# Feature comparisons of 3-D vector fields using earth mover's distance

@article{Batra1999FeatureCO, title={Feature comparisons of 3-D vector fields using earth mover's distance}, author={Rajesh Batra and Lambertus Hesselink}, journal={Proceedings Visualization '99 (Cat. No.99CB37067)}, year={1999}, pages={105-114} }

A method for comparing three-dimensional vector fields constructed from simple critical points is described. This method is a natural extension of previous work (Y. Lavin et al., 1998), which defined a distance metric for comparing two-dimensional fields. The extension to three-dimensions follows the path of our previous work, rethinking the representation of a critical point signature and the distance measure between the points. Since the method relies on topologically based information…

## 32 Citations

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A new topology based metric for 2D vector fields based on the concept of feature flow fields is proposed that incorporates both the characteristics and the local distribution of the critical points while keeping the computing time reasonably small even for topologically complex vector fields.

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An algorithm for compressing 2D vector fields that preserves topology using constrained clustering is presented and results indicate that one can obtain significant compression with low errors without losing topology information.

Topology preserving compression of 2D vector fields

- Computer ScienceProceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145)
- 2000

An algorithm for compressing 2D vector fields that preserves topology using constrained clustering is presented and results indicate that one can obtain significant compression with low errors without losing topology information.

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This paper extends Bhatia’s idea to compute the Poincaré index of critical points in piecewise linear vector fields, and considers all kinds of simplical complexes, including 2D/3D triangulated meshes, and also triangulate surfaces.

Vector Field Metrics Based on Distance Measures of First Order Critical Points

- Computer Science, MathematicsWSCG
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An advanced and complete classification of all first order critical points of 2D vector fields is given, which forms the foundation of the definition of vector field metrics.

Feature-based Vector Field Representation and Comparison

- Computer Science
- 2016

This thesis replaces the visual processing of data in the traditional workflow with an automated, statistical method that enables a quantitative analysis and describes the input data and demonstrates the advantages of the developed representation and its use for the analysis of vector fields using flow graphs.

Topology Preserving Top-Down Compression of 2D Vector Fields Using Bintree and Triangular Quadtrees

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- 2003

A hierarchical top-down refinement algorithm for compressing 2D vector fields that preserves topology is presented and results indicate that one can obtain significant compression with low errors without losing topological information.

Saddle connectors - an approach to visualizing the topological skeleton of complex 3D vector fields

- Computer ScienceIEEE Visualization, 2003. VIS 2003.
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It is shown that the use of saddle connectors makes topological skeletons available as a valuable visualization tool even for topologically complex 3D flow data.

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