Topological Descriptors for 3D Surface Analysis

  • Matthias ZeppelzauerEmail author
  • Bartosz ZielińskiEmail author
  • Mateusz Juda
  • Markus Seidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9667)


We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for a 2D cubical filtration. In the next step we investigate different topological descriptors and measure their ability to discriminate structurally different 3D surface patches. We evaluate their sensitivity to different parameters and compare the performance of the resulting topological descriptors to alternative (non-topological) descriptors. We present a comprehensive evaluation that shows that topological descriptors are (i) robust, (ii) yield state-of-the-art performance for the task of 3D surface analysis and (iii) improve classification performance when combined with non-topological descriptors.


3D surface classification Surface topology analysis Surface representation Persistence diagram Persistence images 



Parts of the work for this paper has been carried out in the project 3D-Pitoti which is funded from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no 600545; 2013-2016.


  1. 1.
    Adams, H., Chepushtanova, S., Emerson, T., Hanson, E., Kirby, M., Motta, F., Neville, R., Peterson, C., Shipman, P., Ziegelmeier, L.: Persistent images: A stable vector representation of persistent homology (2015). arXiv preprint arXiv:1507.06217
  2. 2.
    Bauer, U., Kerber, M., Reininghaus, J.: Phat - persistent homology algorithms toolbox (2013).
  3. 3.
    Bauer, U., Kerber, M., Reininghaus, J., Wagner, H.: PHAT – Persistent homology algorithms toolbox. In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 137–143. Springer, Heidelberg (2014). Google Scholar
  4. 4.
    Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. Pattern Anal. Mach. Intell. 24(4), 509–522 (2002)CrossRefGoogle Scholar
  5. 5.
    Crandall, D., Owens, A., Snavely, N., Huttenlocher, D.: Discrete-continuous optimization for large-scale structure from motion. In: 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3001–3008. IEEE (2011)Google Scholar
  6. 6.
    Dalal, N., Triggs, B.: Histograms of oriented gradients for human detection. In: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005, vol. 1, pp. 886–893. IEEE (2005)Google Scholar
  7. 7.
    Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete Comput. Geom. 28, 511–533 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Freund, Y., Schapire, R.E.: A decision-theoretic generalization of on-line learning and an application to boosting. J. Comput. Syst. Sci. 55(1), 119–139 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Guo, Z., Zhang, L., Zhang, D.: A completed modeling of local binary pattern operator for texture classification. IEEE Trans. Image Process. 19(6), 1657–1663 (2010)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Haralick, R.M., Shanmugam, K., Dinstein, I.H.: Textural features for image classification. IEEE Trans. Syst. Man Cybern. 6, 610–621 (1973)CrossRefGoogle Scholar
  11. 11.
    ISO-IEC: Information Technology - Multimedia Content Description Interface.15938, ISO/IEC, Moving Pictures Expert Group, 1st edn. (2002)Google Scholar
  12. 12.
    Johnson, A.E., Hebert, M.: Using spin images for efficient object recognition in cluttered 3D scenes. IEEE Trans. Pattern Anal. Mach. Intell. 21(5), 433–449 (1999)CrossRefGoogle Scholar
  13. 13.
    Juda, M., Mrozek, M., Brendel, P., Wagner, H., et al.: CAPD::RedHom (2010–2015).
  14. 14.
    Juda, M., Mrozek, M.: CAPD:RedHom v2 - homology software based on reduction algorithms. In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 160–166. Springer, Heidelberg (2014)Google Scholar
  15. 15.
    Li, C., Ovsjanikov, M., Chazal, F.: Persistence-based structural recognition. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2003–2010. IEEE (2014)Google Scholar
  16. 16.
    López, V., Fernández, A., García, S., Palade, V., Herrera, F.: An insight into classification with imbalanced data: Empirical results and current trends on using data intrinsic characteristics. Inf. Sci. 250, 113–141 (2013)CrossRefGoogle Scholar
  17. 17.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)CrossRefGoogle Scholar
  18. 18.
    Ojala, T., Pietikäinen, M., Harwood, D.: A comparative study of texture measures with classification based on featured distributions. Pattern Recogn. 29(1), 51–59 (1996)CrossRefGoogle Scholar
  19. 19.
    Othmani, A., Lew Yan Voon, L., Stolz, C., Piboule, A.: Single tree species classification from terrestrial laser scanning data for forest inventory. Pattern Recogn. Lett. 34(16), 2144–2150 (2013)CrossRefGoogle Scholar
  20. 20.
    Poincaré, H.J.: Sur le probleme des trois corps et les équations de la dynamique. Acta Math. 13, 1–270 (1890)CrossRefGoogle Scholar
  21. 21.
    Poincaré, H.J.: Les méthodes nouvelles de la mécanique céleste. Gauthiers-Villars, Paris (1892, 1893, 1899)Google Scholar
  22. 22.
    Poincaré, H.J.: Analysis situs. J. Éc. Polytech., ser. 2 1, 1–123 (1895)Google Scholar
  23. 23.
    Reininghaus, J., Huber, S., Bauer, U., Kwitt, R.: A stable multi-scale kernel for topological machine learning (2014). arXiv preprint arXiv:1412.6821
  24. 24.
    Rusu, R.B., Marton, Z.C., Blodow, N., Beetz, M.: Persistent point feature histograms for 3D point clouds. In: Proceedings of the 10th International Conference on Intel Autonomous System (IAS-10), Baden-Baden, Germany, pp. 119–128 (2008)Google Scholar
  25. 25.
    Seiffert, C., Khoshgoftaar, T.M., Van Hulse, J., Napolitano, A.: Rusboost: A hybrid approach to alleviating class imbalance. IEEE Trans. Syst. Man Cybern. Part A: Syst. Hum. 40(1), 185–197 (2010)CrossRefGoogle Scholar
  26. 26.
    Vedaldi, A., Fulkerson, B.: Vlfeat: An open and portable library of computer vision algorithms. In: Proceedings of the International Conference on Multimedia, pp. 1469–1472. ACM (2010)Google Scholar
  27. 27.
    Wohlfeil, J., Strackenbrock, B., Kossyk, I.: Automated high resolution 3D reconstruction of cultural heritage using multi-scale sensor systems and semi-global matching. Int. Arch. Photogrammetry Remote Sens. Spat. Inf. Sci. XL-4 W 4, 37–43 (2013)CrossRefGoogle Scholar
  28. 28.
    Wu, C.: Towards linear-time incremental structure from motion. In: 2013 International Conference on 3DTV, pp. 127–134. IEEE (2013)Google Scholar
  29. 29.
    Zeppelzauer, M., Poier, G., Seidl, M., Reinbacher, C., Breiteneder, C., Bischof, H., Schulter, S.: Interactive segmentation of rock-art in high-resolution 3D reconstructions. In: 2015 Digital Heritage, vol. 2, pp. 37–44, September 2015. doi: 10.1109/DigitalHeritage.2015.7419450
  30. 30.
    Zeppelzauer, M., Seidl, M.: Efficient image-space extraction and representation of 3D surface topography. In: Proceedings of the IEEE International Conference on Image Processing (ICIP). IEEE, Quebec, Canada (2015).

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Media Computing Group, Institute of Creative Media TechnologiesSt. Poelten University of Applied SciencesSt. PoeltenAustria
  2. 2.The Institute of Computer Science and Computer Mathematics, Faculty of Mathematics and Computer ScienceJagiellonian UniversityKrakówPoland

Personalised recommendations