Regularization, Scale-Space, and Edge Detection Filters

Journal of Mathematical Imaging and Vision

Volumn 7, Issue 4, 1997, Pages 291-307

  Nielsen, Mads ^a,b,c,d   Florack, Luc ^{a,b,e,f,g,h,i}   Deriche, Rachid ^b,j  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b INRIA   (France)

^c UNIVERSITY OF COPENHAGEN   (Denmark)

^d UNIVERSITY MEDICAL CENTER UTRECHT   (Netherlands)

^e UTRECHT UNIVERSITY   (Netherlands)

^f University of Utrecht ^*  (Australia)

^g INESC   (Portugal)

^h DIKU   (Denmark)

ⁱ Danish Research Academy   (Denmark)

^j UNIVERSITÉ PARIS SACLAY   (France)

more..

Author keywords

Edge detection filters; Linear filtering; Recursive filtering; Regularization; Scale invariance; Scale space

Indexed keywords

COMPUTATIONAL COMPLEXITY; DIFFERENTIATION (CALCULUS); DIGITAL FILTERS; EDGE DETECTION; INVARIANCE; RECURSIVE FUNCTIONS; SIGNAL FILTERING AND PREDICTION;

CANNY DERICHE FILTER; GAUSSIAN SCALE SPACE; LINEAR FILTERING; RECURSIVE FILTERING;

COMPUTER VISION;

EID: 0031250126     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008282127190     Document Type: Article

References (23)

1. L. Schwartz, "Theorie des distributions," Actualités scientifigues et industrielles, Publications de l'Institut de Mathématique de l'Université de Strasbourg, Vols. I, II, 1950-1951.
2. A.P. Witkin, "Scale-space filtering," Proc. of IJCAI, Karlsruhe, Germany, 1983.
3. J.J. Koenderink, "The structure of images," Biol. Cybern., Vol. 50, pp. 363-370, 1984.
4. L. Florack, "The syntactical structure of scalar images," Ph.D. thesis, University of Utrecht, 1993.
5. A.N. Tikhonov and V.Y. Arseninn, Solution of Ill-posed Problems, V.H. Winston & Sons, John Wiley, 1977.
6. T. Poggio, H. Voorhees, and A. Yuille, "A regularized solution to edge detection," A.I. Memo 883, M.I.T, May 1985.
7. J.F. Canny, "A computational approach to edge detection," IEEE PAMI, Vol. 8, No. 6, Nov. 1986.
8. R. Deriche, "Using Canny's criteria to derive a recursively implemented optimal edge detector," Int. Journal of Computer Vision, Vol. 1, No. 2, pp. 167-187, 1987.
9. M. Nielsen, L. Florack, and R. Deriche, "Regularization, scale-space, and edge detection filters," Proc. of ECCV 96, Cambridge, UK, April 14-18, 1996, pp. 70-81.
10. J. Fourier, The Analytic Theory of Heat, New York: Dover Publications, 1995, Original Théori Analytique de la Chaleur, Paris, 1822.
11. J. Fourier, The Analytic Theory of Heat, New York: Dover Publications, 1995, Original Théori Analytique de la Chaleur, Paris, 1822.
12. T. Lindeberg, Scale-Space Theory in Computer Vision, Kluwer Academic Publishers: Netherlands, 1994.
13. T. Lindeberg, "On the axiomatic foundations of linear scale-space: Combining semi-group structure with causality vs. scale invariance," Technical report, CVAP-159, Royal Institute of Technology, Stockholm, Sweden, 1994.
14. E.J. Pauwels, P. Fiddelaers, T. Moons, and L.J.V Gool, "An extended class of scale-invariant and recursive scale space filters," Katholieke Universiteit Leuven, Tech. Rep. KUL/ESAT/MI2/9316, 1994.
15. D. Hilbert, "Ueber die vollen invariantsystemen," Math. Annalen, Vol. 42, pp. 313-373, 1893.
16. W.E.L. Grimson, From Images to Surfaces, MIT Press: Cambridge, Massachusetts, 1981.
17. R. Deriche, "Fast algorithms for low-level vision," IEEE PAMI, Vol. 12, No. 1, pp. 78-88, Jan. 1990.
18. R. Deriche, "Recursively implementing the Gaussian and its derivatives," Proc. 2nd Int. Conference on Image Processing, Singapore, Sept. 7-11, 1992, pp. 263-267.
19. S. Castan, J. Zhao, and J. Shen, "Optimal filter for edge detection methods and results," ECCV 90, Antibes, France, May 1990.
20. M. Unser, A. Aldroubi, and M. Eden, "Recursive regularization filters: Design, properties and applications," IEEE PAMI, Vol. 13, No. 3, March 1991.
21. M. Nielsen, L. Florack, and R. Deriche, "Regularization and scale-space," Research Report 2352, INRIA, Sophia-Antipolis, France, 1994, URL: http://www.inria.fr/rapports/sophia/RR-2352.html.
22. P. Perona and J. Malik, "Scale space and edge detection using anisotropic diffusion," IEEE PAMI, Vol. 12, pp. 429-439, 1990.
23. N. Nordström, "Biased anisotropic diffusion - A unified regularization and diffusion approach to edge detection," Image and Visual Computing, No. 8, pp. 318-327, 1990.