P-laplacian driven image processing

Proceedings - International Conference on Image Processing, ICIP

Volumn 5, Issue , 2007, Pages

  Kuijper, Arjan ^a  

^a JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

Author keywords

Differential geometry; Image analysis; Image processing; Nonlinear differential equations; Partial differential equations

Indexed keywords

GEOMETRY; IMAGE ANALYSIS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

BALANCED FORWARD-BACKWARD DIFFUSIONS; DIFFERENTIAL GEOMETRY; EDGE PRESERVING; GAUSSIAN FILTERS; NONLINEAR DIFFERENTIAL EQUATION; REAL-LIFE IMAGES; SECOND ORDER DERIVATIVES; TOTAL VARIATION;

IMAGE PROCESSING;

EID: 48149096557     PISSN: 15224880     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICIP.2007.4379814     Document Type: Conference Paper

References (21)

1. L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D, vol. 60, no. 259-268, 1992.
2. J. J. Koenderink, "The structure of images," Biological Cybernetics, vol. 50, pp. 363-370, 1984.
3. L. M. J. Florack, Image Structure, vol. 10 of Computational Imaging and Vision Series, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.
4. B. M. ter Haar Romeny, Front-end vision and multi-scale image analysis, vol. 27 of Computational Imaging and Vision Series, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003.
5. A.Friedman, Variational principles and free boundary problems, Wiley, New York, 1982.
6. yy = 0," Arkiv für Matematik, vol. 7, pp. 395-425, 1968.
7. M.G. Aronsson, G. and; Crandall and P. Juutinen, "A tour of the theory of absolutely minimizing functions," Bull. Amer. Math. Soc., vol. 41, pp. 439-505, 2004.
8. M. G. Crandall, L. C. Evans, and R. F. Gariepy, "Optimal lipschitz extensions and the infinity laplacian," Calc. Var., vol. 13, pp. 123-139, 2001.
9. A. M. Oberman, "A convergent difference scheme for the infinity laplacian: Construction of absolutely minimizing lipschitz extensions," Mathematics of Computation, vol. 74, no. 251, pp. 1217-1230, 2005.
10. V. Caselles, J.-M. Morel, and C. Sbert, "An axiomatic approach to image interpolation," IEEE Transactions on Image Processing, vol. 7, pp. 376386, 1996.
11. G. Cong, M. Esser, B. Parvin, and G. Bebis, "Shape metamorphism using p-laplacian equation," in ICPR04, 2004, vol. 4, pp. 15-18.
12. G. I. Barenblatt, "On self-similar motions of compressible fuids in porous media," Prikl. Mt. Makh., vol. 16, no. 6, pp. 679-698, 1952, in Russian.
13. Juan Luis Vazquez, Smoothing and Decay Estimates for Non-linear Diffusion Equations Equations of Porous Medium Type, vol. 33 of Oxford Lecture Series in Mathematics and Its Applications, Oxford University Press, 2006.
14. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover, 9th printing edition, 1972.
15. Y. Chen, S. Levine, and M. Rao, "Variable exponent, linear growth functionals in image restoration," SIAM Journal of Applied Mathematics, vol. 66, no. 4, pp. 1383-1406, 2006.
16. B. Tang, G. Sapiro, and V. Caselles, "Diffusion of general data on non-flat manifolds viaharmonic maps theory: The direction diffusion case," International Journal of Computer Vision, vol. 36, no. 2, pp. 149-161, 2000.
17. P. Perona and J. Malik, "Scale space and edge detection using anisotropic diffusion," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629-639, 1990.
18. M. Welk, J. Weickert, and G. Steidl, "A four-pixel scheme for singular differential equations," in Kimmel et al. [21], 2005, pp. 610-621.
19. S. L. Keeling and R. Stollberger, "Nonlinear anisotropic diffusion filtering for multiscale edge enhancement," Inverse Problems, vol. 18, no. 1, pp. 175-190, 2002.
20. S. Kim, "Pde-based image restoration: A hybrid model and color image denoising," IEEE Transactions on Image Processing, vol. 15, no. 5, pp. 1163-1170, 2006.
21. R. Kimmel, N. Sochen, and J. Weickert, Eds., Scale Space and PDE Methods in Computer Vision, vol. 3459 of Lecture Notes in Computer Science, Springer -Verlag, Berlin Heidelberg, 2005.