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SCI Publications


B. Hollister, G. Duffley, C. Butson,, C.R. Johnson. “Visualization for Understanding Uncertainty in Activation Volumes for Deep Brain Stimulation,” In Eurographics Conference on Visualization, Edited by K.L. Ma G. Santucci, and J. van Wijk, 2016.


We have created the Neurostimulation Uncertainty Viewer (nuView or nView) tool for exploring data arising from deep brain stimulation (DBS). Simulated volume of tissue activated (VTA), using clinical electrode placements, are recorded along withpatient outcomes in the Unified Parkinson's disease rating scale (UPDRS). The data is volumetric and sparse, with multi-value patient results for each activated voxel in the simulation. nView provides a collection of visual methods to explore the activated tissue to enhance understanding of electrode usage for improved therapy with DBS.

M. Larsen, K. Moreland, C.R. Johnson,, H. Childs. “Optimizing Multi-Image Sort-Last Parallel Rendering,” In Symposium on Large Data Analysis and Visualization, IEEE, 2016.


Sort-last parallel rendering can be improved by considering the rendering of multiple images at a time. Most parallel rendering algorithms consider the generation of only a single image. This makes sense when performing interactive rendering where the parameters of each rendering are not known until the previous rendering completes. However, in situ visualization often generates multiple images that do not need to be created sequentially. In this paper we present a simple and effective approach to improving parallel image generation throughput by amortizing the load and overhead among multiple image renders. Additionally, we validate our approach by conducting a performance study exploring the achievable speed-ups in a variety of image-based in situ use cases and rendering workloads. On average, our approach shows a 1.5 to 3.7 fold improvement in performance, and in some cases, shows a 10 fold improvement.

P. Rosen, B. Burton, K. Potter, C.R. Johnson. “muView: A Visual Analysis System for Exploring Uncertainty in Myocardial Ischemia Simulations,” In Visualization in Medicine and Life Sciences III, Springer Nature, pp. 49--69. 2016.
DOI: 10.1007/978-3-319-24523-2_3


In this paper we describe the Myocardial Uncertainty Viewer (muView or µView) system for exploring data stemming from the simulation of cardiac ischemia. The simulation uses a collection of conductivity values to understand how ischemic regions effect the undamaged anisotropic heart tissue. The data resulting from the simulation is multi-valued and volumetric, and thus, for every data point, we have a collection of samples describing cardiac electrical properties. µView combines a suite of visual analysis methods to explore the area surrounding the ischemic zone and identify how perturbations of variables change the propagation of their effects. In addition to presenting a collection of visualization techniques, which individually highlight different aspects of the data, the coordinated view system forms a cohesive environment for exploring the simulations.We also discuss the findings of our study, which are helping to steer further development of the simulation and strengthening our collaboration with the biomedical engineers attempting to understand the phenomenon.

X. Tong, J. Edwards, C. Chen, H. Shen, C. R. Johnson, P. Wong. “View-Dependent Streamline Deformation and Exploration,” In Transactions on Visualization and Computer Graphics, Vol. 22, No. 7, IEEE, pp. 1788--1801. July, 2016.
ISSN: 1077-2626
DOI: 10.1109/tvcg.2015.2502583


Occlusion presents a major challenge in visualizing 3D flow and tensor fields using streamlines. Displaying too many streamlines creates a dense visualization filled with occluded structures, but displaying too few streams risks losing important features. We propose a new streamline exploration approach by visually manipulating the cluttered streamlines by pulling visible layers apart and revealing the hidden structures underneath. This paper presents a customized view-dependent deformation algorithm and an interactive visualization tool to minimize visual clutter in 3D vector and tensor fields. The algorithm is able to maintain the overall integrity of the fields and expose previously hidden structures. Our system supports both mouse and direct-touch interactions to manipulate the viewing perspectives and visualize the streamlines in depth. By using a lens metaphor of different shapes to select the transition zone of the targeted area interactively, the users can move their focus and examine the vector or tensor field freely.

Keywords: Context;Deformable models;Lenses;Shape;Streaming media;Three-dimensional displays;Visualization;Flow visualization;deformation;focus+context;occlusion;streamline;white matter tracts


C.R. Johnson, K. Potter. “Visualization,” In The Princeton Companion to Applied Mathematics, Edited by Nicholas J. Higham, Princeton University Press, pp. 843-846. September, 2015.
ISBN: 9780691150390

H. De Sterck, C.R. Johnson. “Data Science: What Is It and How Is It Taught?,” In SIAM News, SIAM, July, 2015.

C.R. Johnson. “Computational Methods and Software for Bioelectric Field Problems,” In Biomedical Engineering Handbook, 4, Vol. 1, Ch. 43, Edited by J.D. Bronzino and D.R. Peterson, CRC Press, pp. 1--28. 2015.


Computer modeling and simulation continue to become more important in the field of bioengineering. The reasons for this growing importance are manyfold. First, mathematical modeling has been shown to be a substantial tool for the investigation of complex biophysical phenomena. Second, since the level of complexity one can model parallels the existing hardware configurations, advances in computer architecture have made it feasible to apply the computational paradigm to complex biophysical systems. Hence, while biological complexity continues to outstrip the capabilities of even the largest computational systems, the computational methodology has taken hold in bioengineering and has been used successfully to suggest physiologically and clinically important scenarios and results.

This chapter provides an overview of numerical techniques that can be applied to a class of bioelectric field problems. Bioelectric field problems are found in a wide variety of biomedical applications, which range from single cells, to organs, up to models that incorporate partial to full human structures. We describe some general modeling techniques that will be applicable, in part, to all the aforementioned applications. We focus our study on a class of bioelectric volume conductor problems that arise in electrocardiography (ECG) and electroencephalography (EEG).

We begin by stating the mathematical formulation for a bioelectric volume conductor, continue by describing the model construction process, and follow with sections on numerical solutions and computational considerations. We continue with a section on error analysis coupled with a brief introduction to adaptive methods. We conclude with a section on software.

C.R. Johnson. “Visualization,” In Encyclopedia of Applied and Computational Mathematics, Edited by Björn Engquist, Springer, pp. 1537-1546. 2015.
ISBN: 978-3-540-70528-4
DOI: 10.1007/978-3-540-70529-1_368


G.P. Bonneau, H.C. Hege, C.R. Johnson, M.M. Oliveira, K. Potter, P. Rheingans, T. Schultz. “Overview and State-of-the-Art of Uncertainty Visualization,” In Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization, Edited by M. Chen and H. Hagen and C.D. Hansen and C.R. Johnson and A. Kauffman, Springer-Verlag, pp. 3--27. 2014.
ISBN: 978-1-4471-6496-8
ISSN: 1612-3786
DOI: 10.1007/978-1-4471-6497-5_1


The goal of visualization is to effectively and accurately communicate data. Visualization research has often overlooked the errors and uncertainty which accompany the scientific process and describe key characteristics used to fully understand the data. The lack of these representations can be attributed, in part, to the inherent difficulty in defining, characterizing, and controlling this uncertainty, and in part, to the difficulty in including additional visual metaphors in a well designed, potent display. However, the exclusion of this information cripples the use of visualization as a decision making tool due to the fact that the display is no longer a true representation of the data. This systematic omission of uncertainty commands fundamental research within the visualization community to address, integrate, and expect uncertainty information. In this chapter, we outline sources and models of uncertainty, give an overview of the state-of-the-art, provide general guidelines, outline small exemplary applications, and finally, discuss open problems in uncertainty visualization.

B. Chapman, H. Calandra, S. Crivelli, J. Dongarra, J. Hittinger, C.R. Johnson, S.A. Lathrop, V. Sarkar, E. Stahlberg, J.S. Vetter, D. Williams. “ASCAC Workforce Subcommittee Letter,” Note: Office of Scientific and Technical Information, DOE ASCAC Committee Report, July, 2014.
DOI: 10.2172/1222711


Simulation and computing are essential to much of the research conducted at the DOE national laboratories. Experts in the ASCR-relevant Computing Sciences, which encompass a range of disciplines including Computer Science, Applied Mathematics, Statistics and domain sciences, are an essential element of the workforce in nearly all of the DOE national laboratories. This report seeks to identify the gaps and challenges facing DOE with respect to this workforce.

The DOE laboratories provided the committee with information on disciplines in which they experienced workforce gaps. For the larger laboratories, the majority of the cited workforce gaps were in the Computing Sciences. Since this category spans multiple disciplines, it was difficult to obtain comprehensive information on workforce gaps in the available timeframe. Nevertheless, five multi-purpose laboratories provided additional relevant data on recent hiring and retention.

Data on academic coursework was reviewed. Studies on multidisciplinary education in Computational Science and Engineering (CS&E) revealed that, while the number of CS&E courses offered is growing, the overall availability is low and the coursework fails to provide skills for applying CS&E to real-world applications. The number of graduates in different fields within Computer Science (CS) and Computer Engineering (CE) was also reviewed, which confirmed that specialization in DOE areas of interest is less common than in many other areas.

Projections of industry needs and employment figures (mostly for CS and CE) were examined. They indicate a high and increasing demand for graduates in all areas of computing, with little unemployment. This situation will be exacerbated by large numbers of retirees in the coming decade. Further, relatively few US students study toward higher degrees in the Computing Sciences, and those who do are predominantly white and male. As a result of this demographic imbalance, foreign nationals are an increasing fraction of the graduate population and we fail to benefit from including women and underrepresented minorities.

There is already a program that supports graduate education that is tailored to the needs of the DOE laboratories. The Computational Science Graduate Fellowship (CSGF) enables graduates to pursue a multidisciplinary program of education that is coupled with practical experience at the laboratories. It has been demonstrated to be highly effective in both its educational goals and in its ability to supply talent to the laboratories. However, its current size and scope are too limited to solve the workforce problems identified. The committee felt strongly that this proven program should be extended to increase its ability to support the DOE mission.

Since no single program can eliminate the workforce gap, existing recruitment efforts by the laboratories were examined. It was found that the laboratories already make considerable effort to recruit in this area. Although some challenges, such as the inability to match industry compensation, cannot be directly addressed, DOE could develop a roadmap to increase the impact of individual laboratory efforts, to enhance the suitability of existing educational opportunities, to increase the attractiveness of the laboratories, and to attract and sustain a full spectrum of human talent, which includes women and underrepresented minorities.

M.G. Genton, C.R. Johnson, K. Potter, G. Stenchikov, Y. Sun. “Surface boxplots,” In Stat Journal, Vol. 3, No. 1, pp. 1--11. 2014.


In this paper, we introduce a surface boxplot as a tool for visualization and exploratory analysis of samples of images. First, we use the notion of volume depth to order the images viewed as surfaces. In particular, we define the median image. We use an exact and fast algorithm for the ranking of the images. This allows us to detect potential outlying images that often contain interesting features not present in most of the images. Second, we build a graphical tool to visualize the surface boxplot and its various characteristics. A graph and histogram of the volume depth values allow us to identify images of interest. The code is available in the supporting information of this paper. We apply our surface boxplot to a sample of brain images and to a sample of climate model outputs.

Y. Gur, C.R. Johnson. “Generalized HARDI Invariants by Method of Tensor Contraction,” In Proceedings of the 2014 IEEE International Symposium on Biomedical Imaging (ISBI), pp. 718--721. April, 2014.


We propose a 3D object recognition technique to construct rotation invariant feature vectors for high angular resolution diffusion imaging (HARDI). This method uses the spherical harmonics (SH) expansion and is based on generating rank-1 contravariant tensors using the SH coefficients, and contracting them with covariant tensors to obtain invariants. The proposed technique enables the systematic construction of invariants for SH expansions of any order using simple mathematical operations. In addition, it allows construction of a large set of invariants, even for low order expansions, thus providing rich feature vectors for image analysis tasks such as classification and segmentation. In this paper, we use this technique to construct feature vectors for eighth-order fiber orientation distributions (FODs) reconstructed using constrained spherical deconvolution (CSD). Using simulated and in vivo brain data, we show that these invariants are robust to noise, enable voxel-wise classification, and capture meaningful information on the underlying white matter structure.

Keywords: Diffusion MRI, HARDI, invariants

C.D. Hansen, M. Chen, C.R. Johnson, A.E. Kaufman, H. Hagen (Eds.). “Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization,” Mathematics and Visualization, Springer, 2014.
ISBN: 978-1-4471-6496-8


A. Abdul-Rahman, J. Lein, K. Coles, E. Maguire, M.D. Meyer, M. Wynne, C.R. Johnson, A. Trefethen, M. Chen. “Rule-based Visual Mappings - with a Case Study on Poetry Visualization,” In Proceedings of the 2013 Eurographics Conference on Visualization (EuroVis), Vol. 32, No. 3, pp. 381--390. June, 2013.


In this paper, we present a user-centered design study on poetry visualization. We develop a rule-based solution to address the conflicting needs for maintaining the flexibility of visualizing a large set of poetic variables and for reducing the tedium and cognitive load in interacting with the visual mapping control panel. We adopt Munzner's nested design model to maintain high-level interactions with the end users in a closed loop. In addition, we examine three design options for alleviating the difficulty in visualizing poems latitudinally. We present several example uses of poetry visualization in scholarly research on poetry.

B. Burton, B. Erem, K. Potter, P. Rosen, C.R. Johnson, D. Brooks, R.S. Macleod. “Uncertainty Visualization in Forward and Inverse Cardiac Models,” In Computing in Cardiology CinC, pp. 57--60. 2013.
ISSN: 2325-8861


Quantification and visualization of uncertainty in cardiac forward and inverse problems with complex geometries is subject to various challenges. Specific to visualization is the observation that occlusion and clutter obscure important regions of interest, making visual assessment difficult. In order to overcome these limitations in uncertainty visualization, we have developed and implemented a collection of novel approaches. To highlight the utility of these techniques, we evaluated the uncertainty associated with two examples of modeling myocardial activity. In one case we studied cardiac potentials during the repolarization phase as a function of variability in tissue conductivities of the ischemic heart (forward case). In a second case, we evaluated uncertainty in reconstructed activation times on the epicardium resulting from variation in the control parameter of Tikhonov regularization (inverse case). To overcome difficulties associated with uncertainty visualization, we implemented linked-view windows and interactive animation to the two respective cases. Through dimensionality reduction and superimposed mean and standard deviation measures over time, we were able to display key features in large ensembles of data and highlight regions of interest where larger uncertainties exist.

J. Chen, A. Choudhary, S. Feldman, B. Hendrickson, C.R. Johnson, R. Mount, V. Sarkar, V. White, D. Williams. “Synergistic Challenges in Data-Intensive Science and Exascale Computing,” Note: Summary Report of the Advanced Scientific Computing Advisory Committee (ASCAC) Subcommittee, March, 2013.


The ASCAC Subcommittee on Synergistic Challenges in Data-Intensive Science and Exascale Computing has reviewed current practice and future plans in multiple science domains in the context of the challenges facing both Big Data and the Exascale Computing. challenges. The review drew from public presentations, workshop reports and expert testimony. Data-intensive research activities are increasing in all domains of science, and exascale computing is a key enabler of these activities. We briefly summarize below the key findings and recommendations from this report from the perspective of identifying investments that are most likely to positively impact both data-intensive science goals and exascale computing goals.

D.K. Hammond, Y. Gur, C.R. Johnson. “Graph Diffusion Distance: A Difference Measure for Weighted Graphs Based on the Graph Laplacian Exponential Kernel,” In Proceedings of the IEEE global conference on information and signal processing (GlobalSIP'13), Austin, Texas, pp. 419--422. 2013.
DOI: 10.1109/GlobalSIP.2013.6736904


We propose a novel difference metric, called the graph diffusion distance (GDD), for quantifying the difference between two weighted graphs with the same number of vertices. Our approach is based on measuring the average similarity of heat diffusion on each graph. We compute the graph Laplacian exponential kernel matrices, corresponding to repeatedly solving the heat diffusion problem with initial conditions localized to single vertices. The GDD is then given by the Frobenius norm of the difference of the kernels, at the diffusion time yielding the maximum difference. We study properties of the proposed distance on both synthetic examples, and on real-data graphs representing human anatomical brain connectivity.

F. Jiao, J.M. Phillips, Y. Gur, C.R. Johnson. “Uncertainty Visualization in HARDI based on Ensembles of ODFs,” In Proceedings of 2013 IEEE Pacific Visualization Symposium, pp. 193--200. 2013.
PubMed ID: 24466504
PubMed Central ID: PMC3898522


In this paper, we propose a new and accurate technique for uncertainty analysis and uncertainty visualization based on fiber orientation distribution function (ODF) glyphs, associated with high angular resolution diffusion imaging (HARDI). Our visualization applies volume rendering techniques to an ensemble of 3D ODF glyphs, which we call SIP functions of diffusion shapes, to capture their variability due to underlying uncertainty. This rendering elucidates the complex heteroscedastic structural variation in these shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. Our uncertainty analysis and visualization framework is then applied to synthetic data, as well as to HARDI human-brain data, to study the impact of various image acquisition parameters and background noise levels on the diffusion shapes.

C.R. Johnson, A. Pang (Eds.). “International Journal for Uncertainty Quantification,” Subtitled “Special Issue on Working with Uncertainty: Representation, Quantification, Propagation, Visualization, and Communication of Uncertainty,” In Int. J. Uncertainty Quantification, Vol. 3, No. 2, Begell House, Inc., pp. vii--viii. 2013.
ISSN: 2152-5080
DOI: 10.1615/Int.J.UncertaintyQuantification.v3.i2

C.R. Johnson, A. Pang (Eds.). “International Journal for Uncertainty Quantification,” Subtitled “Special Issue on Working with Uncertainty: Representation, Quantification, Propagation, Visualization, and Communication of Uncertainty,” In Int. J. Uncertainty Quantification, Vol. 3, No. 3, Begell House, Inc., 2013.
ISSN: 2152-5080
DOI: 10.1615/Int.J.UncertaintyQuantification.v3.i3