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158
Visibility histograms and visibilitydriven transfer functions
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2011
"... Direct volume rendering is an important tool for visualizing complex data sets. However, in the process of generating 2D images from 3D data, information is lost in the form of attenuation and occlusion. The lack of a feedback mechanism to quantify the loss of information in the rendering process m ..."
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Cited by 18 (1 self)
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Direct volume rendering is an important tool for visualizing complex data sets. However, in the process of generating 2D images from 3D data, information is lost in the form of attenuation and occlusion. The lack of a feedback mechanism to quantify the loss of information in the rendering process makes the design of good transfer functions a difficult and time consuming task. In this paper, we present the general notion of visibility histograms, which are multidimensional graphical representations of the distribution of visibility in a volumerendered image. In this paper, we explore the 1D and 2D transfer functions that result from intensity values and gradient magnitude. With the help of these histograms, users can manage a complex set of transfer function parameters that maximize the visibility of the intervals of interest and provide high quality images of volume data. We present a semiautomated method for generating transfer functions, which progressively explores the transfer function space towards the goal of maximizing visibility of important structures. Our methodology can be easily deployed in most visualization systems and can be used together with traditional 1D and 2D opacity transfer functions based on scalar values, as well as with other more sophisticated rendering algorithms.
Topological manipulation of isosurfaces
, 2004
"... In this thesis, I show how to use the topological information encoded in an abstraction called the contour tree to enable interactive manipulation of individual contour surfaces in an isosurface scene, using an interface called the flexible isosurface. Underpinning this interface are several improve ..."
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Cited by 18 (3 self)
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In this thesis, I show how to use the topological information encoded in an abstraction called the contour tree to enable interactive manipulation of individual contour surfaces in an isosurface scene, using an interface called the flexible isosurface. Underpinning this interface are several improvements and extensions to existing work on the contour tree. The first, and most critical, extension, is the path seed: a new method of generating seeds from the contour tree for isosurface extraction. The second extension is to compute geometric information called local spatial measures for contours and store this information in the contour tree. The third extension is to use local spatial measures to simplify both the contour tree and isosurface displays. This simplification can also be used for noise removal. Lastly, this thesis extends work with contour trees from simplicial meshes to arbitrary meshes, interpolants, and tessellation cases. ii Contents ii
Volume MLS ray casting
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2008
"... The method of Moving Least Squares (MLS) is a popular framework for reconstructing continuous functions from scattered data due to its rich mathematical properties and wellunderstood theoretical foundations. This paper applies MLS to volume rendering, providing a unified mathematical framework fo ..."
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Cited by 18 (1 self)
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The method of Moving Least Squares (MLS) is a popular framework for reconstructing continuous functions from scattered data due to its rich mathematical properties and wellunderstood theoretical foundations. This paper applies MLS to volume rendering, providing a unified mathematical framework for ray casting of scalar data stored over regular as well as irregular grids. We use the MLS reconstruction to render smooth isosurfaces and to compute accurate derivatives for highquality shading effects. We also present a novel, adaptive preintegration scheme to improve the efficiency of the ray casting algorithm by reducing the overall number of function evaluations, and an efficient implementation of our framework exploiting modern graphics hardware. The resulting system enables highquality volume integration and shaded isosurface rendering for regular and irregular volume data.
D.: Structuring feature space: A nonparametric method for volumetric transfer function generation
 IEEE Trans. Vis. Comput. Graph
"... Fig. 1. An application of nonparametric clustering to the value vs. value gradient magnitude feature space using the CT visible woman feet dataset. Abstract — The use of multidimensional transfer functions for direct volume rendering has been shown to be an effective means of extracting materials ..."
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Cited by 17 (4 self)
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Fig. 1. An application of nonparametric clustering to the value vs. value gradient magnitude feature space using the CT visible woman feet dataset. Abstract — The use of multidimensional transfer functions for direct volume rendering has been shown to be an effective means of extracting materials and their boundaries for both scalar and multivariate data. The most common multidimensional transfer function consists of a twodimensional (2D) histogram with axes representing a subset of the feature space (e.g., value vs. value gradient magnitude), with each entry in the 2D histogram being the number of voxels at a given feature space pair. Users then assign color and opacity to the voxel distributions within the given feature space through the use of interactive widgets (e.g., box, circular, triangular selection). Unfortunately, such tools lead users through a trialanderror approach as they assess which data values within the feature space map to a given area of interest within the volumetric space. In this work, we propose the addition of nonparametric clustering within the transfer function feature space in order to extract patterns and guide transfer function generation. We apply a nonparametric kernel density estimation to group voxels of similar features within the 2D histogram. These groups are then binned and colored based on their estimated density, and the user may interactively grow and shrink the binned regions to explore feature boundaries and extract regions of interest. We also extend this scheme to temporal volumetric data in which time steps of 2D histograms are composited into a histogram volume. A threedimensional (3D) density estimation is then applied, and users can explore regions within the feature space across time without adjusting the transfer function at each time step. Our work
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.
IRIS: Illustrative Rendering for Integral Surfaces
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2010
"... Integral surfaces are ideal tools to illustrate vector fields and fluid flow structures. However, these surfaces can be visually complex and exhibit difficult geometric properties, owing to strong stretching, shearing and folding of the flow from which they are derived. Many techniques for nonphot ..."
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Cited by 16 (1 self)
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Integral surfaces are ideal tools to illustrate vector fields and fluid flow structures. However, these surfaces can be visually complex and exhibit difficult geometric properties, owing to strong stretching, shearing and folding of the flow from which they are derived. Many techniques for nonphotorealistic rendering have been presented previously. It is, however, unclear how these techniques can be applied to integral surfaces. In this paper, we examine how transparency and texturing techniques can be used with integral surfaces to convey both shape and directional information. We present a rendering pipeline that combines these techniques aimed at faithfully and accurately representing integral surfaces while improving visualization insight. The presented pipeline is implemented directly on the GPU, providing realtime interaction for all rendering modes, and does not require expensive preprocessing of integral surfaces after computation.
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.
Dynamic view selection for timevarying volumes
 IEEE Trans. Vis. Comput. Graph
"... Abstract—Animation is an effective way to show how timevarying phenomena evolve over time. A key issue of generating a good animation is to select ideal views through which the user can perceive the maximum amount of information from the timevarying dataset. In this paper, we first propose an impr ..."
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Cited by 13 (3 self)
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Abstract—Animation is an effective way to show how timevarying phenomena evolve over time. A key issue of generating a good animation is to select ideal views through which the user can perceive the maximum amount of information from the timevarying dataset. In this paper, we first propose an improved view selection method for static data. The method measures the quality of a static view by analyzing the opacity, color and curvature distributions of the corresponding volume rendering images from the given view. Our view selection metric prefers an even opacity distribution with a larger projection area, a larger area of salient features ’ colors with an even distribution among the salient features, and more perceived curvatures. We use this static view selection method and a dynamic programming approach to select timevarying views. The timevarying view selection maximizes the information perceived from the timevarying dataset based on the constraints that the timevarying view should show smooth changes of direction and nearconstant speed. We also introduce a method that allows the user to generate a smooth transition between any two views in a given time step, with the perceived information maximized as well. By combining the static and dynamic view selection methods, the users are able to generate a timevarying view that shows the maximum amount of information from a timevarying data set. Index Terms—Static view selection, image based method, dynamic view selection, information entropy, optimization.
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.
Hierarchical Streamline Bundles
, 2012
"... Effective threedimensional streamline placement and visualization plays an essential role in many science and engineering disciplines. The main challenge for effective streamline visualization lies in seed placement, i.e., where to drop seeds and how many seeds should be placed. Seeding too many o ..."
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Cited by 12 (2 self)
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Effective threedimensional streamline placement and visualization plays an essential role in many science and engineering disciplines. The main challenge for effective streamline visualization lies in seed placement, i.e., where to drop seeds and how many seeds should be placed. Seeding too many or too few streamlines may not reveal flow features and patterns either because it easily leads to visual clutter in rendering or it conveys little information about the flow field. Not only does the number of streamlines placed matter, their spatial relationships also play a key role in understanding the flow field. Therefore, effective flow visualization requires the streamlines to be placed in the right place and in the right amount. This paper introduces hierarchical streamline bundles, a novel approach to simplifying and visualizing 3D flow fields defined on regular grids. By placing seeds and generating streamlines according to flow saliency, we produce a set of streamlines that captures important flow features near critical points without enforcing the dense seeding condition. We group spatially neighboring and geometrically similar streamlines to construct a hierarchy from which we extract streamline bundles at different levels of detail. Streamline bundles highlight multiscale flow features and patterns through clustered yet not cluttered display. This selective visualization strategy effectively reduces visual clutter while accentuating visual foci, and therefore is able to convey the desired insight into the flow data.