SCIENTIFIC COMPUTING AND IMAGING INSTITUTE
at the University of Utah

SCI Publications

2012

C.-S. Chiang, C. Hoffmann, P. Rosen. “A Generalized Malfatti Problem,” In Computational Geometry: Theory and Applications, Vol. 45, No. 8, pp. 425--435. 2012.

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Malfatti's problem, first published in 1803, is commonly understood to ask fitting three circles into a given triangle such that they are tangent to each other, externally, and such that each circle is tangent to a pair of the triangle's sides. There are many solutions based on geometric constructions, as well as generalizations in which the triangle sides are assumed to be circle arcs. A generalization that asks to fit six circles into the triangle, tangent to each other and to the triangle sides, has been considered a good example of a problem that requires sophisticated numerical iteration to solve by computer. We analyze this problem and show how to solve it quickly.

Keywords: Malfatti's problem, circle packing, geometric constraint solving, GPU programming

A.N.M. Imroz Choudhury, Bei Wang, P. Rosen, V. Pascucci. “Topological Analysis and Visualization of Cyclical Behavior in Memory Reference Traces,” In Proceedings of the IEEE Pacific Visualization Symposium (PacificVis 2012), pp. 9--16. 2012.
DOI: 10.1109/PacificVis.2012.6183557

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We demonstrate the application of topological analysis techniques to the rather unexpected domain of software visualization. We collect a memory reference trace from a running program, recasting the linear flow of trace records as a high-dimensional point cloud in a metric space. We use topological persistence to automatically detect significant circular structures in the point cloud, which represent recurrent or cyclical runtime program behaviors. We visualize such recurrences using radial plots to display their time evolution, offering multi-scale visual insights, and detecting potential candidates for memory performance optimization. We then present several case studies to demonstrate some key insights obtained using our techniques.

Keywords: scidac

M. Dannhauer, D.H. Brooks, D. Tucker, R.S. MacLeod. “A pipeline for the simulation of transcranial direct current stimulation for realistic human head models using SCIRun/BioMesh3D,” In Proceedings of the 2012 IEEE Int. Conf. Engineering and Biology Society (EMBC), pp. 5486--5489. 2012.
DOI: 10.1109/EMBC.2012.6347236
PubMed ID: 23367171
PubMed Central ID: PMC3651514

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The current work presents a computational pipeline to simulate transcranial direct current stimulation from image based models of the head with SCIRun [15]. The pipeline contains all the steps necessary to carry out the simulations and is supported by a complete suite of open source software tools: image visualization, segmentation, mesh generation, tDCS electrode generation and efficient tDCS forward simulation.

M. Datar, P. Muralidharan, A. Kumar, S. Gouttard, J. Piven, G. Gerig, R.T. Whitaker, P.T. Fletcher. “Mixed-Effects Shape Models for Estimating Longitudinal Changes in Anatomy,” In Spatio-temporal Image Analysis for Longitudinal and Time-Series Image Data, Lecture Notes in Computer Science, Vol. 7570, Springer Berlin / Heidelberg, pp. 76--87. 2012.
ISBN: 978-3-642-33554-9
DOI: 10.1007/978-3-642-33555-6_7

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In this paper, we propose a new method for longitudinal shape analysis that ts a linear mixed-eects model, while simultaneously optimizing correspondences on a set of anatomical shapes. Shape changes are modeled in a hierarchical fashion, with the global population trend as a xed eect and individual trends as random eects. The statistical signi cance of the estimated trends are evaluated using speci cally designed permutation tests. We also develop a permutation test based on the Hotelling T² statistic to compare the average shapes trends between two populations. We demonstrate the bene ts of our method on a synthetic example of longitudinal tori and data from a developmental neuroimaging study.

Keywords: Computer Science

E.V.R. DiBella, T. Tasdizen. “Edge enhanced spatio-temporal constrained reconstruction of undersampled dynamic contrast enhanced radial MRI,” In Proceedings of the 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp. 704--707. 2012.
DOI: 10.1109/ISBI.2010.5490077

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There are many applications in MRI where it is desirable to have high spatial and high temporal resolution. This can be achieved by undersampling of k-space and requires special techniques for reconstruction. Even if undersampling artifacts are removed, sharpness of the edges can be a problem. We propose a new technique that uses the gradient from a reference image to improve the quality of the edges in the reconstructed image along with a spatio-temporal constraint to reduce aliasing artifacts and noise. The reference is created from undersampled dynamic data by combining several adjacent frames. The method was tested on undersampled radial DCE MRI data with little respiratory motion. The proposed method was compared to reconstruction using the spatio-temporal constrained reconstruction. Sharper edges and an increase in the contrast was observed by using the proposed method.

M.K. Dougherty, H. Gu, J. Bizzell, S. Ramsey, G. Gerig, D.O. Perkins, A. Belger. “Differences in subcortical structures in young adolescents at familial risk for schizophrenia: A preliminary study,” In Psychiatry Res., pp. (Epub ahead of print. Nov. 9, 2012.
DOI: 10.1016/j.pscychresns.2012.04.016
PubMed ID: 23146250

A. Duchowski, M. Price, M.D. Meyer, P. Orero. “Aggregate Gaze Visualization with Real-Time Heatmaps,” In Proceedings of the ACM Symposium on Eye Tracking Research and Applications (ETRA), pp. 13--20. 2012.
DOI: 10.1145/2168556.2168558

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A GPU implementation is given for real-time visualization of aggregate eye movements (gaze) via heatmaps. Parallelization of the algorithm leads to substantial speedup over its CPU-based implementation and, for the first time, allows real-time rendering of heatmaps atop video. GLSL shader colorization allows the choice of color ramps. Several luminance-based color maps are advocated as alternatives to the popular rainbow color map, considered inappropriate (harmful) for depiction of (relative) gaze distributions.

S. Durrleman, M.W. Prastawa, S. Joshi, G. Gerig, A. Trouve. “Topology Preserving Atlas Construction from Shape Data without Correspondence using Sparse Parameters,” In Proceedings of MICCAI 2012, Lecture Notes in Computer Science (LNCS), pp. 223--230. October, 2012.

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Statistical analysis of shapes, performed by constructing an atlas composed of an average model of shapes within a population and associated deformation maps, is a fundamental aspect of medical imaging studies. Usual methods for constructing a shape atlas require point correspondences across subjects, which are difficult in practice. By contrast, methods based on currents do not require correspondence. However, existing atlas construction methods using currents suffer from two limitations. First, the template current is not in the form of a topologically correct mesh, which makes direct analysis on shapes difficult. Second, the deformations are parametrized by vectors at the same location as the normals of the template current which often provides a parametrization that is more dense than required. In this paper, we propose a novel method for constructing shape atlases using currents where topology of the template is preserved and deformation parameters are optimized independently of the shape parameters. We use an L¹-type prior that enables us to adaptively compute sparse and low dimensional parameterization of deformations.We show an application of our method for comparing anatomical shapes of patients with Down’s syndrome and healthy controls, where the sparse parametrization of diffeomorphisms decreases the parameter dimension by one order of magnitude.

S. Durrleman, S. Allassonniere, S. Joshi. “Sparse Adaptive Parameterization of Variability in Image Ensembles,” In International Journal of Computer Vision, pp. 1--23. 2012.

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This paper introduces a new parameterization of diffeomorphic deformations for the characterization of the variability in image ensembles. Dense diffeomorphic deformations are built by interpolating the motion of a finite set of control points that forms a Hamiltonian flow of self-interacting particles. The proposed approach estimates a template image representative of a given image set, an optimal set of control points that focuses on the most variable parts of the image, and template-to-image registrations that quantify the variability within the image set. The method automatically selects the most relevant control points for the characterization of the image variability and estimates their optimal positions in the template domain. The optimization in position is done during the estimation of the deformations without adding any computational cost at each step of the gradient descent. The selection of the control points is done by adding a L¹ prior to the objective function, which is optimized using the FISTA algorithm.

J. Fishbaugh, S. Durrleman, J. Piven, G. Gerig. “A framework for longitudinal data analysis via shape regression,” In Medical Imaging 2012: Image Processing, Edited by David R. Haynor and Sebastien Ourselin, SPIE Intl Soc Optical Eng, Feb, 2012.
DOI: 10.1117/12.911721

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Traditional longitudinal analysis begins by extracting desired clinical measurements, such as volume or head circumference, from discrete imaging data. Typically, the continuous evolution of a scalar measurement is estimated by choosing a 1D regression model, such as kernel regression or fitting a polynomial of fixed degree. This type of analysis not only leads to separate models for each measurement, but there is no clear anatomical or biological interpretation to aid in the selection of the appropriate paradigm. In this paper, we propose a consistent framework for the analysis of longitudinal data by estimating the continuous evolution of shape over time as twice differentiable flows of deformations. In contrast to 1D regression models, one model is chosen to realistically capture the growth of anatomical structures. From the continuous evolution of shape, we can simply extract any clinical measurements of interest. We demonstrate on real anatomical surfaces that volume extracted from a continuous shape evolution is consistent with a 1D regression performed on the discrete measurements. We further show how the visualization of shape progression can aid in the search for significant measurements. Finally, we present an example on a shape complex of the brain (left hemisphere, right hemisphere, cerebellum) that demonstrates a potential clinical application for our framework.

J. Fishbaugh, M.W. Prastawa, S. Durrleman, G. Gerig. “Analysis of Longitudinal Shape Variability via Subject Specific Growth Modeling,” In Medical Image Computing and Computer-Assisted Intervention – Proceedings of MICCAI 2012, Lecture Notes in Computer Science (LNCS), Vol. 7510, pp. 731--738. October, 2012.
DOI: 10.1007/978-3-642-33415-3_90

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Statistical analysis of longitudinal imaging data is crucial for understanding normal anatomical development as well as disease progression. This fundamental task is challenging due to the difficulty in modeling longitudinal changes, such as growth, and comparing changes across different populations. We propose a new approach for analyzing shape variability over time, and for quantifying spatiotemporal population differences. Our approach estimates 4D anatomical growth models for a reference population (an average model) and for individuals in different groups. We define a reference 4D space for our analysis as the average population model and measure shape variability through diffeomorphisms that map the reference to the individuals. Conducting our analysis on this 4D space enables straightforward statistical analysis of deformations as they are parameterized by momenta vectors that are located at homologous locations in space and time. We evaluate our method on a synthetic shape database and clinical data from a study that seeks to quantify growth differences in subjects at risk for autism.

X. Geng, S. Gouttard, A. Sharma, H. Gu, M. Styner, W. Lin, G. Gerig, J.H. Gilmore. “Quantitative Tract-Based White Matter Development from Birth to Age Two Years,” In NeuroImage, pp. 1-44. March, 2012.
DOI: 10.1016/j.neuroimage.2012.03.057

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Few large-scale studies have been done to characterize the normal human brain white matter growth in the first years of life. We investigated white matter maturation patterns in major fiber pathways in a large cohort of healthy young children from birth to age two using diffusion parameters fractional anisotropy (FA), radial diffusivity (RD) and axial diffusivity (RD). Ten fiber pathways, including commissural, association and projection tracts, were examined with tract-based analysis, providing more detailed and continuous spatial developmental patterns compared to conventional ROI based methods. All DTI data sets were transformed to a population specific atlas with a group-wise longitudinal large deformation diffeomorphic registration approach. Diffusion measurements were analyzed along the major fiber tracts obtained in the atlas space. All fiber bundles show increasing FA values and decreasing radial and axial diffusivities during development in the first 2 years of life. The changing rates of the diffusion indices are faster in the first year than the second year for all tracts. RD and FA show larger percentage changes in the first and second years than AD. The gender effects on the diffusion measures are small. Along different spatial locations of fiber tracts, maturation does not always follow the same speed. Temporal and spatial diffusion changes near cortical regions are in general smaller than changes in central regions. Overall developmental patterns revealed in our study confirm the general rules of white matter maturation. This work shows a promising framework to study and analyze white matter maturation in a tract-based fashion. Compared to most previous studies that are ROI-based, our approach has the potential to discover localized development patterns associated with fiber tracts of interest.

S. Gerber, K. Potter. “Data Analysis with the Morse-Smale Complex: The msr Package for R,” In Journal of Statistical Software, Vol. 50, No. 2, 2012.

P.H. Gesteland, Y. Livnat, N. Galli, M.H. Samore, A.V. Gundlapalli. “The EpiCanvas infectious disease weather map: an interactive visual exploration of temporal and spatial correlations,” In J. Amer. Med. Inform. Assoc., Vol. 19, Note: Awarded 1st place for Outstanding Research Article at ISDS 2012 and the Homer R. Warner Award at the AMIA Annual Symposium 2012, pp. 954--959. 2012.
DOI: 10.1136/amiajnl-2011-000486

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Advances in surveillance science have supported public health agencies in tracking and responding to disease outbreaks. Increasingly, epidemiologists have been tasked with interpreting multiple streams of heterogeneous data arising from varied surveillance systems. As a result public health personnel have experienced an overload of plots and charts as information visualization techniques have not kept pace with the rapid expansion in data availability. This study sought to advance the science of public health surveillance data visualization by conceptualizing a visual paradigm that provides an 'epidemiological canvas' for detection, monitoring, exploration and discovery of regional infectious disease activity and developing a software prototype of an 'infectious disease weather map'. Design objectives were elucidated and the conceptual model was developed using cognitive task analysis with public health epidemiologists. The software prototype was pilot tested using retrospective data from a large, regional pediatric hospital, and gastrointestinal and respiratory disease outbreaks were re-created as a proof of concept.

S. Gouttard, C.B. Goodlett, M. Kubicki, G. Gerig. “Measures for Validation of DTI Tractography,” In Medical Imaging 2012: Image Processing, Edited by David R. Haynor and Sebastien Ourselin, SPIE Intl Soc Optical Eng, Feb, 2012.
DOI: 10.1117/12.911546

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The evaluation of analysis methods for diffusion tensor imaging (DTI) remains challenging due to the lack of gold standards and validation frameworks. Significant work remains in developing metrics for comparing fiber bundles generated from streamline tractography. We propose a set of volumetric and tract oriented measures for evaluating tract differences. The different methods developed for this assessment work are: an overlap measurement, a point cloud distance and a quantification of the diffusion properties at similar locations between fiber bundles. The application of the measures in this paper is a comparison of atlas generated tractography to tractography generated in individual images. For the validation we used a database of 37 subject DTIs, and applied the measurements on five specific fiber bundles: uncinate, cingulum (left and right for both bundles) and genu. Each measurments is interesting for specific use: the overlap measure presents a simple and comprehensive metric but is sensitive to partial voluming and does not give consistent values depending on the bundle geometry. The point cloud distance associated with a quantile interpretation of the distribution gives a good intuition of how close and similar the bundles are. Finally, the functional difference is useful for a comparison of the diffusion properties since it is the focus of many DTI analysis to compare scalar invariants. The comparison demonstrated reasonable similarity of results. The tract difference measures are also applicable to comparison of tractography algorithms, quality control, reproducibility studies, and other validation problems.

A. Gupta, M. Escolar, C. Dietrich, J. Gilmore, G. Gerig, M. Styne. “3D Tensor Normalization for Improved Accuracy in DTI Registration Methods,” In Biomedical Image Registration Lecture Notes in Computer Science (LNCS), In Biomedical Image Registration Lecture Notes in Computer Science (LNCS), Vol. 7359, pp. 170--179. 2012.
DOI: 10.1007/978-3-642-31340-0_18

Y. Gur, F. Jiao, S.X. Zhu, C.R. Johnson. “White matter structure assessment from reduced HARDI data using low-rank polynomial approximations,” In Proceedings of MICCAI 2012 Workshop on Computational Diffusion MRI (CDMRI12), Nice, France, Lecture Notes in Computer Science (LNCS), pp. 186-197. October, 2012.

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Assessing white matter fiber orientations directly from DWI measurements in single-shell HARDI has many advantages. One of these advantages is the ability to model multiple fibers using fewer parameters than are required to describe an ODF and, thus, reduce the number of DW samples needed for the reconstruction. However, fitting a model directly to the data using Gaussian mixture, for instance, is known as an initialization-dependent unstable process. This paper presents a novel direct fitting technique for single-shell HARDI that enjoys the advantages of direct fitting without sacrificing the accuracy and stability even when the number of gradient directions is relatively low. This technique is based on a spherical deconvolution technique and decomposition of a homogeneous polynomial into a sum of powers of linear forms, known as a symmetric tensor decomposition. The fiber-ODF (fODF), which is described by a homogeneous polynomial, is approximated here by a discrete sum of even-order linear-forms that are directly related to rank-1 tensors and represent single-fibers. This polynomial approximation is convolved to a single-fiber response function, and the result is optimized against the DWI measurements to assess the fiber orientations and the volume fractions directly. This formulation is accompanied by a robust iterative alternating numerical scheme which is based on the Levenberg- Marquardt technique. Using simulated data and in vivo, human brain data we show that the proposed algorithm is stable, accurate and can model complex fiber structures using only 12 gradient directions.

A. Gyulassy, V. Pascucci, T. Peterka, R. Ross. “The Parallel Computation of Morse-Smale Complexes,” In Proceedings of the Parallel and Distributed Processing Symposium (IPDPS), pp. 484--495. 2012.
DOI: 10.1109/IPDPS.2012.52

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Topology-based techniques are useful for multiscale exploration of the feature space of scalar-valued functions, such as those derived from the output of large-scale simulations. The Morse-Smale (MS) complex, in particular, allows robust identification of gradient-based features, and therefore is suitable for analysis tasks in a wide range of application domains. In this paper, we develop a two-stage algorithm to construct the 1-skeleton of the Morse-Smale complex in parallel, the first stage independently computing local features per block and the second stage merging to resolve global features. Our implementation is based on MPI and a distributed-memory architecture. Through a set of scalability studies on the IBM Blue Gene/P supercomputer, we characterize the performance of the algorithm as block sizes, process counts, merging strategy, and levels of topological simplification are varied, for datasets that vary in feature composition and size. We conclude with a strong scaling study using scientific datasets computed by combustion and hydrodynamics simulations.

A. Gyulassy, P.-T. Bremer, V. Pascucci. “Computing Morse-Smale Complexes with Accurate Geometry,” In IEEE Transactions on Visualization and Computer Graphics, Vol. 18, No. 12, pp. 2014--2022. 2012.
DOI: 10.1109/TVCG.2011.272

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Topological techniques have proven highly successful in analyzing and visualizing scientific data. As a result, significant efforts have been made to compute structures like the Morse-Smale complex as robustly and efficiently as possible. However, the resulting algorithms, while topologically consistent, often produce incorrect connectivity as well as poor geometry. These problems may compromise or even invalidate any subsequent analysis. Moreover, such techniques may fail to improve even when the resolution of the domain mesh is increased, thus producing potentially incorrect results even for highly resolved functions. To address these problems we introduce two new algorithms: (i) a randomized algorithm to compute the discrete gradient of a scalar field that converges under refinement; and (ii) a deterministic variant which directly computes accurate geometry and thus correct connectivity of the MS complex. The first algorithm converges in the sense that on average it produces the correct result and its standard deviation approaches zero with increasing mesh resolution. The second algorithm uses two ordered traversals of the function to integrate the probabilities of the first to extract correct (near optimal) geometry and connectivity. We present an extensive empirical study using both synthetic and real-world data and demonstrates the advantages of our algorithms in comparison with several popular approaches.

A. Gyulassy, N. Kotava, M. Kim, C. Hansen, H. Hagen, and V. Pascucci. “Direct Feature Visualization Using Morse-Smale Complexes,” In IEEE Transactions on Visualization and Computer Graphics, Vol. 18, No. 9, pp. 1549--1562. September, 2012.
DOI: 10.1109/TVCG.2011.272

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In this paper, we characterize the range of features that can be extracted from an Morse-Smale complex and describe a unified query language to extract them. We provide a visual dictionary to guide users when defining features in terms of these queries. We demonstrate our topology-rich visualization pipeline in a tool that interactively queries the MS complex to extract features at multiple resolutions, assigns rendering attributes, and combines traditional volume visualization with the extracted features. The flexibility and power of this approach is illustrated with examples showing novel features.