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Shape modeling and analysis with entropybased particle systems
 In Proceedings of the 20th International Conference on Information Processing in Medical Imaging
, 2007
"... Many important fields of basic research in medicine and biology routinely employ tools for the statistical analysis of collections of similar shapes. Biologists, for example, have long relied on homologous, anatomical landmarks as shape models to characterize the growth and development of species. I ..."
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Cited by 27 (14 self)
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Many important fields of basic research in medicine and biology routinely employ tools for the statistical analysis of collections of similar shapes. Biologists, for example, have long relied on homologous, anatomical landmarks as shape models to characterize the growth and development of species. Increasingly, however, researchers are exploring the use of more detailed models that are derived computationally from threedimensional images and surface descriptions. While computationallyderived models of shape are promising new tools for biomedical research, they also present some significant engineering challenges, which existing modeling methods have only begun to address. In this dissertation, I propose a new computational framework for statistical shape modeling that significantly advances the stateoftheart by overcoming many of the limitations of existing methods. The framework uses a particlesystem representation of shape, with a fast correspondencepoint optimization based on information content. The optimization balances the simplicity of the model (compactness) with the accuracy of the shape representations by using two commensurate entropy
Topology, accuracy, and quality of isosurface meshes using dynamic particles
 IEEE Transactions on Visualization and Computer Graphics
, 2007
"... This paper describes a method for constructing isosurface triangulations of sampled, volumetric, threedimensional scalar fields. The resulting meshes consist of triangles that are of consistently high quality, making them well suited for accurate interpolation of scalar and vectorvalued quantities ..."
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Cited by 15 (3 self)
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This paper describes a method for constructing isosurface triangulations of sampled, volumetric, threedimensional scalar fields. The resulting meshes consist of triangles that are of consistently high quality, making them well suited for accurate interpolation of scalar and vectorvalued quantities, as required for numerous applications in visualization and numerical simulation. The proposed method does not rely on a local construction or adjustment of triangles as is done, for instance, in advancing wavefront or adaptive refinement methods. Instead, a system of dynamic particles optimally samples an implicit function such that the particles ’ relative positions can produce a topologically correct Delaunay triangulation. Thus, the proposed method relies on a global placement of triangle vertices. The main contributions of the paper are the integration of dynamic particles systems with surface sampling theory and PDEbased methods for controlling the local variability of particle densities, as well as detailing a practical method that accommodates Delaunay sampling requirements to generate sparse sets of points for the production of highquality tessellations. Index Terms—Isosurface extraction, particle systems, Delaunay triangulation.
Interactive highquality visualization of higherorder finite elements
 Computer Graphics Forum
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GPUbased interactive cutsurface extraction from highorder finite element fields
 IEEE Transactions on Visualization and Computer Graphics
, 2011
"... This Article is brought to you for free and open access by the Space Dynamics Lab at ..."
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Cited by 6 (2 self)
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This Article is brought to you for free and open access by the Space Dynamics Lab at
COMBA J.: Efficient parallel vectors feature extraction from higherorder data
 CGF
"... The parallel vectors (PV) operator is a feature extraction approach for defining linetype features such as creases (ridges and valleys) in scalar fields, as well as separation, attachment, and vortex core lines in vector fields. In this work, we extend PV feature extraction to higherorder data rep ..."
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Cited by 5 (2 self)
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The parallel vectors (PV) operator is a feature extraction approach for defining linetype features such as creases (ridges and valleys) in scalar fields, as well as separation, attachment, and vortex core lines in vector fields. In this work, we extend PV feature extraction to higherorder data represented by piecewise analytical functions defined over grid cells. The extraction uses PV in two distinct stages. First, seed points on the feature lines are placed by evaluating the inclusion form of the PV criterion with reduced affine arithmetic. Second, a feature flow field is derived from the higherorder PV expression where the features can be extracted as streamlines starting at the seeds. Our approach allows for guaranteed bounds regarding accuracy with respect to existence, position, and topology of the features obtained. The method is suitable for parallel implementation and we present results obtained with our GPUbased prototype. We apply our method to higherorder data obtained from discontinuous Galerkin fluid simulations. Categories and Subject Descriptors (according to ACM CCS): Generation—Line and curve generation
Interactive Isocontouring of HighOrder Surfaces
"... Scientists and engineers are making increasingly use of hpadaptive discretization methods to compute simulations. While techniques for isocontouring the highorder data generated by these methods have started to appear, they typically do not facilitate interactive data exploration. This work presen ..."
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Cited by 5 (5 self)
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Scientists and engineers are making increasingly use of hpadaptive discretization methods to compute simulations. While techniques for isocontouring the highorder data generated by these methods have started to appear, they typically do not facilitate interactive data exploration. This work presents a novel interactive approach for approximate isocontouring of highorder data. The method is based on a twophase hybrid rendering algorithm. In the first phase, coarsely seeded particles are guided by the gradient of the field for obtaining an initial sampling of the isosurface in object space. The second phase performs ray casting in the image space neighborhood of the initial samples. Since the neighborhood is small, the initial guesses tend to be close to the isosurface, leading to accelerated root finding and thus efficient rendering. The object space phase affects the density of the coarse samples on the isosurface, which can lead to holes in the final rendering and overdraw. Thus, we also propose a heuristic, based on dynamical systems theory, that adapts the neighborhood of the seeds in order to obtain a better coverage of the surface. Results for datasets from computational fluid dynamics are shown and performance measurements for our GPU implementation are given.
GlyphBased SPECT Visualization for the Diagnosis of Coronary Artery Disease
"... Abstract—Myocardial perfusion imaging with single photon emission computed tomography (SPECT) is an established method for the detection and evaluation of coronary artery disease (CAD). Stateoftheart SPECT scanners yield a large number of regional parameters of the leftventricular myocardium (e. ..."
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Abstract—Myocardial perfusion imaging with single photon emission computed tomography (SPECT) is an established method for the detection and evaluation of coronary artery disease (CAD). Stateoftheart SPECT scanners yield a large number of regional parameters of the leftventricular myocardium (e.g., blood supply at rest and during stress, wall thickness, and wall thickening during heart contraction) that all need to be assessed by the physician. Today, the individual parameters of this multivariate data set are displayed as stacks of 2D slices, bull’s eye plots, or, more recently, surfaces in 3D, which depict the leftventricular wall. In all these visualizations, the data sets are displayed sidebyside rather than in an integrated manner, such that the multivariate data have to be examined sequentially and need to be fused mentally. This is time consuming and errorprone. In this paper we present an interactive 3D glyph visualization, which enables an effective integrated visualization of the multivariate data. Results from semiotic theory are used to optimize the mapping of different variables to glyph properties. This facilitates an improved perception of important information and thus an accelerated diagnosis. The 3D glyphs are linked to the established 2D views, which permit a more detailed inspection, and to relevant metainformation such as known stenoses of coronary vessels supplying the myocardial region. Our method has demonstrated its potential for clinical routine use in real application scenarios assessed by nuclear physicians. Index Terms—Multivariate visualization, glyph techniques, SPECT, myocardial perfusion imaging. 1
Coherencybased curve compression for highorder finite element model visualization
 IEEE Transactions on Visualization and Computer Graphics
, 2012
"... Fig. 1. Application of our visualization approach to a multiparametric FE model of the left ventricle of a human heart. The images show volumetric renderings of different strain directions defined over the FE model: radial strain, circumferential strain, longitudinal strain as well as the three for ..."
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Fig. 1. Application of our visualization approach to a multiparametric FE model of the left ventricle of a human heart. The images show volumetric renderings of different strain directions defined over the FE model: radial strain, circumferential strain, longitudinal strain as well as the three former combined (left to right). The presented approach allows for interactive data exploration by changing the transfer function and other relevant rendering parameters. Abstract—Finite element (FE) models are frequently used in engineering and life sciences within timeconsuming simulations. In contrast with the regular grid structure facilitated by volumetric data sets, as used in medicine or geosciences, FE models are defined over a nonuniform grid. Elements can have curved faces and their interior can be defined through highorder basis functions, which pose additional challenges when visualizing these models. During raycasting, the uniformly distributed sample points along each viewing ray must be transformed into the material space defined within each element. The computational complexity of this transformation makes a straightforward approach inadequate for interactive data exploration. In this paper, we introduce a novel coherencybased method which supports the interactive exploration of FE models by decoupling the expensive worldtomaterial space transformation from the rendering stage, thereby allowing it to be performed within a precomputation stage. Therefore, our approach computes viewindependent proxy rays in material space, which are clustered to facilitate data reduction. During rendering, these proxy rays are accessed, and it becomes possible to visually analyze highorder FE models at interactive frame rates, even when they are timevarying or consist of multiple modalities. Within this paper, we provide the necessary background about the FE data, describe our decoupling method, and introduce our interactive rendering algorithm. Furthermore, we provide visual results and analyze the error introduced by the presented approach. Index Terms—Finite element visualization, GPUbased raycasting.
ElVis: A System for the Accurate and Interactive Visualization of HighOrder Finite Element Solutions
"... contour lines on curved and planar surfaces. Abstract—This paper presents the Element Visualizer (ElVis), a new, opensource scientific visualization system for use with highorder finite element solutions to PDEs in three dimensions. This system is designed to minimize visualization errors of these ..."
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contour lines on curved and planar surfaces. Abstract—This paper presents the Element Visualizer (ElVis), a new, opensource scientific visualization system for use with highorder finite element solutions to PDEs in three dimensions. This system is designed to minimize visualization errors of these types of fields by querying the underlying finite element basis functions (e.g., highorder polynomials) directly, leading to pixelexact representations of solutions and geometry. The system interacts with simulation data through runtime plugins, which only require users to implement a handful of operations fundamental to finite element solvers. The data in turn can be visualized through the use of cut surfaces, contours, isosurfaces, and volume rendering. These visualization algorithms are implemented using NVIDIA’s OptiX GPUbased raytracing engine, which provides accelerated ray traversal of the highorder geometry, and CUDA, which allows for effective parallel evaluation of the visualization algorithms. The direct interface between ElVis and the underlying data differentiates it from existing visualization tools. Current tools assume the underlying data is composed of linear primitives; highorder data must be interpolated with linear functions as a result. In this work, examples drawn from aerodynamic simulations–highorder discontinuous Galerkin finite element solutions of aerodynamic flows in particular–will demonstrate the superiority of ElVis ’ pixelexact approach when compared with traditional linearinterpolation methods. Such methods can introduce a number of inaccuracies in the resulting visualization, making it unclear if visual artifacts are genuine to the solution data or if these artifacts are the result of interpolation errors. Linear methods additionally cannot properly visualize curved geometries (elements or boundaries) which can greatly inhibit
Submitted to the IEEE Visualization Conference. ElVis: A System for the Accurate and Interactive Visualization of HighOrder Finite Element Solutions
"... contour lines on curved and planar surfaces. Abstract — This paper presents the Element Visualizer (ElVis), a new scientific visualization system for use with highorder finite element solutions to PDEs in three dimensions. This system is designed to minimize visualization errors of these types of f ..."
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contour lines on curved and planar surfaces. Abstract — This paper presents the Element Visualizer (ElVis), a new scientific visualization system for use with highorder finite element solutions to PDEs in three dimensions. This system is designed to minimize visualization errors of these types of fields by querying the underlying finite element basis functions (e.g., highorder polynomials) directly, leading to pixelexact representations of solutions and geometry. The system interacts with simulation data through runtime plugins, which only require users to implement a handful of operations fundamental to finite element solvers. The data in turn can be visualized through the use of cut surfaces, contours, isosurfaces, and volume rendering. These visualization algorithms are implemented using NVIDIA’s OptiX GPUbased raytracing engine, which provides accelerated ray traversal of the highorder geometry, and CUDA, which allows for effective parallel evaluation of the visualization algorithms. The direct interface between ElVis and the underlying data differentiates it from existing visualization tools. Current tools assume the underlying data is composed of linear primitives; highorder data must be interpolated with linear functions as a result. In this work, examples drawn from aerodynamic simulations–highorder discontinuous Galerkin finite element solutions of aerodynamic flows in particular–will demonstrate the superiority of ElVis ’ pixelexact approach when compared with traditional linearinterpolation methods. Such methods can introduce a number of inaccuracies in the resulting visualization, making it unclear if visual artifacts are genuine to the solution data or if these artifacts are the result of interpolation errors. Linear methods additionally cannot properly visualize curved geometries (elements or boundaries) which can greatly inhibit developers’