Vector median filters, inf-sup operations, and coupled PDE's: Theoretical connections

Journal of Mathematical Imaging and Vision

Volumn 12, Issue 2, 2000, Pages 109-119

  Caselles, Vicent ^a   Sapiro, Guillermo ^b   Chung, Do Hyun ^b  

^a UNIVERSITAT DE LES ILLES BALEARS   (Spain)

^b University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ITERATIVE METHODS; MATHEMATICAL MORPHOLOGY; PARTIAL DIFFERENTIAL EQUATIONS; SIGNAL FILTERING AND PREDICTION; VECTORS;

ANISOTROPIC DIFFUSION; VECTOR MEDIAN FILTERING;

IMAGE PROCESSING;

EID: 0033893336     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008310305351     Document Type: Article

References (17)

1. L. Alvarez, P.L. Lions, and J.M. Morel, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Anal., Vol. 29, pp. 845-866, 1992.
2. V. Caselles, J.M. Morel, G. Sapiro, and A. Tannenbaum (Eds.), "Special issue on partial differential equations and geometry-driven diffusion in image processing and analysis," IEEE Trans. Image Processing, Vol. 7, pp. 269-273, 1998.
3. L.C. Evans and J. Spruck, "Motion of level-sets by mean curvature II," in Trans. American Mathematical Society, Vol. 30, No. 1, pp. 321-332, 1992.
4. F. Guichard and J.M. Morel, Introduction to Partial Differential Equations in Image Processing. Tutorial Notes, IEEE Int. Conf. Image Proc., Washington, DC, Oct. 1995.
5. H.J.A.M. Heijmans and J.B.T.M. Roerdink (Eds.), Mathematical Morphology and Its Applications to Image and Signal Processing, Kluwer: Dordrecht, The Netherlands, 1998.
6. D.G. Karakos and RE. Trahanias, "Generalized multichannel image-filtering structures," IEEE Trans. Image Processing, Vol. 6, pp. 1038-1045, 1997.
7. R. Kimmel, R. Malladi, and N. Sochen, "Image processing via the Beltrami operator," in Proc. of 3rd Asian Conf. on Computer Vision, Hong Kong, Jan. 8-11, 1998.
8. R. Kimmel, Personal communication.
9. P. Maragos and R.W. Schafer, "Morphological systems for multidimensional image processing," Proc. IEEE, Vol. 78, pp. 690-710, 1990.
10. P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern. Anal. Machine Intell., Vol. 12, pp. 629-639, 1990.
11. G. Sapiro and D. Ringach, "Anisotropic diffusion of multivalued images with applications to color filtering," IEEE Trans. Image Processing Vol. 5, pp. 1582-1586, 1996.
12. B. Tang, G. Sapiro, and V. Caselles, "Direction diffusion," ECE Department Technical Report, University of Minnesota, Feb. 1999.
13. B. Tang, G. Sapiro, and V. Caselles, "Direction diffusion," in Proc. Int. Conference Comp. Vision, Greece, Sept. 1999.
14. B. Tang, G. Sapiro, and V. Caselles, "Color image enhancement via chromaticity diffusion," ECE Department Technical Report, University of Minnesota, March 1999.
15. P.E. Trahanias and A.N. Venetsanopoulos, "Vector directional filters - A new class of multichannel image processing filters," IEEE Trans. Image Processing, Vol. 2, pp. 528-534, 1993.
16. P.E. Trahanias, D. Karakos, and A.N. Venetsanopoulos, "Directional processing of color images: Theory and experimental results," IEEE Trans. Image Processing, Vol. 5, pp. 868-880, 1996.
17. R.T. Whitaker and G. Gerig, "Vector-valued diffusion," in Geometry Driven Diffusion in Computer Vision, B. ter Haar Romeny (Ed.), Kluwer: Boston, MA, 1994.