[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Segmentation-based semi-regular remeshing of 3D models using curvature-adapted subdivision surface fitting

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

Abstract

This paper proposes a novel method of semi-regular remeshing for triangulated surfaces to achieve superior triangles lead to advanced visualization of 3D model. It is based on mesh segmentation and subdivision surface fitting which uses curvature-adapted polygon patches. Our contribution lies in building a sophisticated system with three stages, i.e., curvature-aware mesh segmentation, submesh surface fitting to generate a high-quality semi-regular mesh and finally, stitching the segments using an efficient algorithm. Our method uses centroidal Voronoi tessellation and Lloyd’s relaxation to generate curvature-adapted site centers. Geodesic distances from site centers are used for labeling segments and indexing corner vertices for each segment boundary. Using information of site centers and corner vertices, feature-adapted polygonal patches are generated for each segment. These patches are then subdivided and optimized using squared distance metric to adjust position of the subdivision sampling with segment details and prevent oversampling. At last, an efficient stitching algorithm is introduced to connect regular submeshes together and build the final semi-regular mesh. We have demonstrated the results of our semi-regular remeshing algorithm on meshes with different topology and complexity and compared them with known methods. Superior triangle quality with higher aspect ratio together with acceptable distortion error is achieved according to the experimental results.

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

Subscribe and save

Springer+ Basic
£29.99 /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 includes VAT (United Kingdom)

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

Similar content being viewed by others

References

  • Alliez P, de Verdiere EC, Devillers O, Isenberg M (2005) Centroidal Voronoi diagrams for isotropic surface remeshing. J Graph Models 67(3):204–231

    Article  MATH  Google Scholar 

  • Alliez P, Ucelli G, Gotsman C, Attene M (2007) Recent advances in remeshing of surfaces. In: de Floriani L, Spagnuolo M (eds) Shape analysis and structuring. Springer, Heidelberg

    Google Scholar 

  • Aspert N, Santa-Cruz D, Ebrahimi T (2002) Mesh: measuring errors between surfaces using the Hausdorff distance. In: IEEE international conference in multimedia and expo (ICME)

  • Attene M, Falcidieno B, Spagnuolo M (2006) Hierarchical mesh segmentation based on fitting primitives. J Vis Comput 22(3):181–193

    Article  Google Scholar 

  • Cheng K-SD, Wang W, Qin H, Wong K-YK, Yang H, Liu Y (2004) Fitting subdivision surfaces to unorganized point data using SDM. In: Proceedings of the 12th Pacific conference on comput graphics and applications, 6–8 Oct 2004, PG’04, pp 16–24

  • Cheng K-SD, Wang W, Qin H, Wong K-YK, Yang H, Liu Y (2007) Design and analysis of optimization methods for subdivision surface fitting. J IEEE Trans Vis Comput GR 13(5):878–890

    Article  Google Scholar 

  • Chiang C, Jong B, Lin T (2011) A robust feature-preserving semi-regular remeshing method for triangular meshes. J Vis Comput 27:811–825

    Article  Google Scholar 

  • Choi CP, Gu X, Lui LM (2014) Quasi-conformal Surface Remeshing. UCLA Comput Appl Math Rep. https://www.math.ucla.edu/applied/cam

  • Ciarlet PG (1991) Basic error estimates for elliptic problems. In: Ciarlet PG, Lions JL (eds) Handbook of numerical analysis, vol 2. Finite Element Methods (Part 1), North-Holland, Amsterdam, pp 17–351

  • Dassi Franco, Mola Andrea, Si Hang (2014) Curvature-adapted remeshing of cad surfaces, 23rd international meshing roundtable (IMR23). Proced Eng 82:253–265

    Article  Google Scholar 

  • Du Q, Faber V, Gunzberger M (1999) Centroidal Voronoi tesselations, applications and algorithms. J SIAM Rev 41(4):637–676

    Article  MATH  Google Scholar 

  • Du Q, Gunzberger MD, Ju L (2003) Constrained centroidal Voronoi tesselation for surfaces. SIAM J Sci Comput 24(5):1488–1506

    Article  MathSciNet  MATH  Google Scholar 

  • Eck M, DeRose T, Duchamp T, Hoppe H, Lounsbery M, Stuetzle W (1995) Multiresolution analysis of arbitrary meshes. In: Proceedings ACM SIGGRAPH. ACM, New York, pp 173–182

  • Garland M, Heckbert PS (1997) Surface simplification using quadric error metric. J Comput Graph 31:209–216

    Google Scholar 

  • Gu X, Gortler SJ, Hoppe H (2002) Geometry images. In: Proceedings ACM SIGGRAPH, Association for Computing Machinery. San Antonio, Texas, New York, pp 355–361

  • Hoppe H, Praun E (2005) Shape compression using spherical geometry images. Mathematics and visualization . In: Dodgson N, Floater M, Sabin M (eds) Advances in multi resolution for geometric modelling. Springer, Berlin, pp 27–46

  • Hoschek J (1988) Intrinsic parameterization for approximation. J Comput Aided Geom Des 5:27–31

    Article  MathSciNet  MATH  Google Scholar 

  • Kammoun A, Payan F, Antonini M (2012) Sparsity-based optimization of two lifting-based wavelet transforms for semi-regular mesh compression. J Comput Graph 36:272–282

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Lavou G, Dupont F, Baskurt A (2004) Curvature tensor based triangle mesh segmentation with boundary rectification. IEEE Comput Graph 1:10–17

    Google Scholar 

  • Lee AWF, Sweldens W, Schroder P, Cowsar L, Dobkin D (1998) MAPS: multiresolution adaptive parameterization of surfaces. In: Proceedings ACM SIGGRAPH. ACM, New York, pp 95–104

  • Lee A, Moreton H, Hoppe H (2000) Displaced subdivision surfaces. In: Proceedings ACM SIGGRAPH, pp 85–94

  • Lee J, Kim C-H, Kim S-J (2014) Remeshing visual hull approximation by displaced butterfly subdivision surfaces. J Appl Math Inf Sci 8(4):1891–1899

    Article  Google Scholar 

  • Lia Y, Zhou Q, Hu S, Martin RR (2006) Feature sensitive mesh segmentation. In: Proceedings of the 2006 ACM symposium on solid and physical modeling. ACM, pp 17–25

  • Lien JM, Keyser J, Amato NM (2006) Simultaneous shape decomposition and skeletonization. In: Proceedings of ACM solid and physical modeling symposium, pp 219–228

  • Lloyd S (1982) Least square quantization in PCM. J IEEE Trans Inform Theory 28:129–137

    Article  MathSciNet  MATH  Google Scholar 

  • Loop C (1987) Smooth subdivision surfaces based on triangles. MSc, Department of Mathematics, University of Utah, Utah

  • Medioni G, Chen Y (1992) Object modeling by registration of multiple range images. J Image Vis Comput 10(3):145–155. http://www.sciencedirect.com/science/article/pii/026288569290066C

    Article  Google Scholar 

  • Meyer M, Desbrun M, Schroder P, Barr PH (2003) Discrete differential geometry operators for triangulated 2-manifolds. In: Hege H-C, Polthier K (eds) Visualization and mathematics III. Springer, Berlin, pp 35–57

    Chapter  Google Scholar 

  • Natarajan V, Wang Y, Bremer PT, Pascucci V, Hamann B (2006) Segmenting molecular surfaces. J Comput Aided Geom D 23(6):495–509

    Article  MathSciNet  MATH  Google Scholar 

  • Page DL, Koschan A, Abidi M (2003) Perception-based 3D triangle mesh segmentation using fast marching watersheds. In: Proceedings of computer vision and pattern recognition, pp 27–32

  • Pellerin Jeanne, Lévy Bruno, Caumon Guillaume, Botella Arnaud (2014) Automatic surface remeshing of 3D structural models at specified resolution: a method based on Voronoi diagrams. Comput Geosci 62:103–116

    Article  Google Scholar 

  • Pottmann H, Leopoldseder S (2003) A concept for parametric surface fitting which avoids the parametrization problem. J Comput Aided Geom Des 20:343–362

    Article  MathSciNet  MATH  Google Scholar 

  • Praun E, Hoppe H (2003) Spherical parametrization and remeshing. ACM Trans Graph 22(3):340–349

    Article  Google Scholar 

  • Shamir A (2008) A survey on mesh segmentation techniques. Comput Graph Forum 27(6):1539–1556

    Article  MATH  Google Scholar 

  • Sun Yankui, Dong Yafeng, Maoa Kaimin, Tang Zesheng (2014) View-dependent progressive transmission and rendering for lunar model based on bicubic subdivision-surface wavelet. Adv Space Res 53:1848–1857

    Article  Google Scholar 

  • Surazhsky V, Alliez P, Gotsman C (2003) Isotropic remeshing of surfaces: a local parameterization approach. In: Proceedings of 12th international meshing roundtable, pp. 215–224

  • Valette S, Chassery J, Prost R (2008) Generic remeshing of 3D triangular meshes with metric-dependent discrete Voronoi diagrams. J IEEE Trans Vis Comput Graph 14(2):369–381

    Article  Google Scholar 

  • Yan D-M, Levy B, Lin Y, Sun F, Wang W (2009) Isotropic remeshing with fast computation of restricted Voronoi diagram. Eurograp Symp Geom Proc 28(5):1445–1454

    Google Scholar 

  • Yao H-T, Kuo C-C, Yeh C-H (2003) Extension of surface reconstruction algorithm to the global stitching and repairing of STL models. J Comput-Aided Des 35:477–486

    Article  Google Scholar 

  • Zhong Z, Shuai L, Jinb M, Guo XH (2014) Anisotropic surface meshing with conformal embedding. Graphical Models 76(5):468–483. http://www.sciencedirect.com/science/article/pii/S1524070314000186

  • Zorin D, Schröder P, Sweldens W (1996) Interpolating subdivision for meshes with arbitrary topology. In: Proceeding SIGGRAPH '96, 23rd annual conference on computer graphics and interactive techniques. ACM, New York, pp 189–192. http://dl.acm.org/citation.cfm?id=237254

Download references

Author information

Authors and Affiliations

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

    Saeid Mansouri & Hossein Ebrahimnezhad

Authors
  1. Saeid Mansouri
    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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mansouri, S., Ebrahimnezhad, H. Segmentation-based semi-regular remeshing of 3D models using curvature-adapted subdivision surface fitting. J Vis 19, 141–155 (2016). https://doi.org/10.1007/s12650-015-0288-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12650-015-0288-8

Keywords

Search

Navigation