Skip to main content
Springer Nature Link
Log in

Stable Semi-local Features for Non-rigid Shapes

  • Chapter
  • First Online:
Innovations for Shape Analysis

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

  • 3205 Accesses

Abstract

Feature-based analysis is becoming a very popular approach for geometric shape analysis. Following the success of this approach in image analysis, there is a growing interest in finding analogous methods in the 3D world. Maximally stable component detection is a low computation cost and high repeatability method for feature detection in images.In this study, a diffusion-geometry based framework for stable component detection is presented, which can be used for geometric feature detection in deformable shapes.The vast majority of studies of deformable 3D shapes models them as the two-dimensional boundary of the volume of the shape. Recent works have shown that a volumetric shape model is advantageous in numerous ways as it better captures the natural behavior of non-rigid deformations. We show that our framework easily adapts to this volumetric approach, and even demonstrates superior performance.A quantitative evaluation of our methods on the SHREC’10 and SHREC’11 feature detection benchmarks as well as qualitative tests on the SCAPE dataset show its potential as a source of high-quality features. Examples demonstrating the drawbacks of surface stable components and the advantage of their volumetric counterparts are also presented.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    In this evaluation we used SHREC11, rather than SHREC10 that was used previously in 2D. this is due to the fact that results of the 3D and 2D versions were too similar on SHREC10, and dataset with a wider, and more challenging range and strength of transformations was needed to emphasize the difference.

References

  1. Anguelov, D., Srinivasan, P., Koller, D., Thrun, S., Rodgers, J., Davis, J.: SCAPE: shape completion and animation of people. TOG 24(3), 408–416 (2005)

    Article  Google Scholar 

  2. Aubry, M., Schlickewei, U., Cremers, D.: The wave kernel signature-a quantum mechanical approach to shape analyis. In: Proceedings of the CVPR, Colorado Springs (2011)

    Google Scholar 

  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 ’11: Robust feature detection and description benchmark. In: Proceedings of the 3DOR, Llandudno, pp. 71–78 (2011)

    Google Scholar 

  4. Bronstein, M.M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: Computer Vision and Pattern Recognition, San Francisco, pp. 1704–1711 (2010)

    Google Scholar 

  5. Bronstein, A., Bronstein, M.M., Bronstein, M., Kimmel, R.: Numerical Geometry of Non-rigid Shapes. Springer, New York (2008)

    MATH  Google Scholar 

  6. Bronstein, A., Bronstein, M.M., Bustos, B., Castellani, U., Crisani, M., Falcidieno, B., Guibas, L.J., Kokkinos, I., Murino, V., Ovsjanikov, M., et al.: SHREC 2010: robust feature detection and description benchmark. In: Eurographics Workshop on 3D Object Retrieval (2010)

    Google Scholar 

  7. Chazal, F., Guibas, L.J., Oudot, S.Y., Skraba, P.: Persistence-based clustering in riemannian manifolds. Research Report RR-6968, INRIA (2009)

    Google Scholar 

  8. Coifman, R.R., Lafon, S.: Diffusion maps. Appl. Comput. Harmonic Anal. 21(1), 5–30 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Couprie, M., Bertrand, G.: Topological grayscale watershed transformation. In: SPIE Vision Geometry V Proceedings, San Diego, vol. 3168, pp. 136–146 (1997)

    Google Scholar 

  10. Dey, T.K., Li, K., Luo, C., Ranjan, P., Safa, I., Wang, Y.: Persistent heat signature for pose-oblivious matching of incomplete models. Comput. Graph. Forum 29(5), 1545–1554 (2010)

    Article  Google Scholar 

  11. Digne, J., Morel, J.-M., Audfray, N., Mehdi-Souzani, C.: The level set tree on meshes. In: Proceedings of the Fifth International Symposium on 3D Data Processing, Visualization and Transmission, Paris (2010)

    Google Scholar 

  12. Donoser, M., Bischof, H.: 3d segmentation by maximally stable volumes (msvs). In: Proceedings of the 18th International Conference on Pattern Recognition, vol. 1, pp. 63–66. IEEE Computer Society, Los Alamitos (2006)

    Google Scholar 

  13. Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discret.Comput. Geom. 28(4), 511–533 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Floater, M.S., Hormann, K.: Surface parameterization: a tutorial and survey. In: Advances in Multiresolution for Geometric Modelling, vol. 1, pp. 157–186. Springer, Berlin (2005)

    Google Scholar 

  15. Forssen, P.E.: Maximally stable colour regions for recognition and matching. In: Proceedings of the CVPR, Minneapolis, pp. 1–8 (2007)

    Google Scholar 

  16. Huang, Q.X., Flöry, S., Gelfand, N., Hofer, M., Pottmann, H.: Reassembling fractured objects by geometric matching. ACM Trans. Graph. 25(3), 569–578 (2006)

    Article  Google Scholar 

  17. Johnson, A.E., Hebert, M.: Using spin images for efficient object recognition in cluttered 3D scenes. Trans. PAMI 21(5), 433–449 (1999)

    Article  Google Scholar 

  18. Kimmel, R., Zhang, C., Bronstein, A.M., Bronstein, M.M.: Are mser features really interesting? IEEE Trans. PAMI 33(11), 2316–2320 (2011)

    Article  Google Scholar 

  19. Levy, B.: Laplace-Beltrami eigenfunctions towards an algorithm that understands geometry. In: Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006, pp. 13. IEEE Computer Society, Los Alamitos (2006)

    Google Scholar 

  20. Litman, R., Bronstein, A.M., Bronstein, M.M.: Diffusion-geometric maximally stable component detection in deformable shapes. Comput. Graph. 35, 549–560 (2011)

    Article  Google Scholar 

  21. Lowe, D.: Distinctive image features from scale-invariant keypoint. IJCV 60(2), 91–110 (2004)

    Article  Google Scholar 

  22. Matas, J., Chum, O., Urban, M., Pajdla, T.: Robust wide-baseline stereo from maximally stable extremal regions. Image Vis. Comput. 22(10), 761–767 (2004)

    Article  Google Scholar 

  23. Meyer, M., Desbrun, M., Schroder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Visualization and Mathematics III, pp. 35–57. Springer, Berlin (2003)

    Google Scholar 

  24. Mikolajczyk, K., Tuytelaars, T., Schmid, C., Zisserman, A., Matas, J., Schaffalitzky, F., Kadir, T., Gool, L.V.: A comparison of affine region detectors. IJCV 65(1), 43–72 (2005)

    Article  Google Scholar 

  25. Najman, L., Couprie, M.: Building the component tree in quasi-linear time. IEEE Trans. Image Proc. 15(11), 3531–3539 (2006)

    Article  Google Scholar 

  26. Ovsjanikov, M., Sun, J., Guibas, L.: Global intrinsic symmetries of shapes. Comput. Graph. Forum 27(5), 1341–1348 (2008)

    Article  Google Scholar 

  27. Ovsjanikov, M., Bronstein, A.M., Bronstein, M.M., Guibas, L.J.: Shape google: a computer vision approach to isometry invariant shape retrieval. In: Computer Vision Workshops (ICCV Workshops), Kyoto, pp. 320–327 (2009)

    Google Scholar 

  28. Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Exp. Math. 2(1), 15–36 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  29. Raviv, D., Bronstein, M.M., Bronstein, A.M., Kimmel, R.: Volumetric heat kernel signatures. In: Proceedings of the ACM Workshop on 3D Object Retrieval, Firenze, pp. 39–44 (2010)

    Google Scholar 

  30. Reuter, M., Wolter, F.-E., Peinecke, N.: Laplace-spectra as fingerprints for shape matching. In: Proceedings of the ACM Symposium on Solid and Physical Modeling, Cambridge, pp. 101–106 (2005)

    Google Scholar 

  31. Rustamov, R.M.: Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of the SGP, Barcelona, pp. 225–233 (2007)

    Google Scholar 

  32. Sivic, J., Zisserman, A.: Video google: A text retrieval approach to object matching in videos. In: Proceedings of the CVPR, Madison, vol. 2, pp. 1470–1477 (2003)

    Google Scholar 

  33. Skraba, P. Ovsjanikov, M., Chazal, F., Guibas, L.: Persistence-based segmentation of deformable shapes. In: Proceedings of the NORDIA, San Francisco, pp. 45–52 (2010)

    Google Scholar 

  34. Sumner, R.W., Popović, J.: Deformation transfer for triangle meshes. ACM Transactions on Graphics (Proceedings of the SIGGRAPH), Los Angeles, vol. 23, pp. 399–405 (2004)

    Google Scholar 

  35. Sun, J., Ovsjanikov, M., Guibas, L.: A concise and provably informative multi-scale signature based on heat diffusion. Comput. Graph. Forum 28, 1383–1392 (2009)

    Article  Google Scholar 

  36. Thorstensen, N., Keriven, R.: Non-rigid shape matching using geometry and photometry. In: Computer Vision – ACCV 2009, Xi’an, vol. 5996, pp. 644–654 (2010)

    Google Scholar 

  37. Toldo, R., Castellani, U., Fusiello, A.: Visual vocabulary signature for 3d object retrieval and partial matching. In: Proceedings of the 3DOR, Munich, pp. 21–28 (2009)

    Google Scholar 

  38. Tuzel, O., Porikli, F., Meer, P.: Region covariance: a fast descriptor for detection and classification. In: Computer Vision ECCV 2006. Lecture Notes in Computer Science, vol. 3952, pp. 589–600. Springer, Berlin/Heidelberg (2006)

    Google Scholar 

  39. Vincent, L., Soille, P.: Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Trans. PAMI, 13(6), 583–598 (2002)

    Article  Google Scholar 

  40. Wardetzky, M., Mathur, S., Kaelberer, F., Grinspun, E.: Discrete laplace operators: no free lunch. In: Proceedings of the of Eurographics Symposium on Geometry Processing, Barcelona, pp. 33–37 (2007)

    Google Scholar 

  41. Zaharescu, A., Boyer, E., Varanasi, K., Horaud, R.: Surface feature detection and description with applications to mesh matching. In: Proceedings of the CVPR, Miami, pp. 373–380 (2009)

    Google Scholar 

Download references

Acknowledgements

We are grateful to Dan Raviv for providing us his volume rasterization and Laplacian disretization code. M. M. Bronstein is partially supported by the Swiss High-Performance and High-Productivity Computing (HP2C) grant. A. M. Bronstein is partially supported by the Israeli Science Foundation and the German-Israeli Foundation.

Author information

Authors and Affiliations

  1. School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel

    Roee Litman & Alexander M. Bronstein

  2. Institute of Computational Science, Faculty of Informatics, Universita della Svizzera Italiana, Lugano, Switzerland

    Michael M. Bronstein

Authors
  1. Roee Litman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander M. Bronstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael M. Bronstein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roee Litman .

Editor information

Editors and Affiliations

  1. , Inst. for Appl. Math.&Scient.Comp., Brandenburg Technical University, Platz der Deutschen Einheit 1, Cottbus, 03046, Germany

    Michael Breuß

  2. Department of Computer Science, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Alfred Bruckstein

  3. School of Electrical &, Computer Engineering, National Technical University of Athens, Athens, 15773, Greece

    Petros Maragos

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Litman, R., Bronstein, A.M., Bronstein, M.M. (2013). Stable Semi-local Features for Non-rigid Shapes. In: Breuß, M., Bruckstein, A., Maragos, P. (eds) Innovations for Shape Analysis. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34141-0_8

Download citation

Publish with us

Policies and ethics