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39
Diffusion tensor visualization with glyph packing
 Visualization and Computer Graphics, IEEE Transactions on
"... Abstract—A common goal of multivariate visualization is to enable data inspection at discrete points, while also illustrating largerscale continuous structures. In diffusion tensor visualization, glyphs are typically used to meet the first goal, and methods such as texture synthesis or fiber tracto ..."
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Cited by 30 (2 self)
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Abstract—A common goal of multivariate visualization is to enable data inspection at discrete points, while also illustrating largerscale continuous structures. In diffusion tensor visualization, glyphs are typically used to meet the first goal, and methods such as texture synthesis or fiber tractography can address the second. We adapt particle systems originally developed for surface modeling and anisotropic mesh generation to enhance the utility of glyphbased tensor visualizations. By carefully distributing glyphs throughout the field (either on a slice, or in the volume) into a dense packing, using potential energy profiles shaped by the local tensor value, we remove undue visual emphasis of the regular sampling grid of the data, and the underlying continuous features become more apparent. The method is demonstrated on a DTMRI scan of a patient with a brain tumor. Index Terms—Diffusion tensor, glyphs, particle systems, anisotropic sampling, fiber tractography. F 1
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
Entropybased particle systems for shape correspondence
 In proc. of MICCAI Workshop Mathematical Foundations of Computational Anatomy
, 2006
"... Abstract. This paper presents a new method for constructing statistical representations of ensembles of similar shapes. The proposed method relies on an optimal distribution of a large set of surface point correspondences, rather than the manipulation of a specific surface parameterization. The opti ..."
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Cited by 18 (3 self)
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Abstract. This paper presents a new method for constructing statistical representations of ensembles of similar shapes. The proposed method relies on an optimal distribution of a large set of surface point correspondences, rather than the manipulation of a specific surface parameterization. The optimal configuration is defined as one in which the entropy or information content of each shape is balanced against the entropy of the ensemble of shapes. The correspondences are modeled as sets of dynamic particles that are manipulated using a gradient descent on the entropies of the shapes and the ensemble, but constrained to lie on a set of implicit surfaces. The proposed, particlebased method for finding correspondences requires very little preprocessing of data or parameter tuning, and therefore makes the problem of shape analysis more practical for a wider range of problems. This paper presents the formulation and several synthetic and real shape examples in two and three dimensions. 1
Particle systems for efficient and accurate highorder finite element visualization
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS (UNDER REVIEW
, 2007
"... Visualization has become an important component of the simulation pipeline, providing scientists and engineers a visual intuition of their models. Simulations that make use of the highorder finite element method for spatial subdivision, however, present a challenge to conventional isosurface visua ..."
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Cited by 17 (4 self)
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Visualization has become an important component of the simulation pipeline, providing scientists and engineers a visual intuition of their models. Simulations that make use of the highorder finite element method for spatial subdivision, however, present a challenge to conventional isosurface visualization techniques. Highorder finite element isosurfaces are often defined by basis functions in reference space, which give rise to a worldspace solution through a coordinate transformation, which does not necessarily have a closedform inverse. Therefore, worldspace isosurface rendering methods such as marching cubes and ray tracing must perform a nested root finding, which is computationally expensive. We thus propose visualizing these isosurfaces with a particle system. We present a framework that allows particles to sample an isosurface in reference space, avoiding the costly inverse mapping of positions from world space when evaluating the basis functions. The distribution of particles across the reference space isosurface is controlled by geometric information from the worldspace isosurface such as the surface gradient and curvature. The resulting particle distributions can be distributed evenly or adapted to accommodate worldspace surface features. This provides compact, efficient, and accurate isosurface representations of these challenging data sets.
Fast Ray Tracing of Arbitrary Implicit Surfaces with Interval and Affine Arithmetic
"... Existing techniques for rendering arbitraryform implicit surfaces are limited, either in performance, correctness or flexibility. Ray tracing algorithms employing interval arithmetic (IA) or affine arithmetic (AA) for rootfinding are robust and general in the class of surfaces they support, but tr ..."
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Cited by 16 (4 self)
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Existing techniques for rendering arbitraryform implicit surfaces are limited, either in performance, correctness or flexibility. Ray tracing algorithms employing interval arithmetic (IA) or affine arithmetic (AA) for rootfinding are robust and general in the class of surfaces they support, but traditionally slow. Nonetheless, implemented efficiently using a stackdriven iterative algorithm and SIMD vector instructions, these methods can achieve interactive performance for common algebraic surfaces on the CPU. A similar algorithm can also be implemented stacklessly, allowing for efficient ray tracing on the GPU. This paper presents these algorithms, as well as an inclusionpreserving reduced affine arithmetic (RAA) for faster raysurface intersection. Shader metaprogramming allows for immediate and automatic generation of symbolic expressions and their interval or affine extensions. Moreover, we are able to render even complex forms robustly, in realtime at high resolution.
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.
Particlebased Sampling and Meshing of Surfaces in Multimaterial Volumes
"... Abstract — Methods that faithfully and robustly capture the geometry of complex material interfaces in labeled volume data are important for generating realistic and accurate visualizations and simulations of realworld objects. The generation of such multimaterial models from measured data poses tw ..."
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Cited by 13 (1 self)
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Abstract — Methods that faithfully and robustly capture the geometry of complex material interfaces in labeled volume data are important for generating realistic and accurate visualizations and simulations of realworld objects. The generation of such multimaterial models from measured data poses two unique challenges: first, the surfaces must be wellsampled with regular, efficient tessellations that are consistent across material boundaries; and second, the resulting meshes must respect the nonmanifold geometry of the multimaterial interfaces. This paper proposes a strategy for sampling and meshing multimaterial volumes using dynamic particle systems, including a novel, differentiable representation of the material junctions that allows the particle system to explicitly sample corners, edges, and surfaces of material intersections. The distributions of particles are controlled by fundamental sampling constraints, allowing Delaunaybased meshing algorithms to reliably extract watertight meshes of consistently highquality. Index Terms—Sampling, meshing, visualizations. 1
Superquadric glyphs for symmetric secondorder tensors
 IEEE Transactions on Visualization and Computer Graphics
"... Abstract—Symmetric secondorder tensor fields play a central role in scientific and biomedical studies as well as in image analysis and featureextraction methods. The utility of displaying tensor field samples has driven the development of visualization techniques that encode the tensor shape and o ..."
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Cited by 12 (4 self)
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Abstract—Symmetric secondorder tensor fields play a central role in scientific and biomedical studies as well as in image analysis and featureextraction methods. The utility of displaying tensor field samples has driven the development of visualization techniques that encode the tensor shape and orientation into the geometry of a tensor glyph. With some exceptions, these methods work only for positivedefinite tensors (i.e. having positive eigenvalues, such as diffusion tensors). We expand the scope of tensor glyphs to all symmetric secondorder tensors in two and three dimensions, gracefully and unambiguously depicting any combination of positive and negative eigenvalues. We generalize a previous method of superquadric glyphs for positivedefinite tensors by drawing upon a larger portion of the superquadric shape space, supplemented with a coloring that indicates the tensor’s quadratic form. We show that encoding arbitrary eigenvalue sign combinations requires design choices that differ fundamentally from those in previous work on traceless tensors (arising in the study of liquid crystals). Our method starts with a design of 2D tensor glyphs guided by principles of symmetry and continuity, and creates 3D glyphs that include the 2D glyphs in their axisaligned crosssections. A key ingredient of our method is a novel way of mapping from the shape space of threedimensional symmetric secondorder tensors to the unit square. We apply our new glyphs to stress tensors from mechanics, geometry tensors and Hessians from image analysis, and rateofdeformation tensors in computational fluid dynamics.
Sketching, Scaffolding, and Inking: A Visual History for Interactive 3D Modeling
 PROCEEDINGS OF THE FIFTH INTERNATIONAL SYMPOSIUM ON NONPHOTOREALISTIC ANIMATION AND RENDERING (NPAR 2007, AUGUST 4–5, 2007, SAN DIEGO, CALIFORNIA, USA)
, 2007
"... Inspired by the comicbook production pipeline, a method is proposed for integrating visual aspects of the sketching process into 3D sketchbased modeling systems. In particular, artistdrawn construction aids called visual scaffolding are explored. Two scaffolding components which simulate elements ..."
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Cited by 11 (4 self)
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Inspired by the comicbook production pipeline, a method is proposed for integrating visual aspects of the sketching process into 3D sketchbased modeling systems. In particular, artistdrawn construction aids called visual scaffolding are explored. Two scaffolding components which simulate elements of pencil sketching, geometric massing and eraser marks, are integrated into a rendering pipeline which also includes a suite of new objectspace techniques for highfidelity penandink depiction of implicit surfaces. Based on a hybrid, hierarchical approach which leverages both the implicit surface definition and an underlying coarse tessellation, new methods are described for computing silhouettes, suggestive contours, surface stippling, and surfelbased visibility culling. These techniques are realtime but require no precomputation, allowing them to be applied to dynamic hierarchical implicit surfaces, and are demonstrated in ShapeShop, an interactive sketchbased modeling tool. The result is a realtime display pipeline which composites these novel scaffolding and penandink techniques to depict a visual history of the modeling process.
Fast sampling of implicit surfaces by particle systems
 In Proceedings of Shape Modeling International
, 2006
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