Skip to main content
SpringerLink
Log in

How many sample points are sufficient for 3D model surface representation and accurate mesh simplification?

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

Growing of 3D model products and its applications in mobile devices and multimedia tools increases demands to establish an effective approach for representing and compressing of these models. In this paper, we propose an algorithm to simplify a complex 3D mesh and reduce the number of vertices by re-sampling the mesh based on the Nyquist theorem in order to find the sufficient number of samples that is necessary to save the quality of the reconstructed mesh, precisely. To achieve the optimum number of samples in the simplified mesh, both maximum curvature (Cmax) and minimum curvature (Cmin) in the original mesh are employed for adaptive sampling in different directions. Since the samples are adaptively taken regarding the curvature variations in both directions of maximum and minimum curvatures, the least number of vertices is obtained to represent the model. Hence, the method not only simplifies the complex mesh, but also preserves fine scale features in the mesh. The proposed method is applied to different complex mesh surfaces. The experimental results demonstrate that our proposed framework can represent a mesh surface with the least number of samples besides preserving important features in the surface.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

References

  1. Abdul J (1977) The Shannon sampling theorem—lts various extensions and applications. Proc IEEE 65(11):1565–1596

    Article  Google Scholar 

  2. Alliez P, Cohen-Steiner D, Devillers O, Lévy B, Desbrun M (2003) Anisotropic polygonal remeshing. ACM Trans Graph 22(3):485–493

    Article  Google Scholar 

  3. Bronstein AM, Bronstein MM, Kimmel R (2008) Numerical geometry of non-rigid shapes. Springer Science & Business Media

  4. Cai XT, He F, Li WD, Li XX, Wu YQ (2015) Encryption based partial sharing of CAD models. Integr Comput Aided Eng 22(3):243–260

    Article  Google Scholar 

  5. Chen HK (2017) Evaluation of triangular mesh layout techniques using large mesh simplification. Multimed Tools Appl 76(23):25391–25419

    Article  Google Scholar 

  6. Cignoni P, Rocchini C, Scopigno R (1998) Metro: measuring error on simplified surfaces. Comput Graph Forum 17(2):167–174

    Article  Google Scholar 

  7. Cignoni P, Callieri M, Corsini M, Dellepiane M, Ganovelli F, Ranzuglia G (2008 ) Meshlab: an open-source mesh processing tool. In: Sixth Eurographics Italian Chapter conference. 129–136

  8. Cohen LD (2001) Multiple contour finding and perceptual grouping using minimal paths. J Math Imaging Vision 14(3):225–236

    Article  MathSciNet  MATH  Google Scholar 

  9. Cohen J, Varshney A, Manocha D, Turk G, Weber H, Agarwal P, Brooks F, Wright W (1996) Simplification envelopes. In: Proc ACM SIGGRAPH Comput Graph 119–128

  10. Curtis S, Shitz S, Oppenheim A (1987) Reconstruction of nonperiodic two-dimensional signals from zero crossings. IEEE Trans Acoustic, Speech, Signal Proc 35(6):890–893

    Article  Google Scholar 

  11. Dyn N, Levine D, Gregory JA (1990) A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans Graph 9(2):160–169

    Article  MATH  Google Scholar 

  12. Eck M, DeRose T, Duchamp T, Hoppe H, Lounsbery M, Stuetzle W (1995) Multiresolution analysis of arbitrary meshes. In: Proc ACM SIGGRAPH Comput Graph 173–182

  13. Fang W, Fazhi H, Chen F, Fei D (2010) A simplification algorithm based on appearance maintenance. J Multimed 5(6):629–638

    Google Scholar 

  14. Garland M, Heckbert PS (1997) Surface simplification using quadric error metrics. In: Proceedings of the 24th annual conference on Computer graphics and interactive techniques 1997. ACM Press/Addison-Wesley Publishing Co, pp 209–216

  15. Hajizadeh M, Ebrahimnezhad H (2018) Eigenspace compression: dynamic 3D mesh compression by restoring fine geometry to deformed coarse models. Multimed Tools Appl 77(15):19347–19375

    Article  Google Scholar 

  16. He T, Hong L, Kaufman A, Varshney A, Wang S (1995) Voxel based object simplification. Proc IEEE Vis 95:296–303

    Google Scholar 

  17. Hoppe H (1996) Progressive meshes. Proc ACM SIGGRAPH 96:99–108

    MathSciNet  Google Scholar 

  18. Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1993) Mesh optimization. Proc ACM SIGGRAPH 93:19–26

    Google Scholar 

  19. Jing Z, Guohua G (2016) The application of level-set mesh simplification algorithm in digital cultural heritage. In: Proc IEEE Int Conf Online Anal Comput Sci. 202–205

  20. Kim SK, An SO, Hong M, Park DS, Kang SJ (2010) Decimation of human face model for real-time animation in intelligent multimedia systems. Multimed Tools Appl 47(1):147–162

    Article  Google Scholar 

  21. Lavoué G (2011) A multiscale metric for 3D mesh visual quality assessment. Comput Graph Forum 30(5):1427–1437

    Article  Google Scholar 

  22. Lee H, Kyung MH (2016) Parallel mesh simplification using embedded tree collapsing. Vis Comput 32(6–8):967–976

    Article  Google Scholar 

  23. Li K, He F, Chen X (2016) Real-time object tracking via compressive feature selection. Front Comput Sci 10(4):689–701

    Article  Google Scholar 

  24. Li H, He F, Liang Y, Quan Q (2019) A dividing-based many-objective evolutionary algorithm for large-scale feature selection. Soft Comput 24:6851–6870. https://doi.org/10.1007/s00500-019-04324-5

    Article  Google Scholar 

  25. Liu X, Lin L, Wu J, Wang W, Yin B, Wang CC (2018) Generating sparse self-supporting wireframe models for 3D printing using mesh simplification. Graph Model 98:14–23

    Article  Google Scholar 

  26. Loop C (1987) Smooth subdivision surfaces based on triangles. Master's thesis, University of Utah, Department of Mathematics

  27. Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. Proc ACM SIGGRAPH Comput Graph 21(4):163–169

    Article  Google Scholar 

  28. Low KL, Tan TS (1997) Model simplification using vertex-clustering. In: Proc ACM Sympos Interact 3D Graph 75–82

  29. Luebke DP (2001) A Developer’s survey of polygonal simplification algorithms. IEEE Comput Graph Appl 21(3):24–35

    Article  Google Scholar 

  30. Luebke D, Erikson C (1997) View-dependent simplification of arbitrary polygonal environments. Proc ACM SIGGRAPH Comput Graph 97:199–208

    Google Scholar 

  31. Marvasti FA (1989) Reconstruction of two-dimensional signals from nonuniform samples or partial information. JOSA A 6(1):52–55

    Article  Google Scholar 

  32. Marvasti FA (1993) Nonuniform sampling. In: Advanced Topics in Shannon Sampling and Interpolation Theory, Springer Verlag, New York

  33. Marvasti FA (2001) Theory and practice of nonuniform sampling. Kluwer Academic/Plenum Publishers, New-York, 2001

  34. Mirloo M, Ebrahimnezhad H (2018) Non-rigid 3D object retrieval using directional graph representation of wave kernel signature. Multimed Tools Appl 77(6):6987–7011

    Article  Google Scholar 

  35. Mount DM (1985) Voronoi diagrams on the surface of a polyhedron. Department of Computer Science CAR-TR-121, CS-TR-1496, University of Maryland

  36. Papageorgiou A, Platis N (2015) Triangular mesh simplification on the GPU. Vis Comput 31(2):235–244

    Article  Google Scholar 

  37. Park J, Lee H (2016) A hierarchical framework for large 3D mesh streaming on mobile systems. Multimed Tools Appl 75(4):1983–2004

    Article  Google Scholar 

  38. Peyré G, Cohen LD (2006) Geodesic remeshing using front propagation. Int J Comput Vis 69(1):145–156

    Article  Google Scholar 

  39. Ramos F, Ripolles O, Chover M (2014) Efficient visualization of 3D models on hardware-limited portable devices. Multimed Tools Appl 73(2):961–976

    Article  Google Scholar 

  40. Rossignac J, Borrel P (1993) Multi-resolution 3D approximations for rendering complex scenes. In: Proceeding of modeling in computer graphics. Springer, Berlin Heidelberg, pp 455–465

    Chapter  Google Scholar 

  41. Salomon D (2007) Curves and surfaces for computer graphics. Springer Science & Business Media

  42. Schroeder WJ, Zarge JA, Lorensen WE (1992) Decimation of triangle meshes. Proc ACM SIGGRAPH 92:65–70

    Article  Google Scholar 

  43. Sumner RW, Popović J (2004) Deformation transfer for triangle meshes. ACM Trans Graph 23(3):399–405

    Article  Google Scholar 

  44. Unity3d (2020) Level of detail https://docs.unity3d.com/Manual/LevelOfDetail.html (accessed 10 June 2020)

  45. Wang SW, Kaufman AE (1994) Volume-sampled 3D modeling. IEEE Comput Graph Appl 14(5):26–32

    Article  Google Scholar 

  46. Windowscentral (2018) how to simplify your model for 3d printing https://www.windowscentral.com/how-simplify-your-model-3d-printing (accessed 17 September 2018)

  47. Yirci M, Ulusoy I (2009) A comparative study on polygonal mesh simplification algorithms. In: Proc 17th IEEE Conf Signal Proc Commun Appl 736–739

Download references

Author information

Authors and Affiliations

  1. Computer Vision Research Lab, Electrical Engineering Faculty, Sahand University of Technology, Tabriz, Iran

    Lida Asgharian & Hossein Ebrahimnezhad

Authors
  1. Lida Asgharian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hossein Ebrahimnezhad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hossein Ebrahimnezhad.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Asgharian, L., Ebrahimnezhad, H. How many sample points are sufficient for 3D model surface representation and accurate mesh simplification?. Multimed Tools Appl 79, 29595–29620 (2020). https://doi.org/10.1007/s11042-020-09395-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-020-09395-3

Keywords

Search

Navigation