Grid Smoothing: A Graph-Based Approach

  • Guillaume Noel
  • Karim Djouani
  • Yskandar Hamam
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6419)


In the past few years, mesh representation of images has attracted a lot of research interest due to its wide area of applications in image processing. In the mesh framework, an image is represented by a graph in which the nodes represent the pixels and the edges reflect the connectivity. The definition of the most adapted mesh for a given image is a challenge in terms of computation cost and information representation. In this paper, a new method for content adaptive mesh representation of gray scale images, called grid smoothing, is presented. A cost function is defined using the spatial coordinates of the nodes and the gray levels present in the image. The minimisation of the cost function leads to new spatial coordinates for each node. Using an adequate cost function, the grid is compressed in the regions with large gradient values and relaxed in the other regions. The result is a grid which better fits the objects in the image. The mathematical framework of the method is introduced in the paper. An in-depth study of the convergence is presented as well as results on real gray scale images.


Content adaptative mesh grid smoothing image coding non-linear optimisation 


  1. 1.
    Demaret, L., Dyn, N., Iske, A.: Image compression by linear splines over adaptive traingulations. IEEE Trans. on Signal Processing 86(7), 1604–1616 (2006)zbMATHGoogle Scholar
  2. 2.
    Han, S.-R., Yamasaki, T., Aizawa, K.: Time-varying mesh compression using an extended block matching algorithm. IEEE Trans. on Circuits and Systems for Video Technology 17(11), 1506–1518 (2007)CrossRefGoogle Scholar
  3. 3.
    Bu, S., Shiina, T., Yamakawa, M., Takizawa, H.: Adaptive dynamic grid interpolation: A robust, high-performance displacement smoothing filter for myocardial strain imaging. In: Ultrasonics Symposium, IUS 2008, vol. 2(5), pp. 753–756. IEEE, Los Alamitos (2008)CrossRefGoogle Scholar
  4. 4.
    Prassl, A.J., Kickinger, F., Ahammer, H., Grau, V., Schneider, J.E., Hofer, E., Vigmond, E.J., Trayanova, N.A., Plank, G.: Automatically generated, anatomically accurate meshes for cardiac electrophysiology problems. IEEE Trans. on Biomedical Engineering 56(5), 1318–1329 (2009)CrossRefGoogle Scholar
  5. 5.
    Yang, Y., Wernick, M.N., Brankov, J.G.: A fast approach for accurate content-adaptative mesh generation. IEEE Trans. on Image Processing 12(8), 866–880 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ramponi, G., Carrato, S.: An adaptive sampling algorithm and its application to image coding. Image Vis. Comput. 19(7), 451–460 (2001)CrossRefGoogle Scholar
  7. 7.
    Sarkis, M., Dieplod, K.: Content adaptive mesh representation of images using binary space partitions. IEEE Trans. on Image ProcessingGoogle Scholar
  8. 8.
    Hamam, Y., Couprie, M.: An Optimisation-Based Approach to Mesh Smoothing: Reformulation and Extension. In: Torsello, A., Escolano, F., Brun, L. (eds.) GbRPR 2009. LNCS, vol. 5534, pp. 31–41. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Guillaume Noel
    • 1
  • Karim Djouani
    • 1
  • Yskandar Hamam
    • 1
  1. 1.French South African Institute of TechnologyTshwane University of TechologyPretoriaSouth Africa

Personalised recommendations