An axiomatic approach to image interpolation

IEEE Transactions on Image Processing

Volumn 7, Issue 3, 1998, Pages 376-386

  Caselles, Vicent ^a,c   Morel, Jean Michel ^b   Sbert, Catalina ^a  

^a UNIVERSITAT DE LES ILLES BALEARS   (Spain)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

^c IEEE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE CODING; IMAGE PROCESSING; INTERPOLATION; MATHEMATICAL MODELS; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS;

IMAGE INTERPOLATION; LINEAR MEAN VALUE ALGORITHMS; WAVEFORM CODING TECHNIQUE;

ALGORITHMS;

EID: 0032023750     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.661188     Document Type: Article

References (26)

1. L. Alvarez, F. Guichard, P. L. Lions, and J. M. Morel, "Axioms and fundamental equations of image processing," Arch. Rational Mechan. Anal., vol. 16, no. IX, pp. 200-257, 1993.
2. G. Aronsson, "Extension of functions satisfying Lipschitz conditions," Ark. Math., vol. 6, pp. 551-561, 1967.
3. J. Canny, "A computational approach to edge detection," IEEE Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-698, 1986.
4. S. Carlsson, "Sketch based coding of grey level images," Signal Process., vol. 15, pp. 57-83, 1988.
5. J. R. Casas, "Image compression based on perceptual coding techniques," Ph.D. dissertation, Dept. Signal Theory Commun., UPC, Barcelona, Spain, Mar. 1996.
6. J. R. Casas and L. Torres, "Strong edge features for image coding," in Mathematical Morphology and Its Applications to Image and Signal Processing, R. W. Schafer, P. Maragos, and M. A. Butt, Eds. Boston, MA: Kluwer, May 1996, pp. 443-450.
7. V. Caselles, F. Catte, B. Coll, and F. Dibos, "A geometric model for active contours in image processing," Numer. Math., vol. 66, pp. 1-31, 1993.
8. V. Caselles, J. M. Morel, and C. Sbert, "An axiomatic approach to image interpolation," preprint, C, 1997 (text containing all mathematical proofs).
9. M. G. Crandall, H. Ishii, and P. L. Lions, "User's guide to viscosity solutions of second order partial differential equations," Bull. Amer. Math. Soc., vol. 27, pp. 1-67, 1992.
10. L. C. Evans and J. Spruck, "Motion of level sets by mean curvature," J. Differ. Geom., vol. 33, pp. 635-681, 1991.
11. O. Faugeras, Three-Dimensional Computer Vision: A Geometric newpoint. Cambridge, MA: MIT Press, 1993.
12. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations. New York: Springer-Verlag, 1983.
13. F. Guichard and J. M. Morel, "Introduction to partial differential equations on image processing," Tutorial, in Proc. ICIP-95; extended version to be published by Cambridge Univ. Press.
14. W. S. Havens and J. C. Strikwerda, "An improved operator for edge detection," 1984.
15. R. Jensen, "Uniqueness of Lipschitz extensions: Minimizing the Sup Norm of the Gradient," Arch. Rational Mechan. Anal., vol. 123, pp. 51-74, 1993.
16. O. A. Ladyzhenskaja, V. A. Solonnikov, and N. N. Ural'ceva, "Linear and quasilinear equations of parabolic type," Trans. Math. Monographs, vol. 23. Providence, RI: Amer. Math. Soc., 1968.
17. H. Le Floch and C. Labit, "Irregular image subsampling and reconstruction by adaptative sampling," in Proc. Int. Conf. Image Processing ICIP-96, Sept. 1996, Lausanne, Switzerland, vol. III, pp. 379-382.
18. D. Marr, Vision. New York: Freeman, 1982.
19. D. Marr and E. Hildreth, "Theory of edge detection," Proc. R. Soc. Lond. B, vol. 207, pp. 187-217, 1980.
20. M. J. D. Powell, "A review of methods for multivariable interpolation at scattered data points," Numer. Anal. Rep., NA11, DAMTP. Cambridge, U.K.: Cambridge Univ. Press, 1996;
21. to be published in State of the Art in Numerical Analysis. Cambridge, U.K.: Cambridge Univ. Press.
22. J. M. S. Prewitt, "Object enhancement and extraction," Picture Processing and Psychopictorics, B. Lipkin and A. Rosenfeld, Eds. New York: Academic, 1970, pp. 75-149.
23. X. Ran and N. Favardin, "A perceptually motivated three-component image model. Part II: Applications to image compression," IEEE Trans. Image Processing, vol. 4, pp. 430-447, 1995.
24. D. Shepard, "A two dimensional interpolation function for irregularly spaced data," in Proc. 23rd Nat. Conf. ACM, 1968, pp. 517-523.
25. V. Torre and T.A. Poggio, "On edge detection," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 147-163, 1986.
26. A. L. Yuille and T. A. Poggio, "Scaling theorems for zero-crossings," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 15-25, 1986