Institute for Data Analysis and Visualization

In the context of vector field data visualization, it is often desirable to construct a hierarchical data representation. One possibility to construct a hierarchy is based on clustering vectors using cerain similarity criteria. We combine two fundemental approaches to cluster vectors and construct hierarchical vector field representations. For clustering, a locally constructed linear least-squares approxiamation is incorporated into a similarity measure that considers both Euclidean distance between point pairs (for which dependent vector data are given) and difference in vector values. A modified normalized cut (NC) method is used to obtain a near-optimal clustering of a given discrete vector field data set. To obtain a hierarchical representation, the NC method is applied recursively after the construction of coarse-level clusters. We have applied our NC-based segmentation method to simple, analytically defined vector fields as well as discrete vector field data generated by turbulent flow simulation. Our test results indicate that our proposed adaptation of the original NC method is promising method as it leads to segmentation results that capture the qualitative and topological nature of vector field data.