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## Volume refinement fairing isosurfaces

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Venue: | In Proceedings of IEEE Visualization (2004 |

Citations: | 5 - 1 self |

### Citations

2694 | Marching cubes: A high resolution 3d surface construction algorithm
- Lorensen, Cline
- 1987
(Show Context)
Citation Context ...s functions is not optimized for the representation of smooth contours. Isosurfaces can be emphasized in volume renderings by a proper transfer function [8] or they can be extracted by Marching Cubes =-=[10]-=-. Figures 1a) and b) illustrate the lacking smoothness of isolines based on bilinear and bicubic interpolation, despite of the fact that bicubic spline surfaces minimize thin-plate energy. All linear ... |

542 | Implicit fairing of irregular meshes using diffusion and curvature flow
- Desbrun, Meyer, et al.
- 1999
(Show Context)
Citation Context ..., but they often modify the data. Diffusion and filtering methods are mostly useful for smoothing noisy data. Diffusion-based fairing techniques are also applicable to the fairing of geometric shapes =-=[3, 2]-=-. Variational modeling [16, 7] is often used for fairing parametric surfaces. Using smooth basis functions, like B-splines or quadratic splines on tetrahedra [13], interpolation and fairness constrain... |

246 | and T.Ertl. High-Quality Pre-Integrated Volume Rendering Using Hardware-Accelerated Pixel Shading.
- Engel
- 2001
(Show Context)
Citation Context ...kl.de significant interpolation artifacts to finer scales where they can be eliminated by recursion. Our method can be globally applied, for example in combination with texture-based volume rendering =-=[9, 5]-=-, or it can be used for local refinement. These are the contents of our work: In section 2, we review related work. Our algorithm for the bivariate case (linear and bilinear scalar fields) is describe... |

186 | Variational Surface Modeling,”
- Welch, Witkin
- 1992
(Show Context)
Citation Context ...ata. Diffusion and filtering methods are mostly useful for smoothing noisy data. Diffusion-based fairing techniques are also applicable to the fairing of geometric shapes [3, 2]. Variational modeling =-=[16, 7]-=- is often used for fairing parametric surfaces. Using smooth basis functions, like B-splines or quadratic splines on tetrahedra [13], interpolation and fairness constraints can be specified for the sc... |

157 | Curvature-based transfer functions for direct volume rendering: Methods and applications. In:
- Kindlmann, Whitaker, et al.
- 2003
(Show Context)
Citation Context ...rlying scalar field with locally supported basis functions is not optimized for the representation of smooth contours. Isosurfaces can be emphasized in volume renderings by a proper transfer function =-=[8]-=- or they can be extracted by Marching Cubes [10]. Figures 1a) and b) illustrate the lacking smoothness of isolines based on bilinear and bicubic interpolation, despite of the fact that bicubic spline ... |

147 | Multiresolution techniques for interactive textured-based volume visualization.
- LaMar, Hamann, et al.
- 1999
(Show Context)
Citation Context ...kl.de significant interpolation artifacts to finer scales where they can be eliminated by recursion. Our method can be globally applied, for example in combination with texture-based volume rendering =-=[9, 5]-=-, or it can be used for local refinement. These are the contents of our work: In section 2, we review related work. Our algorithm for the bivariate case (linear and bilinear scalar fields) is describe... |

93 | Real-time Exploration of Regular Volume Data by Adaptive Reconstruction
- Westermann, Kobbelt, et al.
- 1999
(Show Context)
Citation Context ...d in section 4. In section 5, we conclude our work. 2 RELATED WORK Visualization of three-dimensional scalar fields is either done by extraction of isosurfaces or by volume rendering, see for example =-=[17, 6, 8]-=-. In both cases, isosurface quality has a significant impact. Not only geometric smoothness, but also isosurface topology depends on the representation of the underlying scalar fields. In the case of ... |

82 | On marching cubes.
- Nielson
- 2003
(Show Context)
Citation Context ...ng scalar fields. In the case of trilinear scalar fields, isosurface topology is quite complicated. A variant of Marching Cubes [10], extracting topologically correct isosurfaces was recently devised =-=[11]-=-. For trilinear fields, critical points where isosurface topology changes are efficiently detected [14]. Unfortunately, the topology of a trilinear interpolant is often different from the topology of ... |

53 |
Anisotropic Diffusion in Vector Field Visualization on Euclidean Domains and Surfaces,”
- Diewald, Preusser, et al.
- 2000
(Show Context)
Citation Context ...ginal scalar field prior to discretization. The task is to find the best reconstruction of the original shape consistent with the discrete data. Image processing techniques like anisotropic diffusion =-=[15, 4]-=- are capable of recognizing local features, but they often modify the data. Diffusion and filtering methods are mostly useful for smoothing noisy data. Diffusion-based fairing techniques are also appl... |

33 |
Rumpf: Nonlinear anisotropic diffusion in surface processing
- Clarenz, Diewald, et al.
(Show Context)
Citation Context ..., but they often modify the data. Diffusion and filtering methods are mostly useful for smoothing noisy data. Diffusion-based fairing techniques are also applicable to the fairing of geometric shapes =-=[3, 2]-=-. Variational modeling [16, 7] is often used for fairing parametric surfaces. Using smooth basis functions, like B-splines or quadratic splines on tetrahedra [13], interpolation and fairness constrain... |

26 | Visualization of volume data with quadratic super splines
- Rössl, Zeilfelder, et al.
- 2003
(Show Context)
Citation Context ... to the fairing of geometric shapes [3, 2]. Variational modeling [16, 7] is often used for fairing parametric surfaces. Using smooth basis functions, like B-splines or quadratic splines on tetrahedra =-=[13]-=-, interpolation and fairness constraints can be specified for the scalar field. Only few approaches are capable of fairing implicit surfaces. Nielson et al. [12] propose a fairing method for single is... |

18 | Fast multi-resolution Extraction of Multiple Transparent Iso-surfaces
- Gerstner
(Show Context)
Citation Context ...d in section 4. In section 5, we conclude our work. 2 RELATED WORK Visualization of three-dimensional scalar fields is either done by extraction of isosurfaces or by volume rendering, see for example =-=[17, 6, 8]-=-. In both cases, isosurface quality has a significant impact. Not only geometric smoothness, but also isosurface topology depends on the representation of the underlying scalar fields. In the case of ... |

11 |
Detecting critical regions in scalar fields
- Weber, Scheuermann, et al.
(Show Context)
Citation Context ...ariant of Marching Cubes [10], extracting topologically correct isosurfaces was recently devised [11]. For trilinear fields, critical points where isosurface topology changes are efficiently detected =-=[14]-=-. Unfortunately, the topology of a trilinear interpolant is often different from the topology of an original scalar field prior to discretization. The task is to find the best reconstruction of the or... |

9 |
Shrouds: optimal separating surfaces for enumerated volumes
- Nielson, Graf, et al.
- 2003
(Show Context)
Citation Context ...nes or quadratic splines on tetrahedra [13], interpolation and fairness constraints can be specified for the scalar field. Only few approaches are capable of fairing implicit surfaces. Nielson et al. =-=[12]-=- propose a fairing method for single isosurfaces by constrained fairing of curves. The problem of fairing all isolines in a two-dimensional scalar field has been solved at the expense of high computat... |

5 |
Fairing scalar fields by variational modeling of contours
- Bertram
- 2003
(Show Context)
Citation Context ... exhibit more or less the same problem. Hence, the interpolation artifacts of contours (isolines and -surfaces) may only be reduced effectively by a non-linear optimization method. In a previous work =-=[1]-=-, we have presented an iterative variational fairing approach for 2D scalar fields based on bicubic splines, see figure 1c). The method increases the resolution by knot insertion and iteratively smoot... |