Skip to main content

Advertisement

Springer Nature Link
Log in

Geometry completion and detail generation by texture synthesis

  • original article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

We present a novel method for patching holes in polygonal meshes and synthesizing surfaces with details based on existing geometry. The most novel feature of our proposed method is that we transform the 3D geometry synthesis problem into a 2D domain by parameterizing surfaces and solve this problem in that domain. We then derive local geometry gradient images that encode intrinsic local geometry properties, which are invariant to object translation and rotation. The 3D geometry of holes is then reconstructed from synthesized local gradient images. This method can be extended to execute other mesh editing operations such as geometry detail transfer or synthesis. The resulting major benefits of performing geometry synthesis in 2D are more flexible and robust control, better leveraging of the wealth of current 2D image completion methods, and greater efficiency.

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

Access this article

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

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

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Alliez, P., Meyer, M., Desbrun, M.: Interactive geometry remeshing. In: SIGGRAPH ’02: Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques, pp. 347–354. ACM Press, New York (2002)

  2. Ashikhmin, M.: Synthesizing natural textures. In: SI3D ’01: Proceedings of the 2001 Symposium on Interactive 3D Graphics, pp. 217–226. ACM Press, New York (2001)

  3. Bertalmio, M., Sapiro, G., Caselles, V., Ballester, C.: Image inpainting. In: SIGGRAPH ’00: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, pp. 417–424. ACM Press/Addison-Wesley, New York (2000)

  4. Bhat, P., Ingram, S., Turk, G.: Geometric texture synthesis by example. In: SGP ’04: Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 41–44. ACM Press, New York (2004)

  5. do Carmo, M.P.: Differential geometry of curves and surfaces. Prentice-Hall, Englewood Cliffs, NJ (1976)

  6. Davis, J., Stephen, Marschner, R., Garr, M., Levoy, M.: Filling holes in complex surfaces using volumetric diffusion. In: 1st International Symposium on 3D Data Processing, Visualization, and Transmission, pp. 428–438 (2002)

  7. de Berg, M., van Kerveld, M., Overmars, M.: Computational Geometry: Algorithms and Applications, 1st edn. Springer, Berlin Heidelberg New York (1997)

  8. Desbrun, M., Meyer, M., Alliez, P.: Intrinsic parameterizations of surface meshes. In: Proceedings of Eurographics, 21(3), 209–218 (2002)

  9. Efros, A.A., Freeman, W.T.: Image quilting for texture synthesis and transfer. In: SIGGRAPH ’01: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, pp. 341–346. ACM Press, New York (2001)

  10. Fattal, R., Lischinski, D., Werman, M.: Gradient domain high dynamic range compression. In: SIGGRAPH ’02: Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques, pp. 249–256. ACM Press, New York (2002)

  11. Funkhouser, T., Kazhdan, M., Shilane, P., Min, P., Kiefer, W., Tal, A., Rusinkiewicz, S., Dobkin, D.: Modeling by example. ACM Trans. Graph. 23(3), 652–663 (2004)

    Google Scholar 

  12. Gu, X., Gortler, S.J., Hoppe, H.: Geometry images. In: SIGGRAPH ’02: Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques, pp. 355–361. ACM Press, New York (2002)

  13. Gu, X., Wang, Y., Chan, T., Thompson, P., Yau, S.T.: Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans. Med. Imag. 23(7), 949–958 (2004)

    Google Scholar 

  14. Gu, X., Yau, S.T.: Global conformal surface parameterization. In: SGP ’03: Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing, pp. 127–137. Eurographics Association, Aire-la-Ville, Switzerland (2003)

  15. Haeberli, P.: Paint by numbers: Abstract image representations. In: SIGGRAPH ’90: Proceedings of the 17th Annual Conference on Computer Graphics and Interactive Techniques, pp. 207–214. ACM Press, New York (1990)

  16. Hertzmann, A., Jacobs, C.E., Oliver, N., Curless, B., Salesin, D.H.: Image analogies. In: SIGGRAPH ’01: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, pp. 327–340. ACM Press, New York (2001)

  17. Jin, M., Wang, Y., Yau, S.T., Gu, X.: Optimal global conformal surface parameterization. In: IEEE Visualization, pp. 267–274 (2004)

  18. Ju, T.: Robust repair of polygonal models. ACM Trans. Graph. 23(3), 888–895 (2004)

    Google Scholar 

  19. Lai, Y.K., Hu, S.M., Gu, D.X., Martin, R.: Geometric texture synthesis and transfer via geometry images. In: SPM ’05: Proceedings of the 2005 ACM symposium on Solid and Physical Modeling, pp. 15–26. ACM Press, New York (2005)

  20. Levy, B.: Dual domain extrapolation. ACM Trans. Graph. 22(3), 364–369 (2003)

    Google Scholar 

  21. Levy, B., Petitjean, S., Ray, N., Maillot, J.: Least squares conformal maps for automatic texture atlas generation. ACM Trans. Graph. 21(3), 362–371 (2002)

    Google Scholar 

  22. Liang, L., Liu, C., Xu, Y.Q., Guo, B., Shum, H.Y.: Real-time texture synthesis by patch-based sampling. ACM Trans. Graph. 20(3), 127–150 (2001)

    Google Scholar 

  23. Liepa, P.: Filling holes in meshes. In: SGP ’03: Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 200–205. Eurographics Association, Aire-la-Ville, Switzerland (2003)

  24. Ostromoukhov, V., Donohue, C., Jodoin, P.M.: Fast hierarchical importance sampling with blue noise properties. ACM Trans. Graph. 23(3), 488–495 (2004)

    Google Scholar 

  25. Pfeifle, R., Seidel, H.P.: Triangular B-splines for blending and filling of polygonal holes. In: Proceedings of the Conference on Graphics Interface ’96, pp. 186–193 (1996)

  26. Saad, Y.: Iterative Methods for Sparse Linear Systems. Society for Industrial and Applied Mathematics, Philadelphia (2003)

  27. Sharf, A., Alexa, M., Cohen-Or, D.: Context-based surface completion. ACM Trans. Graph. 23(3), 878–887 (2004)

    Google Scholar 

  28. Shewchuk, J.R.: Delaunay refinement algorithms for triangular mesh generation. Comput. Geom. Theory Appl. 22(1–3), 21–74 (2002). http://www-2.cs.cmu.edu/∼quake/triangle.html

    Google Scholar 

  29. Taubin, G.: Estimating the tensor of curvature of a surface from a polyhedral approximation. In: ICCV ’95: Proceedings of the 5th International Conference on Computer Vision, p. 902. IEEE Press, Washington, DC (1995)

  30. Verdera, J., Caselles, V., Bertalmio, M., Sapiro, G.: Inpainting surface holes. In: Proceedings of the International Conference on Image Processing, pp. 903–906 (2003)

  31. Wei, L.Y., Levoy, M.: Fast texture synthesis using tree-structured vector quantization. In: SIGGRAPH ’00: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, pp. 479–488. ACM Press/Addison-Wesley, New York (2000)

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota at Twin Cities, 200 Union Street SE, Minneapolis, MN, 55455, USA

    Minh X. Nguyen, Xiaoru Yuan & Baoquan Chen

Authors
  1. Minh X. Nguyen
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Xiaoru Yuan
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Baoquan Chen
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Minh X. Nguyen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nguyen, M., Yuan, X. & Chen, B. Geometry completion and detail generation by texture synthesis. Visual Comput 21, 669–678 (2005). https://doi.org/10.1007/s00371-005-0315-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-005-0315-1

Keywords