| 1. |
- Günther, D., et al.
(författare)
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Fast and Memory-Efficient Topological Denoising of 2D and 3D Scalar Fields
- 2014
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Ingår i: IEEE Transactions on Visualization and Computer Graphics. - : IEEE Computer Society. - 1077-2626 .- 1941-0506. ; 20:12, s. 2585-2594
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Tidskriftsartikel (refereegranskat)abstract
- Data acquisition, numerical inaccuracies, and sampling often introduce noise in measurements and simulations. Removing this noise is often necessary for efficient analysis and visualization of this data, yet many denoising techniques change the minima and maxima of a scalar field. For example, the extrema can appear or disappear, spatially move, and change their value. This can lead to wrong interpretations of the data, e.g., when the maximum temperature over an area is falsely reported being a few degrees cooler because the denoising method is unaware of these features. Recently, a topological denoising technique based on a global energy optimization was proposed, which allows the topology-controlled denoising of 2D scalar fields. While this method preserves the minima and maxima, it is constrained by the size of the data. We extend this work to large 2D data and medium-sized 3D data by introducing a novel domain decomposition approach. It allows processing small patches of the domain independently while still avoiding the introduction of new critical points. Furthermore, we propose an iterative refinement of the solution, which decreases the optimization energy compared to the previous approach and therefore gives smoother results that are closer to the input. We illustrate our technique on synthetic and real-world 2D and 3D data sets that highlight potential applications.
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| 2. |
- Jacobson, A., et al.
(författare)
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Smooth Shape-Aware Functions with Controlled Extrema
- 2012
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Ingår i: Computer graphics forum (Print). - : Wiley-Blackwell. - 0167-7055 .- 1467-8659. ; 31:5, s. 1577-1586
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Tidskriftsartikel (refereegranskat)abstract
- Functions that optimize Laplacian-based energies have become popular in geometry processing, e.g. for shape deformation, smoothing, multiscale kernel construction and interpolation. Minimizers of Dirichlet energies, or solutions of Laplace equations, are harmonic functions that enjoy the maximum principle, ensuring no spurious local extrema in the interior of the solved domain occur. However, these functions are only C0 at the constrained points, which often causes smoothness problems. For this reason, many applications optimize higher-order Laplacian energies such as biharmonic or triharmonic. Their minimizers exhibit increasing orders of continuity but also increasing oscillation, immediately releasing the maximum principle. In this work, we identify characteristic artifacts caused by spurious local extrema, and provide a framework for minimizing quadratic energies on manifolds while constraining the solution to obey the maximum principle in the solved region. Our framework allows the user to specify locations and values of desired local maxima and minima, while preventing any other local extrema. We demonstrate our method on the smoothness energies corresponding to popular polyharmonic functions and show its usefulness for fast handle-based shape deformation, controllable color diffusion, and topologically-constrained data smoothing.
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| 3. |
- Paolucci, M., et al.
(författare)
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Towards a living earth simulator
- 2012
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Ingår i: The European Physical Journal Special Topics. - : Springer Science and Business Media LLC. - 1951-6355 .- 1951-6401. ; 214:1, s. 77-108
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Tidskriftsartikel (refereegranskat)abstract
- The Living Earth Simulator (LES) is one of the core componentsof the FuturICT architecture. It will work as a federation ofmethods, tools, techniques and facilities supporting all of the FuturICTsimulation-related activities to allow and encourage interactive explorationand understanding of societal issues. Society-relevant problemswill be targeted by leaning on approaches based on complex systemstheories and data science in tight interaction with the other componentsof FuturICT. The LES will evaluate and provide answers to realworldquestions by taking into account multiple scenarios. It will buildon present approaches such as agent-based simulation and modeling,multiscale modelling, statistical inference, and data mining, movingbeyond disciplinary borders to achieve a new perspective on complexsocial systems.
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| 4. |
- Weinkauf, Tino, 1974-, et al.
(författare)
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Cusps of Characteristic Curves and Intersection-Aware Visualization of Path and Streak Lines
- 2012
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Ingår i: Topological Methods in Data Analysis and Visualization II. - : Springer. ; , s. 161-176
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- We analyze characteristic curves of vector fields and report on locations where they have cusps in their spatial projection, i.e., isolated points on the curve with abruptly turning tangent direction. Cusps appear in places where a projection of the corresponding tangent curve vector field exhibits critical points. We show that such cusps are only possible for streak and path lines, whereas they cannot appear on stream and time lines. Cusps turn out to be closely related to self-intersections of characteristic curves. We utilize this information in a new algorithm to create uncluttered static visualizations of path and streak lines.
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| 5. |
- Weinkauf, Tino, 1974-, et al.
(författare)
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Topology-based Smoothing of 2D Scalar Fields with C1-Continuity
- 2010
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Ingår i: Computer graphics forum (Print). - : Wiley. - 0167-7055 .- 1467-8659. ; 29:3, s. 1221-1230
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Tidskriftsartikel (refereegranskat)abstract
- Data sets coming from simulations or sampling of real-world phenomena often contain noise that hinders their processing and analysis. Automatic filtering and denoising can be challenging: when the nature of the noise is unknown, it is difficult to distinguish between noise and actual data features; in addition, the filtering process itself may introduce artificial features into the data set that were not originally present. In this paper, we propose a smoothing method for 2D scalar fields that gives the user explicit control over the data features. We define features as critical points of the given scalar function, and the topological structure they induce (i.e., the Morse-Smale complex). Feature significance is rated according to topological persistence. Our method allows filtering out spurious features that arise due to noise by means of topological simplification, providing the user with a simple interface that defines the significance threshold, coupled with immediate visual feedback of the remaining data features. In contrast to previous work, our smoothing method guarantees a C1-continuous output scalar field with the exact specified features and topological structures.
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| 6. |
- Zhou, Q., et al.
(författare)
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Feature-Based Mesh Editing
- 2011
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Ingår i: Proceedings. Eurographics, Short Papers.
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Konferensbidrag (refereegranskat)abstract
- Editing and deformation of irregular meshes have become standard tools in geometric modeling. Most approaches try to preserve low-level differential properties of the surface during editing, whereas the global structure and shape of the features are not explicitly taken into account. In this paper, we introduce a feature-driven editing approach that puts global structural properties of the shape into the center of attention. We start by segmenting the mesh by ridges and valleys and use the so-defined curves and surface regions as intuitive handles for all subsequent editing operations. Our framework supports manipulations the positions and curvature values of the handles and the various mesh regions. In order to preserve the existing features, prevent unwanted appearance of new features, and maintain or manipulate global aspects of the shape, we apply curvature optimization in the affected areas. We show that the combination of feature extraction and curvature optimization leads to an intuitive modeling tool for high-quality surface manipulation.
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