The Visual Computer

, Volume 27, Issue 10, pp 887–903 | Cite as

Template-based quadrilateral mesh generation from imaging data

  • Mario A. S. Liziér
  • Marcelo F. Siqueira
  • Joel DanielsII
  • Claudio T. Silva
  • L. Gustavo Nonato
Original Article

Abstract

This paper describes a novel template-based meshing approach for generating good quality quadrilateral meshes from 2D digital images. This approach builds upon an existing image-based mesh generation technique called Imeshp, which enables us to create a segmented triangle mesh from an image without the need for an image segmentation step. Our approach generates a quadrilateral mesh using an indirect scheme, which converts the segmented triangle mesh created by the initial steps of the Imesh technique into a quadrilateral one. The triangle-to-quadrilateral conversion makes use of template meshes of triangles. To ensure good element quality, the conversion step is followed by a smoothing step, which is based on a new optimization-based procedure. We show several examples of meshes generated by our approach, and present a thorough experimental evaluation of the quality of the meshes given as examples.

Keywords

Image-based mesh generation Template-based mesh Quadrilateral mesh Mesh smoothing Mesh segmentation Bézier patches 

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References

  1. 1.
    Alliez, P., Ucelli, G., Gotsman, C., Attene, M.: Recent advances in remeshing of surfaces. In: Floriani, L.D., Spagnuolo, M. (eds.) Shape Analysis and Structuring, Mathematics and Visualization. Springer, Berlin Heidelberg (2008) Google Scholar
  2. 2.
    Allman, D.: A quadrilateral finite element including vertex rotations for plane elasticity analysis. Int. J. Numer. Methods Eng. 26, 717–730 (1988) MATHCrossRefGoogle Scholar
  3. 3.
    Atalay, F.B., Ramaswami, S., Xu, D.: Quadrilateral meshes with bounded minimum angle. In: Proceedings of the 17th International Meshing Roundtable (IMR), pp. 73–91 (2008) CrossRefGoogle Scholar
  4. 4.
    Bern, M., Plassmann, P.: Mesh generation. In: Sack, J.R., Urrutia, J. (eds.) Handbook of Comput. Geom. Elsevier, Amsterdam (2000) Google Scholar
  5. 5.
    Berti, G.: Image-based unstructured 3D mesh generation for medical applications. In: ECCOMAS—European Congress on Computational Methods in Applied Sciences and Engineering (2004) Google Scholar
  6. 6.
    Boissonnat, J.D., Pons, J.P., Yvinec, M.: From segmented images to good quality meshes using Delaunay refinement. In: Lecture Notes in Computer Science, vol. 5416, pp. 13–37. Springer, Berlin (2009) Google Scholar
  7. 7.
    Johnston, B.P., Sullivan, J.M., Kwasnik, A.: Automatic conversion of triangular finite meshes to quadrilateral meshes. Int. J. Numer. Methods Eng. 31(1), 67–84 (1991) MATHCrossRefGoogle Scholar
  8. 8.
    Cebral, J., Lohner, R.: From medical images to CFD meshes. In: Proc. of the 8th Intern. Meshing Roundtable, pp. 321–331 (1999) Google Scholar
  9. 9.
    Coleman, S., Scotney, B.: Mesh modeling for sparse image data set. In: IEEE ICIP, pp. 1342–1345. IEEE Computer Society, Los Alamitos (2005) Google Scholar
  10. 10.
    Cuadros-Vargas, A.J., Lizier, M.A.S., Minghim, R., Nonato, L.G.: Generating segmented quality meshes from images. J. Math. Imaging Vis. 33, 11–23 (2009) MathSciNetCrossRefGoogle Scholar
  11. 11.
    Douglas, D.H., Peucker, T.K.: Algorithms for the reduction of the number of points required to represent a line or its caricature. Can. Cartogr. 10(2), 122–122 (1973) Google Scholar
  12. 12.
    Everett, H., Lenhart, W., Overmars, M., Shermer, T., Urrutia, J.: Strictly convex quadrilateralizations of polygons. In: Proceedings of the 4th Canadian Conference on Computational Geometry, pp. 77–82 (1992) Google Scholar
  13. 13.
    García, M., Sappa, A., Vintimilla, B.: Efficient approximation of gray-scale images through bounded error triangular meshes. In: IEEE Intern. Conf. on Image Processing, pp. 168–170 (1999) Google Scholar
  14. 14.
    Gevers, T., Smeulders, A.: Combining region splitting and edge detection through guided Delaunay image subdivision. In: IEEE Proceedings of CVPR, pp. 1021–1026 (1997) Google Scholar
  15. 15.
    Green, P., Sibson, R.: Computing Dirichlet tesselation in the plane. Comput. J. 21(2), 168–173 (1977) MathSciNetGoogle Scholar
  16. 16.
    Herman, G.: Geometry of Digital Spaces. Birkhäuser, Boston (1998) MATHGoogle Scholar
  17. 17.
    Knupp, P.M.: Algebraic mesh quality metrics. SIAM J. Sci. Comput. 23(1), 193–218 (2001) MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Kocharoen, P., Ahmed, K., Rajatheva, R., Fernando, W.: Adaptive mesh generation for mesh-based image coding using node elimination approach. In: IEEE International Conference on Image Processing, pp. 2052–2056 (2005) Google Scholar
  19. 19.
    Lai, M.J.: Scattered data interpolation and approximation using bivariate c 1 piecewise cubic polynomials. Comput. Aided Geom. Des. 13(1), 81–88 (1996) MATHCrossRefGoogle Scholar
  20. 20.
    Lawson, C.L., Hanson, R.J.: Solving least squares problem. In: Classics in Applied Mathematics, vol. 15. SIAM, Philadelphia (1995) Google Scholar
  21. 21.
    Lizier, M.A.S., Martins, D.C. Jr., Cuadros-Vargas, A.J., Cesar, R.M. Jr., Nonato, L.G.: Generating segmented meshes from textured color images. J. Vis. Commun. Image Represent. 20, 190–203 (2009) CrossRefGoogle Scholar
  22. 22.
    Malanthara, A., Gerstle, W.: Comparative study of unstructured meshes made of triangles and quadrilaterals. In: Proceedings of the 6th International Meshing Roundtable (IMR), pp. 437–447 (1997) Google Scholar
  23. 23.
    Miller, G., Pave, S., Walkington, N.: When and why Ruppert’s algorithm works. In: Proceedings of the 12th International Meshing Roundtable (IMR), pp. 91–102 (2003) Google Scholar
  24. 24.
    Owen, S., Staten, M., Cannan, S., Saigal, S.: Q-morph: an indirect approach to advancing front quad meshing. Int. J. Numer. Methods Eng. 9(44), 1317–1340 (1999) CrossRefGoogle Scholar
  25. 25.
    Powell, M.J.D.: An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J. 7(2), 155–162 (1964) MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Ramaswami, S., Ramos, P., Toussaint, G.: Converting triangulations to quadrangulations. Comput. Geom. Theory Appl. 9(4), 257–276 (1998) MathSciNetMATHGoogle Scholar
  27. 27.
    Ramaswami, S., Siqueira, M., Sundaram, T., Gallier, J., Gee, J.: Constrained quadrilateral meshes of bounded size. Int. J. Comput. Geom. Appl. 15(1), 55–98 (2005) MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Ruppert, J.: A Delaunay refinement algorithm for quality 2-dimensional mesh generation. J. Algorithms 18(3), 548–585 (1995) MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Schneiders, R.: Refining quadrilateral and hexahedral element meshes. In: Proc. 5th International Conference on Numerical Grid Generation in Computational Field Simulations, pp. 679–688 (1996) Google Scholar
  30. 30.
    Shamir, A.: A survey on mesh segmentation techniques. Comput. Graph. Forum 27(6), 1539–1556 (2007) MathSciNetCrossRefGoogle Scholar
  31. 31.
    Shewchuk, J.: What is a good linear element? Interpolation, conditioning, and quality measures. In: Proceeding of the 11th International Meshing Roundtable, pp. 115–126 (2002) Google Scholar
  32. 32.
    Shimada, K., Liao, J.H., Itoh, T.: Quadrilateral meshing with directionality control through the packing of square cells. In: Proceedings of the 7th International Meshing Roundtable, Dearborn, Michigan, USA, pp. 61–76 (1998) Google Scholar
  33. 33.
    Skrinjar, O., Bistoquet, A.: Generation of myocardial wall surface meshes from segmented MRI. Int. J. Biomed. Imaging (2009). doi:10.1155/2009/313517 MATHGoogle Scholar
  34. 34.
    Staples, J., Eades, P., Katoh, N., Moffat, A. (eds.): No Quadrangulation is Extremely Odd. Lecture Notes in Computer Science, Cairns, Australia, vol. 1004. Springer, Berlin (1995) Google Scholar
  35. 35.
    Velho, L., Zorin, D.: 4–8 subdivision. Comput. Aided Geom. Des. 18(5), 397–427 (2001) MathSciNetMATHCrossRefGoogle Scholar
  36. 36.
    Viswanath, N., Shimada, K., Itoh, T.: Quadrilateral meshing with anisotropy and directionality control via close packing of rectangular cells. In: Proceedings of the 9th International Meshing Roundtable, New Orleans, Louisiana, USA, pp. 217–225 (2000) Google Scholar
  37. 37.
    Yang, Y., Wernick, M., Brankov, J.: A fast approach for accurate content-adaptive mesh generation. IEEE Trans. Image Process. 12(8), 866–881 (2003) MathSciNetCrossRefGoogle Scholar
  38. 38.
    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) CrossRefGoogle Scholar
  39. 39.
    Teng, S.-H., Wong, C.W.: Unstructured mesh generation: theory, practice, and perspectives. Int. J. Comput. Geom. Appl. 10(3), 227–266 (2000) MathSciNetMATHCrossRefGoogle Scholar
  40. 40.
    Daniels, J., Nonato, L.G., Siqueira, M., Liziér, M., Silva, C.T.: In: SMI’11: Proceedings of the Shape Modeling International (2011, to appear) Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Mario A. S. Liziér
    • 1
  • Marcelo F. Siqueira
    • 2
  • Joel DanielsII
    • 3
  • Claudio T. Silva
    • 4
  • L. Gustavo Nonato
    • 5
  1. 1.Departamento de ComputaçãoUniversidade Federal de São CarlosSão CarlosBrazil
  2. 2.Departamento de Informática e Matemática AplicadaUniversidade Federal do Rio Grande do NorteNatalBrazil
  3. 3.Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA
  4. 4.Computer Science and Engineering Polytechnic InstituteNew York UniversityNew YorkUSA
  5. 5.Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão PauloBrazil

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