one to effectively concurrently visualize both the mean and (cross-)covariance information for two-dimensional (spatial) simulation results. Most importantly, the visualization provides the scientist a means to identify interesting correlation structure of the solution field. The mathematical setup is discussed, along with several examples to demonstrate the efficacy of this approach.
Consistent Approximation of Local Flow Behavior for 2D Vector Fields|
S. Jadhav, H. Bhatia, P.-T. Bremer, J.A. Levine, L.G. Nonato, V. Pascucci. 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.
Direct Isosurface Visualization of Hex-Based High-Order Geometry and Attribute Representations|
T. Martin, E. Cohen, R.M. Kirby. In IEEE Transactions on Visualization and Computer Graphics (TVCG), Vol. PP, No. 99, pp. 1--14. 2011.
In this paper, we present a novel isosurface visualization technique that guarantees the accuarate visualization of isosurfaces with complex attribute data defined on (un-)structured (curvi-)linear hexahedral grids. Isosurfaces of high-order hexahedralbased finite element solutions on both uniform grids (including MRI and CT scans) and more complex geometry represent a domain of interest that can be rendered using our algorithm. Additionally, our technique can be used to directly visualize solutions and attributes in isogeometric analysis, an area based on trivariate high-order NURBS (Non-Uniform Rational B-splines) geometry and attribute representations for the analysis. Furthermore, our technique can be used to visualize isosurfaces of algebraic functions. Our approach combines subdivision and numerical root-finding to form a robust and efficient isosurface visualization algorithm that does not miss surface features, while finding all intersections between a view frustum and desired isosurfaces. This allows the use of view-independent transparency in the rendering process. We demonstrate our technique through a straightforward CPU implementation on both complexstructured and complex-unstructured geometry with high-order simulation solutions, isosurfaces of medical data sets, and isosurfaces of algebraic functions.
Topology Verfication for Isosurface Extraction|
T. Etiene, L.G. Nonato, C. Scheidegger, J. Tierny, T.J. Peters, V. Pascucci, R.M. Kirby, C.T. Silva. 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.
A Conservered Developmental Patterning Network Produces Quantitatively Different Output in Multiple Species of Drosophila|
C. Fowlkes, K. Eckenrode, M. Bragdon, M.D. Meyer, Z. Wunderlich, L. Simirenko, C. Luengo, S. Keranen, C. Henriquez, D. Knowles, M. Biggin, M. Eisen, A. DePace. In PLoS Genetics, Vol. 7, No. 10:e1002346, pp. 17 pages. October, 2011.
Differences in the level, timing, or location of gene expression can contribute to alternative phenotypes at the molecular and organismal level. Understanding the origins of expression differences is complicated by the fact that organismal morphology and gene regulatory networks could potentially vary even between closely related species. To assess the scope of such changes, we used high-resolution imaging methods to measure mRNA expression in blastoderm embryos of Drosophila yakuba and Drosophila pseudoobscura and assembled these data into cellular resolution atlases, where expression levels for 13 genes in the segmentation network are averaged into species-specific, cellular resolution morphological frameworks. We demonstrate that the blastoderm embryos of these species differ in their morphology in terms of size, shape, and number of nuclei. We present an approach to compare cellular gene expression patterns between species, while accounting for varying embryo morphology, and apply it to our data and an equivalent dataset for Drosophila melanogaster. Our analysis reveals that all individual genes differ quantitatively in their spatio-temporal expression patterns between these species, primarily in terms of their relative position and dynamics. Despite many small quantitative differences, cellular gene expression profiles for the whole set of genes examined are largely similar. This suggests that cell types at this stage of development are conserved, though they can differ in their relative position by up to 3-4 cell widths and in their relative proportion between species by as much as 5-fold. Quantitative differences in the dynamics and relative level of a subset of genes between corresponding cell types may reflect altered regulatory functions between species. Our results emphasize that transcriptional networks can diverge over short evolutionary timescales and that even small changes can lead to distinct output in terms of the placement and number of equivalent cells.
Multi-Resolution-Display System for Virtual Reality Setups|
J. Grueninger, H. Hoffman, U. Kloos, J. Krüger. In Proceedings of the 14th International Conference on Human-Computer Interaction, HCI International, Lecture Notes in Computer Science, Vol. 6779/2011, pp. 180--189. 2011.
Most large-area video projection systems offer only limited spacial resolution. Consequently, images of detailed scenery cannot be displayed at full fidelity. A possible but significantly more costly strategy is a tiled projection display. If this solution is not feasible then either aliasing occurs or some anti-aliasing method is used at the cost of reduced scene quality.
In this paper we describe a novel cost effective multi-resolution display system. It allows users to select any part of a stereoscopic projection and view it in significantly higher resolution than possible with the standard projection alone. To achieve this, a pair of video projectors, which can be moved by stepper motors, project a high-resolution inset into a small portion of the low-resolution image. To avoid crosstalk between the low and high resolution projections, a mask is rendered into the low resolution scene to black out the area on the screen that is covered by the inlay.
To demonstrate the effectiveness of our multi-resolution display setup it has been integrated into a number of real life scenarios: a virtual factory, an airplane cabin simulation, and a focus and context volume visualization application (see Figure 1).
Visualization of Discrete Gradient Construction (Multimedia submission)|
Attila Gyulassy, J.A. Levine, V. Pascucci. In Proceedings of the 27th Symposium on Computational Geometry, Paris, France, ACM, pp. 289--290. June, 2011.
This video presents a visualization of a recent algorithm to compute discrete gradient fields on regular cell complexes . 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.
GPU-Based Interactive Cut-Surface Extraction From High-0rder Finite Element Fields|
B. Nelson, R. Haimes, R.M. Kirby. In IEEE Transactions on Visualization and Computer Graphics (IEEE Visualization Issue), Vol. 17, No. 12, pp. 1803--1811. 2011.
We present a GPU-based ray-tracing system for the accurate and interactive visualization of cut-surfaces through 3D simulations of physical processes created from spectral/hp high-order finite element methods. When used by the numerical analyst to debug the solver, the ability for the imagery to precisely reflect the data is critical. In practice, the investigator interactively selects from a palette of visualization tools to construct a scene that can answer a query of the data. This is effective as long as the implicit contract of image quality between the individual and the visualization system is upheld. OpenGL rendering of scientific visualizations has worked remarkably well for exploratory visualization for most solver results. This is due to the consistency between the use of first-order representations in the simulation and the linear assumptions inherent in OpenGL (planar fragments and color-space interpolation). Unfortunately, the contract is broken when the solver discretization is of higher-order. There have been attempts to mitigate this through the use of spatial adaptation and/or texture mapping. These methods do a better job of approximating what the imagery should be but are not exact and tend to be view-dependent. This paper introduces new rendering mechanisms that specifically deal with the kinds of native data generated by high-order finite element solvers. The exploratory visualization tools are reassessed and cast in this system with the focus on image accuracy. This is accomplished in a GPU setting to ensure interactivity.
Flow Visualization with Quantified Spatial and Temporal Errors using Edge Maps|
H. Bhatia, S. Jadhav, P.-T. Bremer, G. Chen, J.A. Levine, L.G. Nonato, V. Pascucci. In IEEE Transactions on Visualization and Computer Graphics (TVCG), Vol. 18, No. 9, IEEE Society, pp. 1383--1396. 2011.
Asymmetric Tensor Field Visualization for Surfaces|
G. Chen, D. Palke, Z. Lin, H. Yeh, P. Vincent, R.S. Laramee, E. Zhang. In IEEE Transactions on Visualization and Computer Graphics, Vol. 17, No. 12, IEEE, pp. 1979-1988. Dec, 2011.
Combinatorial Vector Field Topology in 3 Dimensions|
W. Reich, Dominic Schneider, Christian Heine, Alexander Wiebel, Guoning Chen, Gerik Scheuermann. In Mathematical Methods in Biomedical Image Analysis (MMBIA) Proceedings IEEE MMBIA 2012, pp. 47--59. November, 2011.
In this paper, we present two combinatorial methods to process 3-D steady vector fields, which both use graph algorithms to extract features from the underlying vector field. Combinatorial approaches are known to be less sensitive to noise than extracting individual trajectories. Both of the methods are a straightforward extension of an existing 2-D technique to 3-D fields. We observed that the first technique can generate overly coarse results and therefore we present a second method that works using the same concepts but produces more detailed results. We evaluate our method on a CFD-simulation of a gas furnace chamber. Finally, we discuss several possibilities for categorizing the invariant sets with respect to the flow.
Automatic Stream Surface Seeding|
M. Edmunds, T. McLoughlin, R.S. Laramee, G. Chen, E. Zhang, N. Max. In EUROGRAPHICS 2011 Short Papers, pp. 53--56. 2011.
|A wildland fire modeling and visualization environment,
J. Mandel, J.D. Beezley, A. Kochanski, V.Y. Kondratenko, L. Zhang, E. Anderson, J. Daniels II, C.T. Silva, C.R. Johnson. In Proceedings of the Ninth Symposium on Fire and Forest Meteorology, pp. (published online). 2011.
Simple and Efficient Mesh Layout with Space-Filling Curves|
H.T. Vo, C.T. Silva, L.F. Scheidegger, V. Pascucci. In Journal of Graphics, GPU, and Game Tools, pp. 25--39. 2011.
Feature-Based Statistical Analysis of Combustion Simulation Data|
J.C. Bennett, V. Krishnamoorthy, S. Liu, R.W. Grout, E.R. Hawkes, J.H. Chen, J. Shepherd, V. Pascucci, P.-T. Bremer. In IEEE Transactions on Visualization and Computer Graphics, Proceedings of the 2011 IEEE Visualization Conference, Vol. 17, No. 12, pp. 1822--1831. 2011.
Branching and Circular Features in High Dimensional Data|
Bei Wang, B. Summa, V. Pascucci, M. Vejdemo-Johansson. In IEEE Transactions of Visualization and Computer Graphics (TVCG), Vol. 17, No. 12, pp. 1902--1911. 2011.
PubMed ID: 22034307
Large observations and simulations in scientific research give rise to high-dimensional data sets that present many challenges and opportunities in data analysis and visualization. Researchers in application domains such as engineering, computational biology, climate study, imaging and motion capture are faced with the problem of how to discover compact representations of high dimensional data while preserving their intrinsic structure. In many applications, the original data is projected onto low-dimensional space via dimensionality reduction techniques prior to modeling. One problem with this approach is that the projection step in the process can fail to preserve structure in the data that is only apparent in high dimensions. Conversely, such techniques may create structural illusions in the projection, implying structure not present in the original high-dimensional data. Our solution is to utilize topological techniques to recover important structures in high-dimensional data that contains non-trivial topology. Specifically, we are interested in high-dimensional branching structures. We construct local circle-valued coordinate functions to represent such features. Subsequently, we perform dimensionality reduction on the data while ensuring such structures are visually preserved. Additionally, we study the effects of global circular structures on visualizations. Our results reveal never-before-seen structures on real-world data sets from a variety of applications.
Keywords: Dimensionality reduction, circular coordinates, visualization, topological analysis