Table of Contents
ISRN Computer Graphics
Volume 2012 (2012), Article ID 846980, 5 pages
http://dx.doi.org/10.5402/2012/846980
Research Article

Superresolution of Images Using Area Preserving Geometric Evolution Laws

Department of Mathematics, Dresden University of Technology, 01062 Dresden, Germany

Received 23 August 2011; Accepted 19 September 2011

Academic Editors: Y. He and L. Ma

Copyright © 2012 Caroline Jäger et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Alvarez, P. L. Lions, and J. M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM Journal on Numerical Analysis, vol. 29, no. 3, pp. 845–866, 1992. View at Google Scholar · View at Scopus
  2. H. A. Aly and E. Dubois, “Image up-sampling using total-variation regularization with a new observation model,” IEEE Transactions on Image Processing, vol. 14, no. 10, pp. 1647–1659, 2005. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Bertalmio, A. Bertozzi, and G. Sapiro, “Navier-stokes, fluid dynamics, and image and video inpainting,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition, pp. 355–362, 2001.
  4. A. L. Bertozzi, S. Esedog̃lu, and A. Gillette, “Inpainting of binary images using the Cahn-Hilliard equation,” IEEE Transactions on Image Processing, vol. 16, no. 1, pp. 285–291, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Burger, C. Stöcker, and A. Voigt, “Finite element-based level set methods for higher order flows,” Journal of Scientific Computing, vol. 35, no. 2-3, pp. 77–98, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. V. Caselles, J. M. Morel, and C. Sbert, “An axiomatic approach to image interpolation,” IEEE Transactions on Image Processing, vol. 7, no. 3, pp. 376–386, 1998. View at Google Scholar · View at Scopus
  7. T. F. Chan, S. H. Kang, and J. Shen, “Euler's elastica and curvature-based inpainting,” SIAM Journal on Applied Mathematics, vol. 63, no. 2, pp. 564–592, 2002. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Droske and M. Rumpf, “A level set formulation for Willmore flow,” Interfaces and Free Boundaries, vol. 6, no. 3, pp. 361–378, 2004. View at Google Scholar · View at Scopus
  9. S. Esedoglu and P. Smereka, “A variational formulation for a level set representation of multiphase flow and area preserving curvature flow,” Communications in Mathematical Sciences, vol. 6, no. 1, pp. 125–148, 2008. View at Google Scholar · View at Scopus
  10. F. Malgouyres and F. Guichard, “Edge direction preserving image zooming: a mathematical and numerical analysis,” SIAM Journal on Numerical Analysis, vol. 39, no. 1, pp. 1–37, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. R. Malladi and J. A. Sethian, “A unified approach to noise removal, image enhancement, and shape recovery,” IEEE Transactions on Image Processing, vol. 5, no. 11, pp. 1554–1568, 1996. View at Google Scholar · View at Scopus
  12. E. Meijering, “A chronology of interpolation: from ancient astronomy to modern signal and image processing,” Proceedings of the IEEE, vol. 90, no. 3, pp. 319–342, 2002. View at Publisher · View at Google Scholar · View at Scopus
  13. B. S. Morse and D. Schwartzwald, “Image magnification using level-set reconstruction,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR '10), pp. 333–340, December 2001. View at Scopus
  14. S. Osher and J. A. Sethian, “Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations,” Journal of Computational Physics, vol. 79, no. 1, pp. 12–49, 1988. View at Google Scholar · View at Scopus
  15. C. Stöckert and A. Voigt, “Geodesic evolution laws—a level set approach,” SIAM Journal on Imaging Sciences, vol. 1, no. 4, pp. 379–399, 2008. View at Google Scholar
  16. S. Vey and A. Voigt, “AMDiS—adaptive multidimensional simulations,” Computing and Visualization in Science, vol. 10, no. 1, pp. 57–66, 2007. View at Publisher · View at Google Scholar · View at Scopus