Skip to main content
Log in

An integral curve attribute based flow segmentation

  • Regular Paper
  • Published:
Journal of Visualization Aims and scope Submit manuscript


We propose a segmentation method for vector fields that employs the accumulated geometric and physical attributes along integral curves to classify their behavior. In particular, we assign to a given spatio-temporal position the attribute value associated with the integral curve initiated at that point. With this attribute information, our segmentation strategy first performs a region classification. Then, connected components are constructed from the derived classification to obtain an initial segmentation. After merging and filtering small segments, we extract and refine the boundaries of the segments. Because points that are correlated by the same integral curve have the same or similar attribute values, the proposed segmentation method naturally generates segments whose boundaries are better aligned with the flow direction. Therefore, additional processing is not required to generate other geometric descriptors within the segmented regions to illustrate the flow behaviors. We apply our method to a number of synthetic and CFD simulation data sets and compare their results with existing methods to demonstrate its effectiveness.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others


  • Chen J-L, Bai Z, Hamann B, Ligocki TJ (2003) Normalized-cut algorithm for hierarchical vector field data segmentation. In: Electronic Imaging 2003. International Society for Optics and Photonics, pp 79–90

  • Chen G, Mischaikow K, Laramee RS, Pilarczyk P, Zhang E (2007) Vector field editing and periodic orbit extraction using Morse decomposition. IEEE Trans Vis Comput Graph 13(4):769–785

  • Chen G, Mischaikow K, Laramee RS, Zhang E (2008) Efficient Morse decompositions of vector fields. IEEE Trans Vis Comput Graph 14(4):848–862

  • Edmunds M, Laramee RS, Chen G, Max N, Zhang E, Ware C (2012) Surface-based flow visualization. Comput Graph 36(8):974–990

    Article  Google Scholar 

  • Garth C, Wiebel A, Tricoche X, Joy KI, Scheuermann G (2008) Lagrangian visualization of flow-embedded surface structures. Comput Graph Forum 27(3):1007–1014

    Article  Google Scholar 

  • Gonzalez RC (2009) Digital image processing. Pearson Education India

  • Guan M, Zhang W, Zheng N, Liu Z (2014) A feature-emphasized clustering method for 2d vector field. In: proceeding of IEEE international conference on systems, man and cybernetics (SMC). IEEE, pp 729–733

  • Haller G (2001) Lagrangian coherent structures and the rate of strain in two-dimensional turbulence. Phys Fluids A 13:3365–3385

    Article  MathSciNet  MATH  Google Scholar 

  • Heckel B, Weber G, Hamann B, Joy KI (1999) Construction of vector field hierarchies. In: Proceedings of the conference on visualization’99. IEEE Computer Society Press, pp 19–25

  • Helman JL, Hesselink L (1989) Representation and display of vector field topology in fluid flow data sets. IEEE Comput 22(8):27–36

  • Jiang M, Machiraju R, Thompson D (2005) Detection and visualization of vortices. In: The visualization handbook. Academic Press, pp 295–309

  • Kuhn A, Lehmann DJ, Gasteiger R, Neugebauer M, Preim B, Theisel H (2011) A clustering-based visualization technique to emphasize meaningful regions of vector fields. In: VMV, pp 191–198

  • Kundu P, Cohen I,Fluid mechanics.(2004) Elsevier Academic Press, San Diego). Two-and three-dimensional self-sustained flow oscillations 307(471–476):2008

  • Laramee R, Hauser H, Zhao L, Post FH (2007) Topology based flow visualization: the state of the art. In: Topology-based methods in visualization (Proceedings of Topo-in-Vis 2005), mathematics and visualization. Springer, pp 1–19

  • Lekien F, Shadden S, Marsden J (2007) Lagrangian coherent structures in n-dimensional systems. J Math Phys 48(6):Art. No. 065404

  • Li H, Chen W, Shen I-F (2006) Segmentation of discrete vector fields. IEEE Trans Vis Comput Graph 12(3):289–300

    Article  MathSciNet  Google Scholar 

  • Lu K, Chaudhuri A, Lee T-Y, Shen HW, Wong PC (2013) Exploring vector fields with distribution-based streamline analysis. In: Proceeding of IEEE pacific visualization symposium, Sydney

  • Matvienko V, Kruger J (2013) A metric for the evaluation of dense vector field visualizations. Vis Comput Graph IEEE Trans 19(7):1122–1132

    Article  Google Scholar 

  • McKenzie A, Lombeyda SV, Desbrun M (2005) Vector field analysis and visualization through variational clustering. In: Proceedings of the Seventh Joint Eurographics / IEEE VGTC conference on Visualization, EUROVIS’05, Aire-la-Ville. Eurographics Association, pp 29–35

  • McLoughlin T, Jones MW, Laramee RS, Malki R, Masters I, Hansen CD (2013) Similarity measures for enhancing interactive streamline seeding. IEEE Trans Vis Comput Graph 19(8):1342–1353

    Article  Google Scholar 

  • Peng Z, Grundy E, Laramee RS, Chen G, Croft N (2012) Mesh-driven vector field clustering and visualization: an image-based approach. IEEE Trans Vis Comput Graph 18(2):283–298

  • Pobitzer A, Lez A, Matkovic K, Hauser H (2012) A statistics-based dimension reduction of the space of path line attributes for interactive visual flow analysis. In: PacificVis, pp 113–120

  • Pobitzer A, Peikert R, Fuchs R, Schindler B, Kuhn A, Theisel H, Matkovic K, Hauser H (2011) The state of the art in topology-based visualization of unsteady flow. Comput Graph Forum 30(6):1789–1811

  • Polthier K, Preuß E (2003) Identifying vector fields singularities using a discrete hodge decomposition. In: Hege HC, Polthier K (eds) Mathematical visualization III, pp 112–134

  • Sadarjoen I, Post F (1999) Geometric methods for vortex extraction. In Proc EG/IEEE Visualization Symposium

  • Sadlo F, Peikert R (2007) Efficient visualization of lagrangian coherent structures by filtered amr ridge extraction. IEEE Trans Vis Comput Graph 13(6):1456–1463

    Article  Google Scholar 

  • Salzbrunn T, Garth C, Scheuermann G, Meyer J (2008) Pathline predicates and unsteady flow structures. Vis Comput 24(12):1039–1051

    Article  Google Scholar 

  • Salzbrunn T, Scheuermann G (2006) Streamline predicates. IEEE Trans Vis Comput Graph 12(6):1601–1612

    Article  MATH  Google Scholar 

  • Salzbrunn T, Wischgoll T, Jänicke H, Scheuermann G (2008) The state of the art in flow visualization: partition-based techniques. In: Hauser H, Strassburger S, Theisel H (eds) Simulation and visualization proceedings. SCS Publishing House, pp 75–92

  • Shadden S, Lekien F, Marsden J (2005) Definition and properties of lagrangian coherent structures from finite-time lyapunov exponents in two-dimensional aperiodic flows. Phys D 212(3–4):271–304

    Article  MathSciNet  MATH  Google Scholar 

  • Shi K, Theisel H, Hauser H, Weinkauf T, Matkovic K, Hege H-C, Seidel H-P (2009) Path line attributes—an information visualization approach to analyzing the dynamic behavior of 3D time-dependent flow fields. In: Hege H-C, Polthier K, Scheuermann G (eds) Topology-based methods in visualization II, Mathematics and visualization, Grimma. Springer, pp 75–88

  • Skraba P, Wang B, Chen G, Rosen P (2014) 2d vector field simplification based on robustness. In: IEEE pacific visualization symposium, pp 49–56

  • Telea A, van Wijk JJ (1999) Simplified representation of vector fields. In: Proceedings of the conference on Visualization’99. IEEE Computer Society Press, pp 35–42

  • Theisel H, Weinkauf T, Seidel H-P (2004) Grid-independent detection of closed stream lines in 2D vector fields. In: Proceedings of the conference on vision, modeling and visualization 2004 (VMV 04), pp 421–428

  • Tricoche X, Scheuermann G, Hagen H (2001) Continuous topology simplification of planar vector fields. Proc IEEE Vis 2001:159–166

    MATH  Google Scholar 

  • Weinkauf T, Theisel H (2010) Streak lines as tangent curves of a derived vector field. IEEE Trans Vis Comput Graph 16(6):1225–1234

  • Weiskopf D, Schafhitzel T, Ertl T (2007) Texture-based visualization of unsteady 3d flow by real-time advection and volumetric illumination. Vis Comput Graph IEEE Trans 13(3):569–582

    Article  Google Scholar 

  • Wischgoll T, Scheuermann G (2001) Detection and visualization of closed streamlines in planar fields. IEEE Trans Vis Comput Graph 7(2):165–172

    Article  Google Scholar 

  • Yu H, Wang C, Shene C-K, Chen JH (2012) Hierarchical streamline bundles. IEEE Trans Vis Comput Graph 18(8):1353–1367

  • Zhang L, Laramee RS, Thompson D, Sescu A, Chen G (2015) Compute and visualize discontinuity among neighboring integral curves of 2D vector fields. In Proceedings of TopoInVis, Germany

Download references


We thank Jackie Chen, Mathew Maltude, Tino Weinkauf for the data. This research was in part supported by NSF IIS-1352722 and IIS-1065107.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Guoning Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, L., Laramee, R.S., Thompson, D. et al. An integral curve attribute based flow segmentation. J Vis 19, 423–436 (2016).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: