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Generating Segmented Quality Meshes from Images

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Abstract

Techniques devoted to generating triangular meshes from intensity images either take as input a segmented image or generate a mesh without distinguishing individual structures contained in the image. These facts may cause difficulties in using such techniques in some applications, such as numerical simulations. In this work we reformulate a previously developed technique for mesh generation from intensity images called Imesh. This reformulation makes Imesh more versatile due to an unified framework that allows an easy change of refinement metric, rendering it effective for constructing meshes for applications with varied requirements, such as numerical simulation and image modeling. Furthermore, a deeper study about the point insertion problem and the development of geometrical criterion for segmentation is also reported in this paper. Meshes with theoretical guarantee of quality can also be obtained for each individual image structure as a post-processing step, a characteristic not usually found in other methods. The tests demonstrate the flexibility and the effectiveness of the approach.

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References

  1. Berti, G.: Image-based unstructured 3d mesh generation for medical applications. In: ECCOMAS—European Congress On Computational Methods in Applied Sciences and Engeneering (2004)

  2. Cebral, J.R., Lohner, R.: From medical images to cfd meshes. In: Proceedings of the 8th International Meshing Roundtable, pp. 321–331 (1999)

  3. Cebral, J.R., Löhner, R.: From medical images to anatomically accurate finite element grids. Int. J. Numer. Methods Eng. 51, 985–1008 (2001)

    Article  MATH  Google Scholar 

  4. Ciampalini, A., Cignoni, P., Montani, C., Scopigno, R.: Multiresolution decimation based on global error. Vis. Comput. 13(5), 228–246 (1997)

    Article  Google Scholar 

  5. Coleman, S.A., Scotney, B.W.: Mesh modeling for sparse image data set. In: IEEE ICIP, pp. 1342–1345. IEEE Comput. Soc., Los Alamitos (2005)

    Google Scholar 

  6. Cuadros-Vargas, A.J., Nonato, L.G., Minghim, R., Etiene, T.: Imesh: An image based quality mesh generation technique. In: IEEE Proceedings SIBGRAPI’05, pp. 341–348 (2005)

  7. Fortune, S.: Voronoi diagrams and Delaunay triangulation. In: Hwang, F.K., Du, D.Z. (eds.) Computing in Euclidean Geometry. Lecture Notes Series on Computing, vol. 1, pp. 193–233. World Scientific, Singapore (1992)

    Google Scholar 

  8. García, M.A., Vintimilla, B.X., Sappa, A.D.: Efficient approximation of gray-scale images through bounded error triangular meshes. In: IEEE Intern. Conf. on Image Processing, pp. 168–170 (1999)

  9. Garland, M., Heckbert, P.S.: Fast polygonal approximation of terrains and height fields. Technical Report CMU-CS-95-181, Carnegie Mellon University (1995)

  10. Gevers, T., Smeulders, A.W.M.: Combining region splitting and edge detection through guided Delaunay image subdivision. In: IEEE Proceedings of CVPR, pp. 1021–1026 (1997)

  11. Hale, D.: Atomic images—a method for meshing digital images. In: 10th International Meshing Roundtable, pp. 185–196 (2001)

  12. Ito, Y., Shum, P.C., Shih, A.M., Soni, B.K., Nakahashi, K.: Robust generation of high-quality unstructured meshes on realistic biomedical geometry. Int. J. Numer. Methods Eng. 65(6), 943–973 (2006)

    Article  MATH  Google Scholar 

  13. Kocharoen, P., Ahmed, K.M., Rajatheva, R.M.A.P., Fernando, W.A.C.: Adaptive mesh generation for mesh-based image coding using node elimination approach. In: IEEE ICIP, pp. 2052–2056 (2005)

  14. Peiró, J., Formaggia, L., Gazzola, M., Radaelli, A., Rigamonti, V.: Shape reconstruction from medical images and quality mesh generation via implicit surfaces. Int. J. Numer. Methods Fluids 53(8), 1339–1360 (2007)

    Article  MATH  Google Scholar 

  15. Rizzi, S.H., Banerjee, P.P., Luciano, C.J.: Automating the extraction of 3d models from medical images for virtual reality and haptic simulations. In: IEEE Conference on Automation Science and Engineering (2007)

  16. Ruppert, J.: A Delaunay refinement algorithm for quality 2-dimensional mesh generation. J. Algorithms 18(3), 548–585 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  17. Shewchuk, J.R.: Lecture notes on Delaunay mesh generation. Technical Report CA 94720, Department of Electrical Engineering and Computer Science, Berkeley (2000)

  18. Shewchuk, J.R.: Delaunay refinement algorithms for triangular mesh generation. Comput. Geom. Theory Appl. 22(2–3), 21–74 (2002)

    MATH  MathSciNet  Google Scholar 

  19. Terzopoulos, D., Vasilescu, M.: Sampling and reconstruction with adaptive meshes. In: IEEE Int. Conf. Comp. Vision, Pattern Recog., pp. 829–831 (1992)

  20. Wang, Y., Lee, O., Vetro, A.: Use of 2d deformable mesh structures for video compression. Part ii—the analysis problem and a region-based coder employing the active mesh representation. IEEE Trans. Circuits Syst. Video Technol. 6, 647–659 (2002)

    Article  Google Scholar 

  21. Yang, Y., Wernick, M.N., Brankov, J.G.: A fast approach for accurate content-adaptive mesh generation. IEEE Trans. Image Process. 12(8), 866–881 (2003)

    Article  MathSciNet  Google Scholar 

  22. Zhang, Y., Bajaj, C., Sohn, B.-S.: Adaptive and quality 3d meshing from imaging data. In: SM’03: Proceedings of the Eighth ACM Symposium on Solid Modeling and Applications, pp. 286–291 (2003)

  23. Zhang, Y., Xu, G., Bajaj, C.: Quality meshing of implicit solvation models of biomolecular structures. Comput. Aided Geom. Des. 23(6), 510–530 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Av. Trab. São Carlense, 400, P.O. Box 668, 13560-970, São Carlos, SP, Brasil

    A. J. Cuadros-Vargas, M. Lizier, R. Minghim & L. G. Nonato

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  1. A. J. Cuadros-Vargas
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  2. M. Lizier
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  3. R. Minghim
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  4. L. G. Nonato
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Correspondence to L. G. Nonato.

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Cuadros-Vargas, A.J., Lizier, M., Minghim, R. et al. Generating Segmented Quality Meshes from Images. J Math Imaging Vis 33, 11–23 (2009). https://doi.org/10.1007/s10851-008-0105-2

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  • DOI: https://doi.org/10.1007/s10851-008-0105-2

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