The Visual Computer

, Volume 29, Issue 6–8, pp 761–771 | Cite as

Scalar field visualization via extraction of symmetric structures

  • Talha Bin Masood
  • Dilip Mathew Thomas
  • Vijay Natarajan
Original Article


Identifying symmetry in scalar fields is a recent area of research in scientific visualization and computer graphics communities. Symmetry detection techniques based on abstract representations of the scalar field use only limited geometric information in their analysis. Hence they may not be suited for applications that study the geometric properties of the regions in the domain. On the other hand, methods that accumulate local evidence of symmetry through a voting procedure have been successfully used for detecting geometric symmetry in shapes. We extend such a technique to scalar fields and use it to detect geometrically symmetric regions in synthetic as well as real-world datasets. Identifying symmetry in the scalar field can significantly improve visualization and interactive exploration of the data. We demonstrate different applications of the symmetry detection method to scientific visualization: query-based exploration of scalar fields, linked selection in symmetric regions for interactive visualization, and classification of geometrically symmetric regions and its application to anomaly detection.


Scalar field visualization Symmetry detection Query based exploration 



This work was supported by a grant from Department of Science and Technology, India (SR/S3/EECE/0086/2012).


  1. 1.
    Alliez, P., Cohen-steiner, D., Devillers, O., Levy, B., Desbrun, M.: Anisotropic polygonal remeshing. ACM Trans. Graph. 3, 485–493 (2003) CrossRefGoogle Scholar
  2. 2.
    Carr, H., Snoeyink, J., Axen, U.: Computing contour trees in all dimensions. Comput. Geom. 24(2), 75–94 (2003) MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Chazal, F., Guibas, L.J., Oudot, S.Y., Skraba, P.: Analysis of scalar fields over point cloud data. In: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA ’09), pp. 1021–1030 (2009) Google Scholar
  4. 4.
    Cohen-steiner, D., Morvan, M.-J.: Restricted Delaunay triangulations and normal cycle. In: Proc. of Symposium on Computational Geometry, pp. 312–321 (2002) Google Scholar
  5. 5.
    Comaniciu, D., Meer, P.: Mean shift: a robust approach towards feature space analysis. IEEE Trans. Pattern Anal. Mach. Intell. 24(5), 603–619 (2002) CrossRefGoogle Scholar
  6. 6.
    Correa, C.D., Lindstrom, P., Bremer, P.T.: Topological spines: a structure-preserving visual representation of scalar fields. IEEE Trans. Vis. Comput. Graph. 17(12), 1842–1851 (2011) CrossRefGoogle Scholar
  7. 7.
    Ester, M., Kriegel, H.P., Sander, J., Xu, X.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Proc. of 2nd International Conference on Knowledge Discovery and Data Mining (1996) Google Scholar
  8. 8.
    Gyulassy, A., Natarajan, V.: Topology-based simplification for feature extraction from 3D scalar fields. In: Visualization (VIS 05), pp. 535–542. IEEE Press, New York (2005) Google Scholar
  9. 9.
    Hong, Y., Shen, H.W.: Parallel reflective transformation for volume data. Comput. Graph. 32(1), 41–54 (2008) CrossRefGoogle Scholar
  10. 10.
    Kazhdan, M.M., Chazelle, B., Dobkin, D.P., Funkhouser, T.A., Rusinkiewicz, S.: A reflective symmetry descriptor for 3D models. Algorithmica 38(1), 201–225 (2003) MathSciNetCrossRefGoogle Scholar
  11. 11.
    Kerber, J., Bokeloh, M., Wand, M., Krüger, J., Seidel, H.P.: Feature preserving sketching of volume data. In: Koch, R., Kolb, A., Rezk-Salama, C. (eds.) Vision, Modeling, and Visualization (2010) Google Scholar
  12. 12.
    Kerber, J., Wand, M., Krüger, J., Seidel, H.P.: Partial symmetry detection in volume data. In: Eisert, P., Polthier, K., Hornegger, J. (eds.) Vision, Modeling, and Visualization (2011) Google Scholar
  13. 13.
    Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. SIGGRAPH Comput. Graph. 21(4), 163–169 (1987) CrossRefGoogle Scholar
  14. 14.
    Mitra, N., Guibas, L.J., Pauly, M.: Partial and approximate symmetry detection for 3D geometry. ACM Trans. Graph. 25, 560–568 (2006) CrossRefGoogle Scholar
  15. 15.
    Mitra, N.J., Pauly, M., Wand, M., Ceylan, D.: Symmetry in 3D geometry: extraction and applications. In: EG 2012—State of the Art Reports, pp. 29–51 (2012) Google Scholar
  16. 16.
    Thomas, D.M., Natarajan, V.: Symmetry in scalar field topology. IEEE Trans. Vis. Comput. Graph. 17(12), 2035–2044 (2011) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Talha Bin Masood
    • 1
  • Dilip Mathew Thomas
    • 1
  • Vijay Natarajan
    • 2
  1. 1.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia
  2. 2.Department of Computer Science and Automation, Supercomputer Education and Research CentreIndian Institute of ScienceBangaloreIndia

Personalised recommendations