Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3757))

  • 1990 Accesses

Abstract

A general algorithm framework for 3D mesh parametrization is proposed in this paper. Under this framework, a parametrization algorithm is divided into three steps. In the first step, the linearly reconstructing weights of each vertex with respect to its neighbours are computed. These weights are then used to computed a initial parametrization mesh, and in the third step, this initial mesh is rotated and scaled to obtain a parametrization mesh with high isometric precision. Four parametrization algorithms are proposed based on this framework. Examples show the effectiveness and applicability of the parametrization algorithms proposed in the paper.

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

Access this chapter

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
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

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. Borg, I., Groenen, P.: Modern Multidimensional Scaling Theory and Application. Springer, Heidelberg (1997)

    Google Scholar 

  2. Floater, M.S.: Parametrization and smooth approximation of surface triangulations. Comp. Aided Geom. Design. 14, 231–250 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Floater, M.S.: Mean value coordinates. Comp. Aided Geom. Design 20, 19–27 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Floater, M.S., Hormann, K.: Surface parameterization: a tutorial and survey. In: Dodgson, N.A., Floater, M.S., Sabin, M.A. (eds.) Advances in Multiresolution for Geometric Modelling, pp. 157–186. Springer, Heidelberg (2004)

    Google Scholar 

  5. Praun, E., Hoppe, H.: Spherical parametrization and remeshing. ACM Trans. Graphics. 22, 340–349 (2003)

    Article  Google Scholar 

  6. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)

    Article  Google Scholar 

  7. Saul, L.K., Roweis, S.T.: An introduction to locally linear embedding. Technical report, AT & T Labs-Research (2000)

    Google Scholar 

  8. Saul, L.K., Roweis, S.T.: Think globally, fit locally: unsupervised learning of low dimensional manifolds. Journal of Machine Learning Research 4, 119–155 (2003)

    Article  MathSciNet  Google Scholar 

  9. Surazhsky, V., Gotsman, C.: Intrinsic morphing of compatible triangulations. Int. J. Shape Modelling. 9, 191–201 (2003)

    Article  MATH  Google Scholar 

  10. Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)

    Article  Google Scholar 

  11. Tutte, W.T.: How to draw a graph. Proc. London Math. Soc. 13, 743–768 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  12. Welch, W., Witkin, A.: Free-form shape design using triangulated surfaces. In: Computer Graphics, SIGGRAPH 1994, pp. 247–256 (1994)

    Google Scholar 

  13. Zigelman, G., Kimmel, R., Kiryati, N.: Texture mapping using surface flattening via multi-dimensional scaling. IEEE Trans. Visualization Comp. Graphics 8, 198–207 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sun, X., Hancock, E.R. (2005). Locally Linear Isometric Parameterization. In: Rangarajan, A., Vemuri, B., Yuille, A.L. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2005. Lecture Notes in Computer Science, vol 3757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11585978_36

Download citation

  • DOI: https://doi.org/10.1007/11585978_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30287-2

  • Online ISBN: 978-3-540-32098-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics