Skip to main content
Springer Nature Link
Log in

Harmonic Shape Images: A Representation for 3D Free-Form Surfaces Based on Energy Minimization

  • Conference paper
  • First Online:
Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1654))

  • 392 Accesses

Abstract

A new representation called Harmonic Shape Images for 3D free-form surfaces is proposed in this paper. This representation is based on the well-studied theory of Harmonic Maps which studies the mapping between different metric manifolds from the energyminimization point of view. The basic idea of Harmonic Shape Images is to map a 3D surface patch with disc topology to a 2D domain and encode the shape information of the surface patch into the 2D image. Due to the application of harmonic maps in generating Harmonic Shape Images, Harmonic Shape Images have the following advantages: they preserve both the shape and the continuity of the underlying surfaces, they are robust to occlusion and they are independent of surface sampling strategy. The proposed representation is applied to solve the surface-registration problem. Experiments have been conducted on real data and results are presented in the paper.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Y. Xin: Geometry of Harmonic Maps. Birkhauser, 1996

    Google Scholar 

  2. J. Eells and L.H, Sampson: Harmonic Mappings of Riemannian Manifords. Amer. J. Math., 86:109–160, 1964

    Article  MATH  MathSciNet  Google Scholar 

  3. B. O’Neill: Elementary differential geometry. Academic Press, Inc., 1996

    Google Scholar 

  4. M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle,: Multi-resolution Analysis of Arbitrary Meshes. Proc. SIGGRAPH.96, 325–334

    Google Scholar 

  5. B. K. P. Horn: Extended Gaussian Image. Proc. IEEE, vol. 72, pp. 1671–1686, 1984

    Article  Google Scholar 

  6. M. Hebert, K. Ikeuchi and H. Delingette,: A Spherical Representation for Recognition of Free-form Surfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, No.7, pp. 681–689, 1995

    Article  Google Scholar 

  7. K. Higuchi, M. Hebert and K. Ikeuchi: Building 3D Models from Unregistered Range Images. CVGIP-Image Understanding, vol. 57, No.4, 1995

    Google Scholar 

  8. D. Zhang, M. Hebert: Multi-scale Classification of 3D Objects. Proc. CVPR’97, pp. 864–869

    Google Scholar 

  9. D. Zhang, M. Hebert, A. Johnson and Y. Liu: On Generating Multi-resolution Representations of Polygonal Meshes. Proc. ICCV’98 Workshop on Modelbased 3-D Image Analysis, Jan. 3, 1998, Bombay, India

    Google Scholar 

  10. O. D. Faugeras and M. Hebert: The Representation, Recognition And Locating of 3-D Objects. Int’l J. of Robotics Research, vol. 5, No. 3, pp. 27–52, 1986.

    Article  Google Scholar 

  11. C. Dorai, A. Jain: COSMOS-A Representation Scheme for 3D Free-form Objects. IEEE Transaction Pattern on Pattern Analysis and Machine Intelligence, vol. 19, No. 10: pp.1115–1130, 1997.

    Article  Google Scholar 

  12. P. J. Besl: Triangles as A Primary Representation. Object Representation in Computer Vision, M. Hebert, J. Ponce, T. Boult and A. Gross, eds., Berlin, Springer-Verlag, pp.191–206, 1995.

    Google Scholar 

  13. T. Joshi, J. Ponce, B. Vijayakumar and D.J. Kriegman: HOT Curves for Modeling and Recognition of Smooth Curved 3D Objects. Proc. CVPR.94, pp.876–880, 1994

    Google Scholar 

  14. F. Stein and G. Medioni: Structural Indexing: Efficient 3-D Object Recognition, IEEE Transactions Pattern on Pattern Analysis and Machine Intelligence, vol. 14, No. 2: pp.125–145, 1992.

    Article  Google Scholar 

  15. D. Keren, K. Cooper and J. Subrahmonia: Describing Complicated Objects by Implicit Polynomials. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, No.1, pp. 38–53, 1994

    Article  Google Scholar 

  16. A. Johnson and M. Hebert: Efficient Multiple Model Recognition in Cluttered 3-D Scenes. CVPR’ 98, pp. 671–677

    Google Scholar 

  17. C. S. Chua and R. Jarvis: 3D Free-form Surface Registration and Object Recognition. Int’l J. of Computer Vision, vol. 17, pp.77-99, 1996

    Google Scholar 

  18. P. J. Besl: The Free-form Surface Matching Problem. Machine Vision for Threedimensional Scenes. H. Freeman, ed., Academic Press, pp.25–71, 1990

    Google Scholar 

  19. P. J. Besl and N.D. Mckay: A Method for Registration of 3-D Shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, No. 2, pp.239–256, 1992

    Article  Google Scholar 

  20. Y. Chen and G. Medioni: Object Modeling by Registration of Multiple Range Images. Image Vision Computing, vol. 10, No. 3, pp.145–155, 1992

    Article  Google Scholar 

  21. R. Bergevin, D. Laurendeau and D. Poussart: Estimating The 3D Rigid Transformation between Two Range Views of A Complex Object. Proc. 11th IAPR, Int’l Conf. Patt. Recog., The Hague, The Netherlands, pp. 478–482, Aug. 30-Sep. 3, 1992

    Google Scholar 

  22. J. Deovre: Probability and statistics for engineering and science. Brooks/Cole, Belmont, CA, 1987

    Google Scholar 

  23. D. Zhang and M. Hebert: Harmonic Maps and Their Applications in Surface Matching. To appear in CVPR.99

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, 15213

    Dongmei Zhang & Martial Hebert

Authors
  1. Dongmei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martial Hebert
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of York, York, Y01 5DD, UK

    Edwin R. Hancock

  2. Dipartimento di Informatica, Università Ca’ Foscari di Venezia, Via Torino 155, I-30172, Venezia Mestre, Italy

    Marcello Pelillo

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhang, D., Hebert, M. (1999). Harmonic Shape Images: A Representation for 3D Free-Form Surfaces Based on Energy Minimization. In: Hancock, E.R., Pelillo, M. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 1999. Lecture Notes in Computer Science, vol 1654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48432-9_3

Download citation

  • DOI: https://doi.org/10.1007/3-540-48432-9_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66294-5

  • Online ISBN: 978-3-540-48432-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics