Journal of Computer Science and Technology

, Volume 24, Issue 4, pp 734–744 | Cite as

Edge-Aware Level Set Diffusion and Bilateral Filtering Reconstruction for Image Magnification

  • Hua HuangEmail author
  • Yu Zang
  • Paul L. Rosin
  • Chun Qi
Regular Paper


In this paper we propose an image magnification reconstruction method. In recent years many interpolation algorithms have been proposed for image magnification, but all of them have defects to some degree, such as jaggies and blurring. To solve these problems, we propose applying post-processing which consists of edge-aware level set diffusion and bilateral filtering. After the initial interpolation, the contours of the image are identified. Next, edge-aware level set diffusion is applied to these significant contours to remove the jaggies, followed by bilateral filtering at the same locations to reduce the blurring created by the initial interpolation and level set diffusion. These processes produce sharp contours without jaggies and preserve the details of the image. Results show that the overall RMS error of our method barely increases while the contour smoothness and sharpness are substantially improved.


computer application image magnification reconstruction edge-aware level set diffusion bilateral filtering 


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Supplementary material

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  1. [1]
    dell’Acqua F, Gamba P. Using image magnification techniques to improve classification of hyperspectral data. In Proc. International Geoscience and Remote Sensing Symposium, Toulouse, France, July 21–25, 2003, pp.737–739.Google Scholar
  2. [2]
    Kwiatkowski J, Kwiatkowska W, Kawa K, Kania P. Using fractal coding in medical image magnification. In Proc. Parallel Processing and Applied Mathematics, Naleczow, Poland, September 9–12, 2002, pp.517–525.Google Scholar
  3. [3]
    Gehani A, Reif J. Advances in digital forensics iii. In Proc. International Federation for Information Processing, Addis Ababa, Ethiopia, August 22–24, 2007.Google Scholar
  4. [4]
    Morse B S, Schwartzwald D. Image magnification using level-set reconstruction. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, Kauai Island of Hawaii, USA, December 11–13, 2001, pp.333–340.Google Scholar
  5. [5]
    Irani M, Peleg S. Motion analysis for image enhancement: Resolution, occlusion, and transparency. Journal of Visual Communication and Image Representation, 1993, 4(4): 324–335.CrossRefGoogle Scholar
  6. [6]
    Naiman A C. Jagged edges: When is filtering needed? ACM Trans. Graphics, 1998, 17(4): 238–258.CrossRefGoogle Scholar
  7. [7]
    Dai S, Han M, Wu Y, Gong Y. Bilateral back-projection for single image super resolution. In Proc. IEEE International Conference on Multimedia and Expo, Beijing, China, July 2–5, 2007, pp.1039–1042.Google Scholar
  8. [8]
    Allebach J, Wong P W. Edge-directed interpolation. In Proc. International Conference on Image Processing, Lausanne, Switzerland, March, 1996, pp.707–710.Google Scholar
  9. [9]
    Li X, Orchard M T. New edge directed interpolation. In Proc. International Conference on Image Processing, Vancouver, Canada, September 10–13, 2000, pp.1521–1527.Google Scholar
  10. [10]
    Zhang S H, Chen T, Zhang Y F, Hu S M, Martin R R. Vectorizing cartoon animations. IEEE Trans. Visualization and Computer Graphics, 2009.(to appare)Google Scholar
  11. [11]
    Fattal R. Image upsampling via imposed edge statistics. ACM Trans. Graphics, 2007, 26(3): 95.CrossRefGoogle Scholar
  12. [12]
    Sun J, Zheng N N, Tao H, Shum H Y. Image hallucination with primal sketch priors. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, Monona Terrace Convention Center Madison, Wisconsin, USA, June 16–22, 2003, pp.729–736.Google Scholar
  13. [13]
    Tumblin J, Choudhury P. Bixels: Picture samples with sharp embedded boundaries. In Proc. Eurographics Workshop on Rendering Techniques, Norköping, Sweden, June 21–23, 2004, pp.255–264.Google Scholar
  14. [14]
    Rubinstein M, Shamir A, Avidan S. Improved seam carving for video retargeting. In Proc. ACM SIGGRAPH, Los Angeles, California, USA, August 11–15, 2008, pp.1–9.Google Scholar
  15. [15]
    Zhang Y F, Hu S M, Martin R R. Shrinkability maps for content-aware video resizing. Comput. Graph. Forum, 2008, 27(7): 1797–1804.CrossRefGoogle Scholar
  16. [16]
    Huang H, Fu T N, Rosin P L, Qi C. Real-time content-aware image resizing. Science in China Series F: Information Sciences, 2009, 52(2): 172–182.CrossRefMathSciNetGoogle Scholar
  17. [17]
    Tsai W H. Moment-preserving thresholding: A new approach. CVGIP: Image Understanding, 1985, 29(3): 377–393.Google Scholar
  18. [18]
    Osher S. A level set formulation for the solution of the Dirichlet problem for Hamilton-Jacobi equations. SIAM Journal on Mathematical Analysis, 1993, 24(5): 1145–1152.zbMATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    Sethian J A. Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Science. Cambridge University Press, 1996.Google Scholar
  20. [20]
    Bajaj C L, Xu G L, Zhang Q. Higher-order level-set method and its application in biomolecular surfaces construction. Journal of Computer Science and Technology, 2008, 23(6): 1026–1036.CrossRefMathSciNetGoogle Scholar
  21. [21]
    Tomasi C, Manduchi R. Bilateral filtering for gray and color images. In Proc. International Conference on Computer Vision, Bombay, India, January 4–7, 1998, pp.839–846.Google Scholar
  22. [22]
    Elad M. On the origin of the bilateral filter and ways to improve it. IEEE Trans. Image Processing, 2002, 11(10): 1141–1151.CrossRefMathSciNetGoogle Scholar
  23. [23]
    Buades A, Coll B, Morel J M. The staircasing effect in neighborhood filters and its solution. IEEE Trans. Image Processing, 2006, 15(6): 1499–1505.CrossRefGoogle Scholar
  24. [24]
    Paris S, Kornprobst P, Tumblin J, Durand F. A gentle introduction to bilateral filtering and its applications. In ACM SIGGRAPH Courses, San Diego, California, USA, August 5–9, 2007.Google Scholar
  25. [25]
    Barash D. A fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation. IEEE Trans. Pattern Analysis and Machine Intelligence, 2002, 24(6): 844–847.CrossRefGoogle Scholar
  26. [26]
    Winnemöller H, Olsen S C, Gooch B. Real-time video abstraction. ACM Trans. Graphics, 2006, 25(3): 1221–1226.CrossRefGoogle Scholar
  27. [27]
    Liu Y L, Wang J, Chen X, Guo Y W, Peng Q S. A robust and fast non-local means algorithm for image denoising. Journal of Computer Science and Technology, 2008, 23(2): 270–279.CrossRefMathSciNetGoogle Scholar
  28. [28]
    Aubert G, Kornprobst P. Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Springer Verlag, 2002.Google Scholar
  29. [29]
    Wang Z, Bovik A C, Sheikh H R, Simoncelli E P. Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Processing, 2004, 13(4): 600–612.Google Scholar
  30. [30]
    Rosin P L. Unimodal thresholding. Pattern Recognition, 2001, 34(11): 2083–2096.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer 2009

Authors and Affiliations

  1. 1.School of Electronics and Information EngineeringXi’an Jiaotong UniversityXi’anChina
  2. 2.School of Computer ScienceCardiff UniversityCardiffU.K.

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