2015

J. Bennett, F. Vivodtzev, V. Pascucci (Eds.).
**“Topological and Statistical Methods for Complex Data,”** Subtitled **“Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces,”** Mathematics and Visualization, 2015.

ISBN: 978-3-662-44899-1

This book contains papers presented at the Workshop on the Analysis of Large-scale,

High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp,

France, June 2013. It features the work of some of the most prominent and recognized

leaders in the field who examine challenges as well as detail solutions to the analysis of

extreme scale data.

The book presents new methods that leverage the mutual strengths of both topological

and statistical techniques to support the management, analysis, and visualization

of complex data. It covers both theory and application and provides readers with an

overview of important key concepts and the latest research trends.

Coverage in the book includes multi-variate and/or high-dimensional analysis techniques,

feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms,

scalar and vector field topology, and multi-scale representations. In addition, the book

details algorithms that are broadly applicable and can be used by application scientists to

glean insight from a wide range of complex data sets.

CIBC.
Note: *Data Sets: NCRR Center for Integrative Biomedical Computing (CIBC) data set archive. Download from: http://www.sci.utah.edu/cibc/software.html*, 2015.

CIBC.
Note: *Cleaver: A MultiMaterial Tetrahedral Meshing Library and Application. Scientific Computing and Imaging Institute (SCI), Download from: http://www.sci.utah.edu/cibc/software.html*, 2015.

S. Durrleman, T.P. Fletcher, G. Gerig, M. Niethammer, X. Pennec (Eds.).
**“Spatio-temporal Image Analysis for Longitudinal and Time-Series Image Data,”** In *Proceedings of the Third International Workshop, STIA 2014*, Image Processing, Computer Vision, Pattern Recognition, and Graphics, Vol. 8682, *Springer LNCS*, 2015.

ISBN: 978-3-319-14905-9

This book constitutes the thoroughly refereed post-conference proceedings of the Third

International Workshop on Spatio-temporal Image Analysis for Longitudinal and Time-

Series Image Data, STIA 2014, held in conjunction with MICCAI 2014 in Boston, MA, USA, in

September 2014.

The 7 papers presented in this volume were carefully reviewed and selected from 15

submissions. They are organized in topical sections named: longitudinal registration and

shape modeling, longitudinal modeling, reconstruction from longitudinal data, and 4D

image processing.

SCI Institute.
Note: *FluoRender: An interactive rendering tool for confocal microscopy data visualization. Scientific Computing and Imaging Institute (SCI) Download from: http://www.fluorender.org*, 2015.

Note: *FusionView: Problem Solving Environment for MHD Visualization. Scientific Computing and Imaging Institute (SCI), Download from: http://www.scirun.org*, 2015.

CIBC.
Note: *ImageVis3D: An interactive visualization software system for large-scale volume data. Scientific Computing and Imaging Institute (SCI), Download from: http://www.imagevis3d.org*, 2015.

CIBC.
Note: *map3d: Interactive scientific visualization tool for bioengineering data. Scientific Computing and Imaging Institute (SCI), Download from: http://www.sci.utah.edu/cibc/software.html*, 2015.

SCI Institute.
Note: *NCR Toolset: A collection of software tools for the reconstruction and visualization of neural circuitry from electron microscopy data. Scientific Computing and Imaging Institute (SCI). Download from: http://www.sci.utah.edu/software.html*, 2015.

Note: *Scientific Computing and Imaging Institute (SCI), University of Utah, www.sci.utah.edu*, 2015.

SCI Institute.
Note: *SCIRun: A Scientific Computing Problem Solving Environment, Scientific Computing and Imaging Institute (SCI), Download from: http://www.scirun.org*, 2015.

CIBC.
Note: *Seg3D: Volumetric Image Segmentation and Visualization. Scientific Computing and Imaging Institute (SCI), Download from: http://www.seg3d.org*, 2015.

SCI Institute.
Note: *ShapeWorks: An open-source tool for constructing compact statistical point-based models of ensembles of similar shapes that does not rely on specific surface parameterization. Scientific Computing and Imaging Institute (SCI). Download from: http://www.sci.utah.edu/software/shapeworks.html*, 2015.

SLASH.
Note: *SLASH: A hybrid system for high-throughput segmentation of large neuropil datasets, SLASH is funded by the National Institute of Neurological Disorders and Stroke (NINDS) grant 5R01NS075314-03.*, 2015.

Note: *VisTrails: A scientific workflow management system. Scientific Computing and Imaging Institute (SCI), Download from: http://www.vistrails.org*, 2015.

2014

G. Adluru, Y. Gur, J. Anderson, L. Richards, N. Adluru, E. DiBella.
**“Assessment of white matter microstructure in stroke patients using NODDI,”** In *Proceedings of the 2014 IEEE Int. Conf. Engineering and Biology Society (EMBC)*, 2014.

Diffusion weighted imaging (DWI) is widely used to study changes in white matter following stroke. In various studies employing diffusion tensor imaging (DTI) and high angular resolution diffusion imaging (HARDI) modalities, it has been shown that fractional anisotropy (FA), mean diffusivity (MD), and generalized FA (GFA) can be used as measures of white matter tract integrity in stroke patients. However, these measures may be non-specific, as they do not directly delineate changes in tissue microstructure. Multi-compartment models overcome this limitation by modeling DWI data using a set of indices that are directly related to white matter microstructure. One of these models which is gaining popularity, is neurite orientation dispersion and density imaging (NODDI). This model uses conventional single or multi-shell HARDI data to describe fiber orientation dispersion as well as densities of different tissue types in the imaging voxel. In this paper, we apply for the first time the NODDI model to 4-shell HARDI stroke data. By computing NODDI indices over the entire brain in two stroke patients, and comparing tissue regions in ipsilesional and contralesional hemispheres, we demonstrate that NODDI modeling provides specific information on tissue microstructural changes. We also introduce an information theoretic analysis framework to investigate the non-local effects of stroke in the white matter. Our initial results suggest that the NODDI indices might be more specific markers of white matter reorganization following stroke than other measures previously used in studies of stroke recovery.

S.P. Awate, R.T. Whitaker.
**“Multiatlas Segmentation as Nonparametric Regression,”** In *IEEE Trans Med Imaging*, April, 2014.

PubMed ID: 24802528

This paper proposes a novel theoretical framework to model and analyze the statistical characteristics of a wide range of segmentation methods that incorporate a database of label maps or atlases; such methods are termed as label fusion or multiatlas segmentation. We model these multiatlas segmentation problems as nonparametric regression problems in the high-dimensional space of image patches. We analyze the nonparametric estimator's convergence behavior that characterizes expected segmentation error as a function of the size of the multiatlas database. We show that this error has an analytic form involving several parameters that are fundamental to the specific segmentation problem (determined by the chosen anatomical structure, imaging modality, registration algorithm, and labelfusion algorithm). We describe how to estimate these parameters and show that several human anatomical structures exhibit the trends modeled analytically. We use these parameter estimates to optimize the regression estimator. We show that the expected error for large database sizes is well predicted by models learned on small databases. Thus, a few expert segmentations can help predict the database sizes required to keep the expected error below a specified tolerance level. Such cost-benefit analysis is crucial for deploying clinical multiatlas segmentation systems.

S.P. Awate, Y.-Y. Yu, R.T. Whitaker.
**“Kernel Principal Geodesic Analysis,”** In *Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD)*, Springer LNAI, 2014.

Kernel principal component analysis (kPCA) has been proposed as a dimensionality-reduction technique that achieves nonlinear, low-dimensional representations of data via the mapping to kernel feature space. Conventionally, kPCA relies on Euclidean statistics in kernel feature space. However, Euclidean analysis can make kPCA inefficient or incorrect for many popular kernels that map input points to a hypersphere in kernel feature space. To address this problem, this paper proposes a novel adaptation of kPCA, namely kernel principal geodesic analysis (kPGA), for hyperspherical statistical analysis in kernel feature space. This paper proposes tools for statistical analyses on the Riemannian manifold of the Hilbert sphere in the reproducing kernel Hilbert space, including algorithms for computing the sample weighted Karcher mean and eigen analysis of the sample weighted Karcher covariance. It then applies these tools to propose novel methods for (i)~dimensionality reduction and (ii)~clustering using mixture-model fitting. The results, on simulated and real-world data, show that kPGA-based methods perform favorably relative to their kPCA-based analogs.

H. Bhatia, V. Pascucci, R.M. Kirby, P.-T. Bremer.
**“Extracting Features from Time-Dependent Vector Fields Using Internal Reference Frames,”** In *Computer Graphics Forum*, Vol. 33, No. 3, pp. 21--30. June, 2014.

DOI: 10.1111/cgf.12358

Extracting features from complex, time-dependent flow fields remains a significant challenge despite substantial research efforts, especially because most flow features of interest are defined with respect to a given reference frame. Pathline-based techniques, such as the FTLE field, are complex to implement and resource intensive, whereas scalar transforms, such as λ

This paper introduces a new data-driven technique to compute internal reference frames for large-scale complex flows. More general than uniformly moving frames, these frames can transform unsteady fields, which otherwise require substantial processing of resources, into a sequence of individual snapshots that can be analyzed using the large body of steady-flow analysis techniques. Our approach is simple, theoretically well-founded, and uses an embarrassingly parallel algorithm for structured as well as unstructured data. Using several case studies from fluid flow and turbulent combustion, we demonstrate that internal frames are distinguished, result in temporally coherent structures, and can extract well-known as well as notoriously elusive features one snapshot at a time.

H. Bhatia, A. Gyulassy, H. Wang, P.-T. Bremer, V. Pascucci .
**“Robust Detection of Singularities in Vector Fields,”** In *Topological Methods in Data Analysis and Visualization III*, Mathematics and Visualization, Springer International Publishing, pp. 3--18. March, 2014.

DOI: 10.1007/978-3-319-04099-8_1

Recent advances in computational science enable the creation of massive datasets of ever increasing resolution and complexity. Dealing effectively with such data requires new analysis techniques that are provably robust and that generate reproducible results on any machine. In this context, combinatorial methods become particularly attractive, as they are not sensitive to numerical instabilities or the details of a particular implementation. We introduce a robust method for detecting singularities in vector fields. We establish, in combinatorial terms, necessary and sufficient conditions for the existence of a critical point in a cell of a simplicial mesh for a large class of interpolation functions. These conditions are entirely local and lead to a provably consistent and practical algorithm to identify cells containing singularities.