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Feature-Sensitive and Adaptive Mesh Generation of Grayscale Images

  • Ming Xu
  • Zhanheng Gao
  • Zeyun Yu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8641)

Abstract

In the current paper, we present a series of algorithms to generate high quality, feature-sensitive, and adaptive meshes from a given grayscale image. The Canny’s edge detector is employed to guarantee that important image features are preserved in the meshes. A halftoning-based sampling strategy is adopted to provide feature-sensitive and adaptive point distributions in the image domain. A Delaunay-triangulation is used to generate initial triangulation of the image, followed by iterative mesh smoothing for mesh quality improvement. Experimental results on several medical images have shown that the proposed method is effective in producing adaptive meshes with high-quality and well-preserved features.

Keywords

Mesh generation Feature sensitivity Adaptivity Delaunay triangulation Medical images 

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References

  1. 1.
    Haidekker, M.A.: Medical Imaging Technology, Springer Briefs in Physics (2013)Google Scholar
  2. 2.
    Chandler, D., Roberson, R.W.: Bioimaging: Current Concept in Light & Electron Microscopy. Jones & Bartlett Learning (2008)Google Scholar
  3. 3.
    Floyd, R., Steinberg, L.: An adaptive algorithm for spatial gray scale. In: SID Int. Symp. Digest of Tech. Papers, pp. 36–37 (1975)Google Scholar
  4. 4.
    Shewchuk, J.: Triangle: A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator, http://www.cs.cmu.edu/~quake/triangle.html
  5. 5.
    Ramponi, G., Carrato, S.: An adaptive irregular sampling algorithm and its application to image coding. Image and Vision Computing 19(7), 451–460 (2001)CrossRefGoogle Scholar
  6. 6.
    Yang, Y., Wernick, M.N., Brankov, J.G.: A fast approach for accurate content-adaptive mesh generation. IEEE Transactions on Image Processing 12(8), 866–881 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Kim, T.-S., Lee, W.H.: 3-D MRI and DT-MRI Content-adaptive Finite Element Head Model Generation for Bioelectromagnetic Imaging. In: Recent Advances in Biomedical Engineering (2009)Google Scholar
  8. 8.
    Cuadros-Vargas, A.J., Nonato, L.G., Minghim, R., Etiene, T.: Imesh: An Image Based Quality Mesh Generation Technique. In: Proceedings of the XVIII Brazilian Symposium on Computer Graphics and Image Processing (2005)Google Scholar
  9. 9.
    Tu, X., Adams, M.D.: Improved Mesh Models of Images Through the Explicit Representation of Discontinuities. Canadian Journal of Electrical and Computer Engineering 36(2), 78–86 (2013)CrossRefGoogle Scholar
  10. 10.
    Garland, M., Heckbert, P.S.: Fast Polygonal Approximation of Terrains and Height Fields. CMU-CS-95-181 (1995)Google Scholar
  11. 11.
    Adams, M.D.: A Highly-Effective Incremental/Decremental Delaunay Mesh-Generation Strategy for Image Representation. Signal Processing 93(4), 749–764 (2013)CrossRefGoogle Scholar
  12. 12.
    Sarkis, M., Diepold, K.: Content Adaptive Mesh Representation of Images Using Binary Space Partitions. IEEE Trans. Image Process. 18(5), 1069–1079 (2009)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Bougleux, S., Peyré, G., Cohen, L.D.: Image Compression with Anisotropic Geodesic Triangulations. In: IEEE 12th International Conference Computer Vision, pp. 2343–2348 (2009)Google Scholar
  14. 14.
    Li, P., Adams, M.D.: A Tuned Mesh-Generation Strategy for Image Representation Based on Data-Dependent Triangulation. IEEE Trans. Image Process. 22(5), 2004–2018 (2013)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Demaret, L., Dyn, N., Iske, A.: Image Compression by Linear Splines over Adaptive Triangulations. Signal Processing 86(7), 1604–1616 (2006)CrossRefzbMATHGoogle Scholar
  16. 16.
    Demaret, L., Iske, A.: Anisotropic Triangulation Methods in Adaptive Image Approximation. In: Approximation Algorithms for Complex Systems. Springer Proceedings in Mathematics, vol. 3, pp. 47–68 (2011)Google Scholar
  17. 17.
    Adams, M.D.: A Flexible Content-Adaptive Mesh-Generation Strategy for Image Representation. IEEE Transactions on Image Processing 20(9), 2414–2427 (2011)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Chen, L.: Mesh smoothing schemes based on optimal Delaunay triangulations. In: Proceedings of the 13th International Meshing Roundtable, pp. 109–120 (2004)Google Scholar
  19. 19.
    Chen, L., Xu, J.: Optimal Delaunay triangulation. Journal of Computational Mathematics 22(2), 299–308 (2004)zbMATHMathSciNetGoogle Scholar
  20. 20.
    Gao, Z., Yu, Z., Holst, M.: Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation. Computer Aided Geometric Design 29(9), 707–721 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Gao, Z., Yu, Z., Holst, M.: Feature-Preserving Surface Mesh Smoothing via Suboptimal Delaunay Triangulation. Graphical Models 75(1), 23–38 (2013)CrossRefGoogle Scholar
  22. 22.
    Goksel, O., Salcudean, S.E.: Image-Based Variational Meshing. IEEE Transactions on Medical Imaging 30(1), 11–21 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ming Xu
    • 1
  • Zhanheng Gao
    • 2
  • Zeyun Yu
    • 1
  1. 1.Department of Computer ScienceUniversity of WisconsinMilwaukeeUSA
  2. 2.College of Computer Science and TechnologyJilin UniversityChangchunChina

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