# Description

The long-term goal of this project is the development of efficient methods for calculating, representing, processing and visualizing aggregated, particle-oriented data on different scales. Using aggregation, the gap between particle models and continuous field descriptions is closed. One main aspect of this project is the presentation and analysis of time-dependent, large data sets, as well as the extraction of meaningful data features.

From a physics point-of-view, aggregation allows the transition from a particle model of statistical physics to significant thermo-dynamical terms that help to understand the simulated phenomena. Therefore, the scientific long-term goal of this project is the development of techniques to build and process multi-scale aggregated data as well as its visualization. Similarly, the effectiveness of the visualization plays an important role especially with regard to time-dependent, large data sets. Traditional visualization methods reach their limits with the ever-growing complexity of data sets, restraining the user to evaluate the visualization. Therefore, our visualizations should automatically highlight interesting, application-specific features. In doing so, a combination of different methods has to be developed – depending on data type, used scale and time-dependency of the data. Besides visualization approaches for scalar fields (e.g. density distributions), velocity vector fields (e.g. flow) and symmetric tensor fields, new methods should be developed for electromagnetic fields, since there is not much previous work found in this area.

##### State of the Art

One aspect of project D.5 is adaptive multi-scale visualization. One part of this adaptive visualization is the acceleration of rendering methods, whereby the hierarchy of multi-scale representations can be exploited. Similar hierarchical approaches are often found in the area of visualization techniques, e.g. wavelet hierarchies for direct volume visualization of large 3D scalar data sets [GWGS02], or Time-Space Partitioning Trees [SCM99] for 4-dimensional, space-time data. Hierarchies can be combined with compression approaches, e.g. wavelet-compression approaches [LLYM04]. Such fundamental strategies of hierarchical representations and data compression will also be used in this project.

In this project, linking particle data with hierarchical and compressed representations, as well as explicit use of multi-attribute fields and their impact on data organization will be examined, since this was done only in a limited way in previous work. The emphasis of the coming funding period will be feature extraction in multi-scale representations. Especially for interactive visual exploration of large data sets, feature extraction is very important [DGH03]. In detail, features for typical scientific data types will be used, e.g. for scalar and flow fields. Corresponding feature definitions for many application areas are known from literature, e.g. for vortices in flow fields [JH95], Lagrangian coherent structures for transport phenomena [SLM05], topology of vector or tensor fields [ST05] or generic edge features or ridge lines and surfaces [Ebe96]. Edge or ridge extraction can be used widely, e.g. to detect flow shocks or feature-based visualization of tensor fields [TKW08].

Our own previous work on feature extraction (which was done outside of SFB 716) is used as a starting point: methods for LCS [SW10] and vortex detection [SVG+08]. Basically, we follow the approach of evaluating the feature description on a point-per-point basis (i.e. at every location in space, regardless of potential features in neighboring locations), as done in e.g. the generic parallel-vector operator [PR99]. While feature extraction for one scale of resolution is well covered in literature, only few previous work exists in the area of feature extraction in multiple scales. One of the few preliminary work in this area treats vortex tracking on multiple vector field scales generated by Gauß-filtering [BP02]. In contrast, the area of image processing knows many works on scale-space approaches. As an example, ridge lines can be extracted easier by considering their local behavior in scale space [Lin98].

Another open question is the generalization to other features which are relevant for visualization, as well as other methods for multi-scale constructions (besides Gauß-filtering). In addition to considering features on a multi-scale basis, their relevance should play a role as well. We would like to use the approach of persistency [ELZ02] which is used successfully for the treating of geometry on 2-manifolds by using Reeb-graphs [PSBM07]. However, it remains an open question how we can adapt or use persistency for SFB-relevant features in multi-scale fields.

##### Literature

[BP02] D. Bauer and R. Peikert. Vortex tracking in scale-space. In Proc. EG / IEEE Symp. Vis. ’02, pages 140–147, 2002.

[DGH03] H. Doleisch, M. Gasser, and H. Hauser. Interactive feature specification for focus+context visualization of complex simulation data. In Proc. EG / IEEE Symp. Vis. ’03, pages 239–248, 2003.

[Ebe96] D. Eberly. Ridges in Image and Data Analysis. Computational Imaging and Vision. Kluver Academic Publishers, 1996.

[ELZ02] H. Edelsbrunner, D. Letscher, and A. Zomorodian. Topological persistence and simplification. Discr. Comp. Geom., 28(4):511–533, 2002.

[GWGS02] S. Guthe, M. Wand, J. Gonser, and W. Strasser. Interactive rendering of large volume data sets. In Proc. IEEE Vis. ’02, pages 53–59, 2002.

[JH95] J. Jeong and F. Hussain. On the identification of a vortex. J. Fluid Mech., 285:69–94, 1995.

[Lin98] T. Lindeberg. Edge detection and ridge detection with automatic scale selection. Intl. J. Comp. Vision, 30(2):117–156, 1998.

[LLYM04] P. Ljung, C. Lundstrom, A. Ynnerman, and K. Museth. Transfer function based adaptive decompression for volume rendering of large medical data sets. In IEEE Symp. Vol. Vis. Graphics, pages 25–32, 2004.

[PR99] R. Peikert and M. Roth. The “parallel vectors” operator: a vector field visualization primitive. In Proc. IEEE Vis. ’99, pages 263–270, 1999.

[PSBM07] V. Pascucci, G. Scorzelli, P.-T. Bremer, and A. Mascarenhas. Robust on-line computation of Reeb graphs: simplicity and speed. ACM Trans. Graphics, 26(3):58.1–58.9, 2007.

[SCM99] H. Shen, L. Chiang, and K. Ma. A fast volume rendering algorithm for timevarying fields using a time-space partitioning (TSP) tree. In Proc. IEEE Vis. ’99, pages 371–378, 1999.

[SLM05] S. C. Shadden, F. Lekien, and J. E. Marsden. Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in twodimensional aperiodic flows. Physica D, 212(3–4):271–304, 2005.

[ST05] G. Scheuermann and X. Tricoche. Topological methods in flow visualization. In C. D. Hansen and C. R. Johnson, editors, The Visualization Handbook, pages 341–356. Elsevier, Amsterdam, 2005.

[SVG+08] T. Schafhitzel, J. Vollrath, J. Gois, D. Weiskopf, A. Castelo, and T. Ertl. Topology-preserving¸ 2-based vortex core line detection for flow visualization. Comp. Graphics Forum, 27(3):1023–1030, 2008.

[SW10] F. Sadlo and D. Weiskopf. Time-dependent 2d vector field topology: An approach inspired by Lagrangian coherent structures. Comp. Graphics Forum, 2010. im Druck.

[TKW08] X. Tricoche, G. Kindlmann, and C.-F. Westin. Invariant crease lines for topological and structural analysis of tensor fields. IEEE Trans. Vis. Comp. Graphics, 14(6):1627–1634, 2008.