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Reconstruction and simplification of high-quality multiple-region models from planar sections

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Abstract

This paper proposes an accurate and efficient process that reconstructs, smoothes, and simplifies large-scale, three-dimensional models with multiple regions from serial sections. Models are reconstructed using a generally classed marching tetrahedra method that is less complex than the recent generally classed marching cubes algorithms, yet still preserves interface conformability between the regions in the model. Surfaces are smoothed using a volume preserving Laplacian filter that also preserves the region interfaces and topologies. Models are simplified using an efficient and accurate quadric-based edge contraction scheme that maintains the interfaces between regions and preserves the topology of the model. The edge contraction process is constrained to produce surface meshes that have high-quality facet shapes. The process both reconstructs as well as simplifies these models on-the-fly in one pass so that huge models may be processed within limited computer memory. The process does not require the entire original model to fit in the memory at one time. Example results of multiple-region models from the fields of materials science and medicine are presented.

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References

  1. Alkemper J, Voorhees PW (2001) Quantitative serial sectioning analysis. J Microsc 201(Pt 3):388–394

    Article  MathSciNet  Google Scholar 

  2. Vedula VR, Glass SJ, Saylor DM, Rohrer GS, Carter WC, Langer SA (2001) Residual stress predictions in polycrystalline alumina. J Am Ceram Soc 84:2947–2954

    Article  Google Scholar 

  3. Groeber MA, Haley BK, Uchic MD, Dimiduk DM, Ghosh S (2006) 3D reconstruction and characterization of polycrystalline microstructures using a FIB-SEM system. Mater Charact 57(4–5):259–273

    Article  Google Scholar 

  4. Poulsen HF, Nielsen SF, Lauridsen EM, Schmidt S, Suter RM, Lienert U, Margulies L, Lorentzen T, Jensen DJ (2001) Three-dimensional maps of grain boundaries and the stress state of individual grains in polycrystals and powders. J Appl Cryst 34:751–756

    Article  Google Scholar 

  5. Lorenson W, Cline H (1987) Marching cubes: a high resolution 3D surface construction algorithm (Proceedings of SIGGRAPH ‘87). Comp Graph 21(4):163–169

    Google Scholar 

  6. Boissonnat JD (1988) Shape reconstruction from planar cross sections. Comput Vis Graph Image Process 44(1):1–29

    Article  Google Scholar 

  7. Boissonnat JD, Geiger B (1992) Three dimensional reconstruction of complex shapes based on the Delaunay triangulation. Technical report no. 1697, INRIA, France

  8. Wallisch B (2000) Internet-based visualization of basin boundaries for three-dimensional dynamical systems. The 4th Central European seminar on computer graphics in 2000. (http://www.cg.tuwien.ac.at/~wallisch/da/)

  9. Hege H-C, Seebaß M, Stalling D, Zöckler M (1997) A generalized marching cubes algorithm based on non-binary classifications. Technical report SC-97-05, Konrad-Zuse-Zentrum für Informationstechnik (ZIB)

  10. Ju T, Losasso F, Schaefer S, Warren J (2002) Dual contouring of hermite data. ACM Trans Graph 21(3):339–346. ISSN 0730-0301 (Proceedings of ACM SIGGRAPH 2002)

    Google Scholar 

  11. Ju T, Udeshi T (2006) Intersection-free contouring on an octree grid. In: Proceedings of Pacific graphics

  12. Wu Z, Sullivan, JM Jr (2003) Multiple material marching cubes algorithm. Int J Numer Methods Eng 58(2):189–207

    Google Scholar 

  13. Weinstein D (2000) Scanline surfacing: building separating surfaces from planar contours. In: IEEE Visualization 2000, pp 283–289

  14. Nielson GM, Franke R (1997) Computing the separating surface for segmented data. In: Proceedings of the 8th conference on visualization ‘97, Phoenix, AZ

  15. Jones TR, Durand F, Desbrun M (2003) Non-iterative, feature-preserving mesh smoothing. In: ACM transactions on graphics, pp 943–949

  16. Nealen A, Igarashi T, Sorkine O, Alexa M (2006) Laplacian mesh optimization. Computer graphics and interactive techniques in Australasia and South East Asia. In: Proceedings of the 4th international conference on computer graphics and interactive techniques in Australasia and Southeast Asia, Kuala Lumpur, Malaysia, pp 381–389. ISBN:1-59593-564-9

  17. Taubin G (1995) A signal processing approach to fair surface design. In: Computer graphics proceedings, pp 351–358

  18. Bade R, Haase J, Preim B (2006) comparison of fundamental mesh smoothing algorithms for medical surface models. In: Simulation and Visualization 2006, Magdeburg

  19. Kuprat A, Khamayseh A, George D, Larkey L (2001) Volume conserving smoothing for piecewise linear curves, surfaces, and triple lines. J Comput Phys 172:99–118

    Article  MATH  Google Scholar 

  20. Grabner M (2002) On-the-fly greedy mesh simplification for 2 1/2-D regular grid data acquisition systems. Vision with nontraditional sensors. In: Leberl F, Fraundorfer F (eds) Proceedings of 26th workshop of the Austrian Association for Pattern Recognition, vol 160. Austrian Computer Society, Graz

  21. Lindstrom P (2000) Out-of-core simplification of large polygonal models. In: Proceedings of SIGGRAPH 2000, pp 259–262

  22. Garland M, Heckbert P (1997) Surface simplification using quadric error metrics. In: SIGGRAPH 97 conference proceedings. Annual conference series, ACM SIGGRAPH. Addison-Wesley, Reading

  23. Lindstrom P, Silva CT (2001) A memory insensitive technique for large model simplification. In: Proceedings of the conference on visualization ’01. IEEE Computer Society, New York, pp 121–126

  24. Wu J, Kobbelt L (2003) A stream algorithm for the decimation of massive meshes. In: Graphics interface ‘03 conference proceedings, pp 185–192

  25. Isenburg M, Lindstrom P, Gumhold S, Snoeyink J (2003) Large mesh simplification using processing sequences. In: Proceedings of visualization ’03, pp 465–472

  26. Isenburg M, Lindstrom P (2005) Streaming meshes. In: Proceedings of visualization ’05, pp 231–238

  27. Mascarenhas A, Isenburg M, Pascucci V, Snoeyink J (2004) Encoding volumetric grids for streaming isosurface extraction. In: Proceedings of 3DPVT’04, pp 665–672

  28. Isenburg M, Lindstrom P, Snoeyink J (2005) Streaming compression of triangle meshes. In: Proceedings of 3rd symposium on geometry processing, pp 111–118

  29. Vo H, Callahan S, Lindstrom P, Pascucci V, Silva C (2005) Streaming simplification of tetrahedral meshes. LLNL technical report UCRL-CONF-208710

  30. Isenburg M, Lindstrom P, Gumhold S, Shewchuk J (2006) Streaming compression of tetrahedral volume meshes. In: Proceedings of graphics interface 2006, pp 115–121

  31. Isenburg M, Gumhold S (2003) Out-of-core compression for gigantic polygon meshes. In: Proceedings of SIGGRAPH’03, pp 935–942

  32. Schroeder W, Zarge J, Lorensen W (1992) Decimation of triangle meshes (Proceedings of SIGGRAPH ’92). Comput Graph 25(3)

  33. Guthe M, Borodin P, Klein R (2005) Fast and accurate Hausdorff distance calculation between meshes. J WSCG 13. ISSN:1213–6964

    Google Scholar 

  34. Cohen J, Varshney A, Manocha D, Turk G, Weber H, Agarwal P, Brooks FP Jr, Wright W (1996) Simplification envelopes. In: Proceedings of ACM SIGGRAPH’96, pp 119–128

  35. Moore RH (2007) PhD Dissertation, Carnegie Mellon University, Pittsburgh

  36. Dey TK, Edelsbrunner H, Guha S, Nekhayev DV (1999) Topology preserving edge contraction. Publ Inst Math (Beograd) (N.S.) 66:23–45

    MathSciNet  Google Scholar 

  37. Vivodtzev F, Bonneau GP, Letexier P (2005) Topology preserving simplification of 2D non-manifold meshes with embedded structures. Vis Comput 21(8)

  38. Cutler B, Dorsey J, McMillan L (2004) Simplication and Improvement of tetrahedral models for simulation. In: Scopigno R, Zorin D (eds) Eurographics symposium on geometry processing

  39. Shewchuk J (2002) What is a good linear element? Interpolation, conditioning, and quality measures. In: Eleventh international meshing roundtable Sandia National Laboratories, Ithaca, NY, pp 115–126

  40. Saylor DM, Morawiec A, Rohrer GS (2003) Distribution of grain boundaries in magnesia as a function of five macroscopic parameters. Acta Mater 51:3663–3674

    Article  Google Scholar 

  41. Zubal IG, Harrell CR, Smith EO, Rattner Z, Gindi GR, Hoffer PB (1994) Computerized three-dimensional segmented human anatomy. Med Phys 21(2):299–302

    Article  Google Scholar 

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Acknowledgments

The authors would like to acknowledge Dr. A. D. Rollett for his many constructive comments for improving this paper. The authors would also like to thank Dr. David Saylor and Mr. Suk-Bin Lee for providing the segmented and aligned serial section data.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    R. H. Moore

  2. Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    G. S. Rohrer

  3. Department of Civil and Environmental Engineering, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    S. Saigal

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  1. R. H. Moore
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  2. G. S. Rohrer
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  3. S. Saigal
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Correspondence to R. H. Moore.

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Moore, R.H., Rohrer, G.S. & Saigal, S. Reconstruction and simplification of high-quality multiple-region models from planar sections. Engineering with Computers 25, 221–235 (2009). https://doi.org/10.1007/s00366-008-0114-1

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  • DOI: https://doi.org/10.1007/s00366-008-0114-1

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