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Visualization and Computer Graphics, IEEE Transactions on

Issue 5 • Date Sept.-Oct. 2004

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Displaying Results 1 - 16 of 16
  • [Front cover]

    Publication Year: 2004 , Page(s): c1
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  • [Inside front cover]

    Publication Year: 2004 , Page(s): c2
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  • Guest Editor's Introduction: Special Section on Mathematics and Visualization

    Publication Year: 2004 , Page(s): 497 - 498
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  • Applications of Forman's discrete Morse theory to topology visualization and mesh compression

    Publication Year: 2004 , Page(s): 499 - 508
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1559 KB) |  | HTML iconHTML  

    Morse theory is a powerful tool for investigating the topology of smooth manifolds. It has been widely used by the computational topology, computer graphics, and geometric modeling communities to devise topology-based algorithms and data structures. Forman introduced a discrete version of this theory which is purely combinatorial. We aim to build, visualize, and apply the basic elements of Forman's discrete Morse theory. We intend to use some of those concepts to visually study the topology of an object. As a basis, an algorithmic construction of optimal Forman's discrete gradient vector fields is provided. This construction is then used to topologically analyze mesh compression schemes, such as Edgebreaker and Grow&Fold. In particular, we prove that the complexity class of the strategy optimization of Grow&Fold is MAX-SNP hard. View full abstract»

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  • Visualizing a sphere eversion

    Publication Year: 2004 , Page(s): 509 - 515
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (944 KB) |  | HTML iconHTML  

    The mathematical process of everting a sphere (turning it inside-out allowing self-intersections) is a grand challenge for visualization because of the complicated, ever-changing internal structure. We have computed an optimal minimax eversion, requiring the least bending energy. Here, we discuss techniques we used to help visualize this eversion for visitors to virtual environments and viewers of our video The Optiverse. View full abstract»

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  • Robust feature detection and local classification for surfaces based on moment analysis

    Publication Year: 2004 , Page(s): 516 - 524
    Cited by:  Papers (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1093 KB) |  | HTML iconHTML  

    The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach. View full abstract»

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  • Fast evolution of image manifolds and application to filtering and segmentation in 3D medical images

    Publication Year: 2004 , Page(s): 525 - 535
    Cited by:  Papers (6)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2335 KB)  

    In many instances, numerical integration of space-scale PDEs is the most time consuming operation of image processing. This is because the scale step is limited by conditional stability of explicit schemes. We introduce the unconditionally stable semiimplicit linearized difference scheme that is fashioned after additive operator split (AOS) [Weickert, J. et al. (1998)], [Goldenberg, R et al., (2001)] for Beltrami and the subjective surface computation. The Beltrami flow [Kimmel, R. (1997) (1999)], [Sochen, N. et al. (1998)], is one of the most effective denoising algorithms in image processing. For gray-level images, we show that the flow equation can be arranged in an advection-diffusion form, revealing the edge-enhancing properties of this flow. This also suggests the application of AOS method for faster convergence. The subjective surface [Sarti, A. et al. (2002)] deals with constructing a perceptually meaningful interpretation from partial image data by mimicking the human visual system. However, initialization of the surface is critical for the final result and its main drawbacks are very slow convergence and the huge number of iterations required. We first show that the governing equation for the subjective surface flow can be rearranged in an AOS implementation, providing a near real-time solution to the shape completion problem in 2D and 3D. Then, we devise a new initialization paradigm where we first "condition" the viewpoint surface using the fast-marching algorithm. We compare the original method with our new algorithm on several examples of real 3D medical images, thus revealing the improvement achieved. View full abstract»

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  • Crest lines for surface segmentation and flattening

    Publication Year: 2004 , Page(s): 536 - 544
    Cited by:  Papers (24)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1292 KB) |  | HTML iconHTML  

    We present a method for extracting feature curves called crest lines from a triangulated surface. Then, we calculate the geodesic Voronoi diagram of crest lines to segment the surface into several regions. Afterward, barycentric surface flattening using theory from graph embeddings is implemented and, using the geodesic Voronoi diagram, we develop a faster surface flattening algorithm. View full abstract»

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  • Editor's Note

    Publication Year: 2004 , Page(s): 545 - 547
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  • On a construction of a hierarchy of best linear spline approximations using a finite element approach

    Publication Year: 2004 , Page(s): 548 - 563
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2042 KB) |  | HTML iconHTML  

    We present a method for the hierarchical approximation of functions in one, two, or three variables based on the finite element method (Ritz approximation). Starting with a set of data sites with associated function, we first determine a smooth (scattered-data) interpolant. Next, we construct an initial triangulation by triangulating the region bounded by the minimal subset of data sites defining the convex hull of all sites. We insert only original data sites, thus reducing storage requirements. For each triangulation, we solve a minimization problem: computing the best linear spline approximation of the interpolant of all data, based on a functional involving function values and first derivatives. The error of a best linear spline approximation is computed in a Sobolev-like norm, leading to element-specific error values. We use these interval/triangle/tetrahedron-specific values to identify the element to subdivide next. The subdivision of an element with largest error value requires the recomputation of all spline coefficients due to the global nature of the problem. We improve efficiency by 1) subdividing multiple elements simultaneously and 2) by using a sparse-matrix representation and system solver. View full abstract»

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  • Point-based probabilistic surfaces to show surface uncertainty

    Publication Year: 2004 , Page(s): 564 - 573
    Cited by:  Papers (25)  |  Patents (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1954 KB) |  | HTML iconHTML  

    Efficient and informative visualization of surfaces with uncertainties is an important topic with many applications in science and engineering. In these applications, the correct course of action may depend not only on the location of a boundary, but on the precision with which that location is known. Examples include environmental pollution borderline detection, oil basin edge characterization, or discrimination between cancerous and healthy tissue in medicine. We present a method for producing visualizations of surfaces with uncertainties using points as display primitives. Our approach is to render the surface as a collection of points and to displace each point from its original location along the surface normal by an amount proportional to the uncertainty at that point. This approach can be used in combination with other techniques such as pseudocoloring to produce efficient and revealing visualizations. The basic approach is sufficiently flexible to allow natural extensions; we show incorporation of expressive modulation of opacity, change of the stroke primitive, and addition of an underlying polygonal model. The method is used to visualize real and simulated tumor formations with uncertainty of tumor boundaries. The point-based technique is compared to pseudocoloring for a position estimation task in a preliminary user study. View full abstract»

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  • Haptics-based dynamic implicit solid modeling

    Publication Year: 2004 , Page(s): 574 - 586
    Cited by:  Papers (15)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1635 KB) |  | HTML iconHTML  

    We systematically present a novel, interactive solid modeling framework, haptics-based dynamic implicit solid modeling, which is founded upon volumetric implicit functions and powerful physics-based modeling. In particular, we augment our modeling framework with a haptic mechanism in order to take advantage of additional realism associated with a 3D haptic interface. Our dynamic implicit solids are semialgebraic sets of volumetric implicit functions and are governed by the principles of dynamics, hence responding to sculpting forces in a natural and predictable manner. In order to directly manipulate existing volumetric data sets as well as point clouds, we develop a hierarchical fitting algorithm to reconstruct and represent discrete data sets using our continuous implicit functions, which permit users to further design and edit those existing 3D models in real-time using a large variety of haptic and geometric toolkits, and visualize their interactive deformation at arbitrary resolution. The additional geometric and physical constraints afford more sophisticated control of the dynamic implicit solids. The versatility of our dynamic implicit modeling enables the user to easily modify both the geometry and the topology of modeled objects, while the inherent physical properties can offer an intuitive haptic interface for direct manipulation with force feedback. View full abstract»

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  • Simplification of three-dimensional density maps

    Publication Year: 2004 , Page(s): 587 - 597
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1600 KB) |  | HTML iconHTML  

    We consider scientific data sets that describe density functions over three-dimensional geometric domains. Such data sets are often large and coarsened representations are needed for visualization and analysis. Assuming a tetrahedral mesh representation, we construct such representations with a simplification algorithm that combines three goals: the approximation of the function, the preservation of the mesh topology, and the improvement of the mesh quality. The third goal is achieved with a novel extension of the well-known quadric error metric. We perform a number of computational experiments to understand the effect of mesh quality improvement on the density map approximation. In addition, we study the effect of geometric simplification on the topological features of the function by monitoring its critical points. View full abstract»

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  • Confetti: object-space point blending and splatting

    Publication Year: 2004 , Page(s): 598 - 608
    Cited by:  Papers (19)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1832 KB) |  | HTML iconHTML  

    We present Confetti, a novel point-based rendering approach based on object-space point interpolation of densely sampled surfaces. We introduce the concept of a transformation-invariant covariance matrix of a set of points which can efficiently be used to determine splat sizes in a multiresolution point hierarchy. We also analyze continuous point interpolation in object-space and we define a new class of parameterized blending kernels as well as a normalization procedure to achieve smooth blending. Furthermore, we present a hardware accelerated rendering algorithm based on texture mapping and α-blending as well as programmable vertex and pixel-shaders. View full abstract»

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  • TVCG Information for authors

    Publication Year: 2004 , Page(s): c3
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    Freely Available from IEEE
  • [Back cover]

    Publication Year: 2004 , Page(s): c4
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    Freely Available from IEEE

Aims & Scope

Visualization techniques and methodologies; visualization systems and software; volume visualization; flow visualization; multivariate visualization; modeling and surfaces; rendering; animation; user interfaces; visual progranuning; applications.

Full Aims & Scope

Meet Our Editors

Editor-in-Chief
Leila De Floriani
Department of Computer Science, Bioengineering, Robotics and Systems Engineering
University of Genova
16146 Genova (Italy)
ldf4tvcg@umiacs.umd.edu