Abstract
Modern time-varying flow visualization techniques that rely on advection are able to convey fluid transport, but cannot provide an accurate insight into local flow behavior over time or locally corresponding patterns in unsteady vector fields. We overcome these limitations of purely Lagrangian approaches by generalizing the concept of function fields to time-varying flows. This representation of unsteady vector-fields as stationary function fields, where every position in space is a vector-valued function supports the application of novel analysis techniques based on function correlation, and allows to answer data analysis questions that remain unanswered with classic time-varying vector field analysis techniques. Our results demonstrate how analysis of time-varying flow fields can benefit from a conversion into function field representations and show the robustness of our presented clustering techniques.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Weiskopf, D., Erlebacher, G.: Flow visualization overview. In: Handbook of Visualization, pp. 261–278. Elsevier, Amsterdam (2005)
McLouglin, T., Laramee, R.S., Peikert, R., Post, F.H., Chen, M.: Over two decades of integration-based geometric flow visualization. Comp. Graph. Forum 29, 1807–1829 (2010)
Shi, K., Theisel, H., Hauser, H., Weinkauf, T., Matkovic, K., Hege, H.-C., Seidel, H.-P.: Path line attributes - an information visualization approach to analyzing the dynamic behavior of 3d time-dependent flow fields. In: Topology-Based Methods in Visualization II, Mathematics and Visualization, pp. 75–88. Springer (2009)
Xu, L., Shen, H.W.: Flow web: a graph based user interface for 3d flow field exploration. Visualization and Data Analysis 7530, 75300F (2010)
Wei, J., Wang, C., Yu, H., Ma, K.: A sketch-based interface for classifying and visualizing vector fields. In: Proc. of PacificVis 2010, pp. 129–136 (2010)
Lez, A., Zajic, A., Matkovic, K., Pobitzer, A., Mayer, M., Hauser, H.: Interactive exploration and analysis of pathlines in flow data. In: Proc. Int. Conf. in Central Europe on Comp. Grap., Vis. and Comp. Vision (WSCG 2011), pp. 17–24 (2011)
Garcke, H., Preußer, T., Rumpf, M., Telea, A., Weikard, U., van Wijk, J.: A continuous clustering method for vector fields. In: Proc. of the Conf. on Visualization 2000, pp. 351–358. IEEE Computer Society Press, Los Alamitos (2000)
Schlemmer, M., Heringer, M., Morr, F., Hotz, I., Bertram, M.H., Garth, C., Kollmann, W., Hamann, B., Hagen, H.: Moment invariants for the analysis of 2d flow fields. IEEE Trans. Vis. Comput. Graph. 13, 1743–1750 (2007)
Nagaraj, S., Natarajan, V., Nanjundiah, R.S.: A gradient-based comparison measure for visual analysis of multifield data. Comp. Graph. Forum 30, 1101–1110 (2011)
Albrecht, H.-E.: Laser doppler and phase doppler measurement technique, 2nd edn. Springer, New York (2003)
Haller, G.: Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D: Nonlinear Phenomena 149, 248–277 (2001)
Anderson, J.C., Gosink, L.J., Duchaineau, M.A., Joy, K.I.: Interactive visualization of function fields by range-space segmentation. Comp. Graph. Forum 28, 727–734 (2009)
Mokhtarian, F., Mackworth, A.: Scale-based description and recognition of planar curves and two-dimensional objects. IEEE Trans. Pattern Anal. Mach. Intell. 8, 34–43 (1986)
Agrawal, R., Lin, K., Sawhney, H.S., Shim, K.: Fast similarity search in the presence of noise, scaling, and translation in time-series databases. In: Proc. Int. Conf. on Very Large Data Bases, pp. 490–501. Morgan Kaufmann Publishers Inc., San Francisco (1995)
Grundy, E., Jones, M.W., Laramee, R.S., Wilson, R.P., Shepard, E.L.C.: Visualisation of Sensor Data from Animal Movement. Comp. Graph. Forum 28, 815–822 (2009)
Van Wijk, J.J., Van Selow, E.R.: Cluster and calendar based visualization of time series data. In: Proc. IEEE Symposium on Information Visualization, pp. 4–9. IEEE Computer Society, Washington, DC (1999)
Hlawatsch, M., Leube, P., Nowak, W., Weiskopf, D.: Flow radar glyphs - static visualization of unsteady flow with uncertainty. IEEE Trans. Vis. Comput. Graph. 17, 1949–1958 (2011)
Yi, B., Jagadish, H.V., Faloutsos, C.: Efficient retrieval of similar time sequences under time warping. In: Proc. of the 14th Int. Conf. on Data Engineering, ICDE 1998, pp. 201–208. IEEE Computer Society, Washington, DC (1998)
Burger, R., Muigg, P., Doleisch, H., Hauser, H.: Interactive cross-detector analysis of vortical flow data. In: Fifth Int. Conf. on Coordinated and Multiple Views in Exploratory Visualization, CMV 2007, pp. 98–110 (2007)
Qu, H., Chan, W., Xu, A., Chung, K., Lau, K., Guo, P.: Visual analysis of the air pollution problem in hong kong. IEEE Trans. Vis. Comput. Graph. 13, 1408–1415 (2007)
Blinn, J.F.: A generalization of algebraic surface drawing. ACM Trans. Graph. 1, 235–256 (1982)
Heyer, L.J., Kruglyak, S., Yooseph, S.: Exploring expression data: identification and analysis of coexpressed genes. Genome Research 9, 1106–1115 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Obermaier, H., Joy, K.I. (2012). Function Field Analysis for the Visualization of Flow Similarity in Time-Varying Vector Fields. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2012. Lecture Notes in Computer Science, vol 7432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33191-6_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-33191-6_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33190-9
Online ISBN: 978-3-642-33191-6
eBook Packages: Computer ScienceComputer Science (R0)