A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Simulating the Grassfire Transform Using an Active Contour Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Imaging vector fields using line integral convolution
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Image-guided streamline placement
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Interactive visualization of 3D-vector fields using illuminated stream lines
Proceedings of the 7th conference on Visualization '96
Voronoi diagrams of polygons: a framework for shape representation
Journal of Mathematical Imaging and Vision
Construction of vector field hierarchies
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Simplified representation of vector fields
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Interactive exploration of volume line integral convolution based on 3D-texture mapping
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Anisotropic nonlinear diffusion in flow visualization
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Hierarchical Representation of Very Large Data Sets Using Wavelets
Scientific Visualization, Overviews, Methodologies, and Techniques
Enhanced Spot Noise for Vector Field Visualization
VIS '95 Proceedings of the 6th conference on Visualization '95
Visualizing flow over curvilinear grid surfaces using line integral convolution
VIS '94 Proceedings of the conference on Visualization '94
Flow Field Clustering via Algebraic Multigrid
VIS '04 Proceedings of the conference on Visualization '04
Centroidal Voronoi Tessellation Based Algorithms for Vector Fields Visualization and Segmentation
VIS '04 Proceedings of the conference on Visualization '04
Display of Vector Fields Using a Reaction-Diffusion Model
VIS '04 Proceedings of the conference on Visualization '04
Segmentation of Discrete Vector Fields
IEEE Transactions on Visualization and Computer Graphics
A nonconforming finite element method for the Cahn-Hilliard equation
Journal of Computational Physics
Manifold learning of vector fields
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Visualization of 4D Blood-Flow Fields by Spatiotemporal Hierarchical Clustering
Computer Graphics Forum
Vector field analysis and visualization through variational clustering
EUROVIS'05 Proceedings of the Seventh Joint Eurographics / IEEE VGTC conference on Visualization
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A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns驴the actual clustering驴during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.