Feature correspondences using Morse Smale complex

  • 327 Accesses

  • 8 Citations


Establishing corresponding features on two non-rigidly deformed 3D surfaces is a challenging and well-studied problem in computer graphics. Unlike previous approaches that constrain the matching between feature pairs using isometry-invariant distance metrics, we constrain the matching using a discrete connectivity graph derived from the Morse–Smale complex of the Auto Diffusion Function. We observed that the graph remains stable even for surfaces differing by topology or by significant deformation. This algorithm is simple to implement and efficient to run. When tested on a range of examples, our algorithm produces comparable results with state-of-art methods on surfaces with strong isometry but with greatly improved efficiency, and often gets better correspondences on surfaces with larger shape variances.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 199

This is the net price. Taxes to be calculated in checkout.

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
Fig. 14
Fig. 15


  1. 1.

    Anguelov, D., Srinivasan, P., Pang, C.H., Koller, D.: The correlated correspondence algorithm for unsupervised registration of nonrigid surfaces. In: NIPS (2004)

  2. 2.

    Bommes, D., Zimmer, H., Kobbelt, L.: Mixed-integer quadrangulation. In: ACM SIGGRAPH 2009 papers, SIGGRAPH ’09, pp. 77:1–77:10. ACM, New York (2009)

  3. 3.

    Boyer, E., Bronstein, A.M., Bronstein, M.M., Bustos, B., Darom, T., Horaud, R., Hotz, I., Keller, Y., Keustermans, J., Kovnatsky, A., Litman, R., Reininghaus, J., Sipiran, I., Smeets, D., Suetens, P., Vandermeulen, D., Zaharescu, A., Zobel, V.: Shrec 2011: robust feature detection and description benchmark. In: Proc. Workshop on 3D Object Retrieval (3DOR’11) (2011)

  4. 4.

    Bremer, P.T., Edelsbrunner, H., Hamann, B., Pascucci, V.: A topological hierarchy for functions on triangulated surfaces. IEEE Trans. Vis. Comput. Graph. 10, 2004 (2004)

  5. 5.

    Bronstein, A., Bronstein, M., Bustos, B., Castellani, U., Crisani, M., Falcidieno, B., Guibas, L., Kokkinos, I., Murino, V., Sipiran, I., Ovsjanikovy, M., Patan, G., Spagnuolo, M., Sun, J.: Shrec 2010: robust feature detection and description benchmark. In: Eurographics 2010 Workshop on 3D Object Retrieval (3DOR’10), pp. 79–86. Eurographics Association, Aire-la-Ville (2010)

  6. 6.

    Bronstein, A.M., Bronstein, M.M., Kimmel, R., Mahmoudi, M., Sapiro, G.: A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching. Int. J. Comput. Vis. 89, 266–286 (2010)

  7. 7.

    Bronstein, M.M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: CVPR, pp. 1704–1711. IEEE, New York (2010)

  8. 8.

    Coifman, R.R., Lafon, S.: Diffusion maps. Appl. Comput. Harmon. Anal. 21(1), 5–30 (2006). Diffusion Maps and Wavelets

  9. 9.

    Dong, S., Bremer, P.T., Garland, M., Pascucci, V., Hart, J.C.: Spectral surface quadrangulation. ACM Trans. Graph. 25, 1057–1066 (2006)

  10. 10.

    Edelsbrunner, H., Harer, J., Zomorodian, A.: Hierarchical Morse complexes for piecewise linear 2-manifolds. In: Proceedings of the Seventeenth Annual Symposium on Computational Geometry, SCG ’01, pp. 70–79. ACM, New York (2001)

  11. 11.

    Gebal, K., Baerentzen, J.A., Aanaes, H., Larsen, R.: Shape analysis using the auto diffusion function. In: Proceedings of the Symposium on Geometry Processing, SGP ’09, pp. 1405–1413. Eurographics Association, Aire-la-Ville (2009)

  12. 12.

    Giorgi, D., Biasotti, S., Paraboschi, L.: Shape retrieval contest 2007: Watertight models track (2007).

  13. 13.

    Huang, Q.X., Adams, B., Wicke, M., Guibas, L.J.: Non-rigid registration under isometric deformations. In: Proceedings of the Symposium on Geometry Processing, SGP ’08, pp. 1449–1457. Eurographics Association, Aire-la-Ville (2008)

  14. 14.

    Jain, V., Zhang, H.: A spectral approach to shape-based retrieval of articulated 3d models. Comput. Aided Des. 39, 398–407 (2007)

  15. 15.

    Kim, V., Lipman, Y., Chen, X., Funkhouser, T.: Mobius transformations for global intrinsic symmetry analysis. Comput. Graph. Forum (Symposium on Geometry Processing) 29(5) (2010)

  16. 16.

    Kim, V.G., Lipman, Y., Funkhouser, T.: Blended intrinsic maps. Trans. Graph. (Proc. of SIGGRAPH 2011) (2011)

  17. 17.

    Leordeanu, M., Hebert, M.: A spectral technique for correspondence problems using pairwise constraints. In: ICCV ’05: Proceedings of the Tenth IEEE International Conference on Computer Vision, pp. 1482–1489. IEEE Computer Society, Washington (2005)

  18. 18.

    Lipman, Y., Funkhouser, T.: Möbius voting for surface correspondence. ACM Trans. Graph. 28(3), 1–12 (2009)

  19. 19.

    Milnor, J.: Morse Theory. Princeton Univ. Press, Princeton (1963)

  20. 20.

    Ovsjanikov, M., Mérigot, Q., Mémoli, F., Guibas, L.: One point isometric matching with the heat kernel. Comput. Graph. Forum 29(5), 1555–1564 (2010)

  21. 21.

    Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Inc., Upper Saddle River (1982)

  22. 22.

    Praun, E., Sweldens, W., Schröder, P.: Consistent mesh parameterizations. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’01, pp. 179–184. ACM, New York (2001).

  23. 23.

    Reuter, M.: Hierarchical shape segmentation and registration via topological features of Laplace-Beltrami eigenfunctions. Int. J. Comput. Vis. 89, 287–308 (2010). doi:10.1007/s11263-009-0278-1

  24. 24.

    Ruggeri, M.R., Patanè, G., Spagnuolo, M., Saupe, D.: Spectral-driven isometry-invariant matching of 3d shapes. Int. J. Comput. Vis. 89, 248–265 (2010)

  25. 25.

    Rustamov, R.M.: Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of the fifth Eurographics Symposium on Geometry Processing, pp. 225–233. Eurographics Association, Aire-la-Ville (2007)

  26. 26.

    Sharma, A., Horaud, R.P.: Shape matching based on diffusion embedding and on mutual isometric consistency. In: Workshop on Nonrigid Shape Analysis and Deformable Image Alignment, NORDIA 2010, June, 2010, pp. 29–36. IEEE, San Francisco, Etats-Unis (2010)

  27. 27.

    Sun, J., Ovsjanikov, M., Guibas, L.: A concise and provably informative multi-scale signature based on heat diffusion. In: Proceedings of the Symposium on Geometry Processing, SGP ’09, pp. 1383–1392. Eurographics Association, Aire-la-Ville (2009)

  28. 28.

    Sun, J., Chen, X., Funkhouser, T.: Fuzzy geodesics and consistent sparse correspondences for deformable shapes. Comput. Graph. Forum (Symposium on Geometry Processing) 29(5) (2010)

  29. 29.

    Tevs, A., Berner, A., Wand, M., Ihrke, I., Seidel, H.P.: Intrinsic shape matching by planned landmark sampling. Comput. Graph. Forum 30, 543–552 (2011)

  30. 30.

    van Kaick, O., Zhang, H., Hamarneh, G., Cohen-Or, D.: A survey on shape correspondence. In: Proc. of Eurographics State-of-the-Art Report, pp. 1–22 (2010)

  31. 31.

    Weinkauf, T., Gingold, Y.I., Sorkine, O.: Topology-based smoothing of 2d scalar fields with c1-continuity. Comput. Graph. Forum 29(3), 1221–1230 (2010)

  32. 32.

    Zeng, Y., Gu, X., Samaras, D., Wang, C., Wang, Y., Paragios, N., Galen, E., de France, I.S.I.: Dense non-rigid surface registration using high-order graph matching. In: CVPR (2010)

  33. 33.

    Zhang, H., Sheffer, A., Cohen-Or, D., Zhou, Q., van Kaick, O., Tagliasacchi, A.: Deformation-driven shape correspondence. In: Proceedings of the Symposium on Geometry Processing, SGP ’08, pp. 1431–1439. Eurographics Association, Aire-la-Ville (2008)

Download references

Author information

Correspondence to Wei Feng.

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

(AVI 34.8 MB)

(AVI 34.8 MB)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Feng, W., Huang, J., Ju, T. et al. Feature correspondences using Morse Smale complex. Vis Comput 29, 53–67 (2013).

Download citation


  • Point matching
  • Correspondence
  • Morse–Smale complex