Skip to main content
SpringerLink
Log in

Bernoulli Embedding Model and Its Application in Texture Mapping

  • Virtual Reality
  • Published:
Journal of Computer Science and Technology Aims and scope Submit manuscript

Abstract

A novel texture mapping technique is proposed based on nonlinear dimension reduction, called Bernoulli logistic embedding (BLE). Our probabilistic embedding model builds texture mapping with minimal shearing effects. A log-likelihood function, related to the Bregman distance, is used to measure the similarity between two related matrices defined over the spaces before and after embedding. Low-dimensional embeddings can then be obtained through minimizing this function by a fast block relaxation algorithm. To achieve better quality of texture mapping, the embedded results are adopted as initial values for mapping enhancement by stretch-minimizing. Our method can be applied to both complex mesh surfaces and dense point clouds.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cox T, Cox M. Multidimensional Scaling. Second Edition, Chapman & Hall/CRC, 2000.

  2. Roweis S, Saul L. Nonlinear dimensionality reduction by locally linear embedding. Science, 2000, 290(22): 2323–2326.

    Google Scholar 

  3. J Tenenbaum, V de Silva, J Langford. A global geometric framework for nonlinear dimensionality reduction. Science, 2000, 290(22): 2319–2323.

    Google Scholar 

  4. Belkin M, Niyogi P. Laplacian eigenmaps and spectral techniques for embedding and clustering. In Proc. Neural Information Processing Systems Conference, Vancouver, Canada, 2001, pp.585–591.

  5. Brand M, Huang K. A unifying theorem for spectral embedding and clustering. In Proc. the 9th Int. Conf. Artificial Intelligence and Statistics, Key West, Florida, 2003.

  6. Brand M. Continuous nonlinear dimensionality reduction by kernel eigenmaps. In Proc. 8th International Joint Conf. Artificial Intelligence, Acapulco, Mexico, 2003, pp.547–554.

  7. Weiss Y. Segmentation using eigenvectors: A unifying view. In Proc. Int. Conf. Computer Vision, Kerkyra, Corfu, Greece, 1999, pp.975–982.

  8. Hinton G, Roweis S. Stochastic neighbor embedding. In Proc. Neural Information Processing Systems Conference, Vancouver and Whistler, BC, Canada, 2003, pp.833–840.

  9. Dekel O, Singer Y. Multiclass learning by probabilistic embeddings. In Proc. Neural Information Processing Systems Conference, Vancouver, BC, Canada, 2002, pp.945–952.

  10. Szummer M, Jaakkola T. Partially labeled classification with Markov random walks. In Proc. Neural Information Processing Systems Conference, Vancouver, BC, Canada, 2001, pp.945–952.

  11. Floater M. Parameterization and smooth approximation of surface triangulations. Computer Aided Geometric Design, 1997, 14: 231–250.

    MATH  MathSciNet  Google Scholar 

  12. Floater M. Mean value coordinates. Computer Aided Geometric Design, 2003, 20: 19–27.

    Article  MATH  MathSciNet  Google Scholar 

  13. Eck M, DeRose T, Duchamp T, Hoppe H, Lounsbery M, Stuetzle W. Multiresolution analysis of arbitrary meshes. In Proc. SIGGRAPH, Los Angeles, CA, USA, 1995, pp.173–182.

  14. Levy B, Mallet J-L. Non-distortion texture mapping for sheared triangulated meshes. In Proc. SIGGRAPH, Orlando, FL, USA, 1998, pp.343–352.

  15. Desbrun M, Meyer M, Alliez P. Intrinsic parameterization of surface meshes. In Proc. Eurographics, Saarbruecken, Germany, 2002, pp.209–218.

  16. Zigelman G, Kimmel R, Kiryati N. Texture mapping using surface flattening via multidimensional scaling. IEEE Trans. Visualization and Computer Graphics, 2002, 8: 198–207.

    Google Scholar 

  17. Zhou K, Synder J, Guo B, Shum H-Y. Iso-charts: Stretch-driven mesh parameterization using spectral analysis. In Proc. Eurographics Symposium on Geometry Processing, Nice, France, 2004, pp.45–54.

  18. Dempster A, Laird N, Rubin D. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 1977, 39(1): 1–38.

    MathSciNet  Google Scholar 

  19. Borg I, Groenen P. Modern Multidimensional Scaling. New York: Springer-Verlag, 1997.

    Google Scholar 

  20. Becker M, Yang I, Lange K. EM algorithms without missing data. Statistical Methods in Medical Research, 1997, pp.38–54.

  21. J de Leeuw. Block Relaxation Algorithms in Statistics. Information Systems and Data Analysis, Bock H H, Lenski W, Richter M M (eds.), Berlin: Springer-Verlag, 1994, pp.308–325.

    Google Scholar 

  22. Böhning D, Lindsay B. Monotonicity of quadratic-approximation algorithms. Annals of the Institute of Statistical Mathematics, 1988, 40: 641–663.

    Article  MathSciNet  Google Scholar 

  23. Böhning D. Multinomial logistic regression algorithm. Annals of the Institute of Statistical Mathematics, 1992, 44: 197–200.

    Article  MATH  MathSciNet  Google Scholar 

  24. Collins M, Schapire R, Singer Y. Logistic regression, Adaboost and Bregman distances. Machine Learning, 2002, 48(1-3): 253–285.

    Google Scholar 

  25. Young D. Iterative Solution of Large Linear Systems. Orlando, Florida: Academic Press, Inc., 1971.

    Google Scholar 

  26. Salakhutdinov R, Roweis S. Adaptive overrelaxed bound optimization methods. In Proc. the 20th Int. Conf. Machine Learning, Washington DC, USA, 2003, pp.664–671.

  27. Salakhutdinov R, Roweis S, Ghahramani Z. On the convergence of bound optimization algorithms. In Proc. Uncertainty in Artificial Intelligence, Acapulco, Mexico, 2003, pp.509–516.

  28. Kimmel R, Sethian J. Computing geodesics on manifolds. In Proc. National Academy of Sciences, USA, 1998, pp.8431–8435.

  29. Sander P, Snyder J, Gortler S, Hoppe H. Texture mapping progressive meshes. In Proc. SIGGRAPH, Los Angeles, CA, USA, 2001, pp.409–416.

  30. Sander P, Wood Z, Gortler S, Snyder J, Hoppe H. Multi-chart geometry images. In Proc. Symposium on Geometry Processing, Aachen, Germany, 2003, pp.146–155.

  31. Wang G, Zhao H, Zhang Z, Lochovsky H. A Bernoulli relational mode for nonlinear embedding. In Proc. IEEE Int. Conf. Data Mining, Houston, Texas, USA, 2005, pp.458–465.

Download references

Author information

Authors and Affiliations

  1. State Key Lab of CAD&CG, Zhejiang University, Hangzhou, 310027, P.R. China

    Hong-Xin Zhang, Ying Tang & Hu-Jun Bao

  2. Automation Department, Xi'an Jiaotong University, Xi'an, 710049, P.R. China

    Hui Zhao

Authors
  1. Hong-Xin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hui Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hu-Jun Bao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hong-Xin Zhang.

Additional information

A preliminary version of this paper appeared in Proc. the 1st Korea-China Joint Conference on Geometric and Visual Computing.

This work is supported in part by the National Basic Research 973 Program of China (Grant No.2002CB312102) and the National Natural Science Foundation of China (Grant Nos. 60021201, 60505001 and 60133020).

Hong-Xin Zhang is an assistant professor of the state key laboratory of CAD&CG at Zhejiang University, P.R. China. He received his BS. and Ph.D. degrees in applied mathematics from Zhejiang University. His research interests include geometric modeling, texture synthesis and machine learning.

Ying Tang is now a post-doctoral researcher in the Computer Science Department at Hong Kong University of Science and technology. Her research interests mainly focus on mesh parameterization, texture synthesis, texture compression and visualization. She received a B.S. degree in 1999, and a Ph.D. degree in 2005, all from Zhejiang University, China.

Hui Zhao is a lecturer of Department of Automatization Science & Technology, Xi’an Jiaotong University. She is also a Ph D. candidate of Xi’an Jiaotong University in control theory. Her research interests are computer control, image processing, data mining, etc.

Hu-Jun Bao is a professor of the State Key Laboratory of CAD&CG at Zhejiang University, P.R. China. He received his M.Sc. and Ph.D. degrees in applied mathematics from Zhejiang University. His research interests include computer graphics, geometric modeling and virtual reality.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, HX., Tang, Y., Zhao, H. et al. Bernoulli Embedding Model and Its Application in Texture Mapping. J Comput Sci Technol 21, 199–203 (2006). https://doi.org/10.1007/s11390-006-0199-1

Download citation

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11390-006-0199-1

Keywords

Search

Navigation