Skip to main content
SpringerLink
Log in

Feature-preserving mesh simplification through anisotropic Nyquist-based adaptive sampling of points inside the segmented regions

  • Regular Paper
  • Published:
Journal of Visualization Aims and scope Submit manuscript

Abstract

A wide increase of 3D applications for using mobile phones and other electrical devices reveals the importance of 3D mesh representation. Since visualization and implementation of a coarse and simplified mesh are easier than analyzing a high-resolution mesh, the simplified mesh is preferred for processing. In this paper, a new 3D mesh simplification method is presented to simplify a mesh by anisotropic Nyquist-based adaptive sampling of each segmented region on the surface. Since the sampling step is completed for each segmented region individually, the algorithm can preserve the sharp features of each segment, precisely. The least number of samples is selected from each segment based on its details. Adjusting the sampling procedure according to the geometrical features of the mesh leads to accurately approximate the overall shape of the original model. In order to connect the selected samples, the original mesh connections are employed to better maintain the structure and shape of the input mesh. The improved quality of the results obtained by the proposed method demonstrates its ability in better preserving fine-scale features of different complex meshes in comparison with the previous studies. The simplified models can be efficiently reconstructed based on the selected samples of each region.

Graphical Abstract

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

Similar content being viewed by others

References

  • Algorri ME, Schmitt F (1996) Mesh simplification. In: Proceedings of the 1996 Eurographics, Tutorials, pp 77–86

  • Alliez P, Laurent N, Sanson H, Schmitt F (1999) Mesh Approximation using a volume-based metric. In: Proceedings of the 7th Pacific conference on computer graphics and applications. PG ’99. IEEE Computer Society, Washington, DC, pp 292–301

  • Álvarez R, Noguera JV, Tortosa L, Zamora A (2007) A mesh optimization algorithm based on neural networks. Inf Sci 177(23):5347–5364

    Article  Google Scholar 

  • Asgharian L, Ebrahimnezhad H (2020) How many sample points are sufficient for 3D model surface representation and accurate mesh simplification. Multimed Tools Appl 79(39):29595–29620

    Article  Google Scholar 

  • Cao Y, Mo Z, Xiao L, Wang H, Ai Z, Zhang Z (2018) Efficient visualization of high-resolution virtual nuclear reactor. J Visual 21(5):857–871

    Article  Google Scholar 

  • 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, pp 129–136

  • Deschamps T, Cohen LD (2001) Fast extraction of minimal paths in 3D images and applications to virtual endoscopy. Med Image Anal 5(4):281–299

    Article  Google Scholar 

  • Fritzke B (1995) A growing neural gas network learns topologies. In: Advances in neural information processing systems 7. MIT Press, pp 625–632

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

  • Hamann B (1994) A data reduction scheme for triangulated surfaces. Comput Aided Geom Desi 11(2):197–214

    Article  MathSciNet  Google Scholar 

  • Hoppe H (1996) Progressive meshes. In: Proceedings of the 23rd annual conference on computer graphics and interactive techniques. ACM, pp 99–108

  • Hou T, Chen L (2016) On-the-fly simplification of large iso-surfaces with per-cube vertex modifiability detection. J Visual 19(4):715–726

    Article  Google Scholar 

  • Kimmel R, Sethian JA (1998) Computing geodesic paths on manifolds. Proc Natl Acad Sci 95(15):8431–8435

    Article  MathSciNet  Google Scholar 

  • Kimmel R, Sethian JA (2000) Fast Voronoi diagrams on triangulated surfaces. In: Proceedings of the 16th European workshop on computational geometry (EUROCG-00), pp 1–4

  • Köse K, Çetin AE, Güdükbay U, Onural L (2010) 3D model compression using connectivity-guided adaptive wavelet transform built into 2D SPIHT. J Visual Commun Image Represent 21(1):17–28

    Article  Google Scholar 

  • Klein R, Liebich G, Straßer W (1996) Mesh reduction with error control. In: Proceedings of seventh annual IEEE visualization'96, pp 311–318

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Li M, Nan L (2021) Feature-preserving 3D mesh simplification for urban buildings. ISPRS J Photogram Remote Sens 173:135–150

    Article  Google Scholar 

  • Lindstrom P, Turk G (2000) Image-driven simplification. ACM Trans Graph (ToG) 19(3):204–241

    Article  Google Scholar 

  • Mansouri S, Ebrahimnezhad H (2016) Segmentation-based semi-regular remeshing of 3D models using curvature-adapted subdivision surface fitting. J Visual 19(1):141–155

    Article  Google Scholar 

  • Miyachi H, Sakamoto N (2005) Data reduction by applying an image-based modeling and rendering technique to CG models. J Visual 8(4):331–338

    Article  Google Scholar 

  • Nan L, Pengdong G, Yongquan L, Ameng L, Wenhua Y (2008) A new adaptive mesh simplification method using vertex clustering with topology-and-detail preserving. In: Proceedings of the 2008 international symposium on information science and engieering-volume 01. ISISE ’08. IEEE Computer Society, Washington, DC, pp 150–153

  • Ng KW, Wong YP (2007) Adaptive model simplification in real-time rendering for visualization. J Visual 10(1):111–121

    Article  Google Scholar 

  • Okuyan E, Güdükbay U, İşler V (2012) Dynamic view-dependent visualization of unstructured tetrahedral volumetric meshes. J Visual 15(2):167–178

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ronfard R, Rossignac J (1996) Full-range approximation of triangulated polyhedra. Comput Graph Forum 15(3):67–76

    Article  Google Scholar 

  • Schaefer S, Warren J (2003) Adaptive vertex clustering using octrees. In: SIAM geometric design computing, pp 491–500

  • Schroeder WJ, Zarge JA, Lorensen WE (1992) Decimation of triangle meshes. In: Proceedings of the 19th annual conference on computer graphics and interactive techniques. SIGGRAPH ’92. ACM, New York, pp 65–70

  • Van J, Shi P, Zhang D (2004) Mesh simplification with hierarchical shape analysis and iterative edge contraction. IEEE Trans vis Comput Graph 10(2):142–151

    Article  Google Scholar 

  • Wang Z, Li HY (2010) User-controlled geometric feature preserving simplification. In: 2010 Fifth international conference on frontier of computer science and technology, pp 335–340

  • Wei J, Lou Y (2010) Feature preserving mesh simplification using feature sensitive metric. J Comput Sci Technol 25(3):595–605

    Article  MathSciNet  Google Scholar 

  • Xia JC, El-Sana J, Varshney A (1997) Adaptive real-time level-of-detail-based rendering for polygonal models. IEEE Trans Visual Comput Graph 3(2):171–183

    Article  Google Scholar 

  • Yuan Z, Zhao Y, Chen F, Reber S, Lu CC, Chen Y (2019) Detail-preserving compression for smoke-based flow visualization. J Visual 22(1):51–64

    Article  Google Scholar 

  • Zhang L, Ma Z, Zhou Z, Wu W (2012) Laplacian-based feature preserving mesh simplification. In: Pacific-rim conference on multimedia, pp 378–389

Download references

Funding

No funding was received for conducting this study.

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.

Ethics declarations

Conflict of interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.

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. Feature-preserving mesh simplification through anisotropic Nyquist-based adaptive sampling of points inside the segmented regions. J Vis 25, 819–838 (2022). https://doi.org/10.1007/s12650-022-00828-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12650-022-00828-9

Keywords

Search

Navigation