Image edge detection with the use of the Tikhonov regularization method

  • V. N. Tsibanov
  • A. S. Krylov


The study considers application of the Tikhonov regularization method for smoothing of 1D signals, noise suppression, and determination of objects’ edges in images. An analytic solution to the Euler equation is obtained in the 1D case for certain stabilizers. Application of the considered method for determination of objects’ edges in noisy images is analyzed.


Euler Equation Image Noise Noisy Image Tikhonov Regularization Noise Suppression 
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  1. 1.
    D. Marr and E. Hildreth, “Theory of Edge Detection,” Proc. R. Soc. London, Ser. B 207, 187–217 (1980).CrossRefGoogle Scholar
  2. 2.
    J. Canny, “A Computational Approach To Edge Detection,” IEEE Trans. Pattern. Anal. Mach. Intell., 8, 679–698 (1986).Google Scholar
  3. 3.
    A. M. Denisov, Introduction in Theory of Inverse Problems (Mosk. Gos. Univ., Moscow, 1994) [in Russian].Google Scholar
  4. 4.
    A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems (Nauka, Moscow, 1979; Wiley, New York, 1977).Google Scholar
  5. 5.
    O. Scherzer and J. Weickert, “Relations Between Regularization and Diffusion Filtering,” J. of Math. Imaging and Vision, No. 12, 43–63 (2000).Google Scholar
  6. 6.
    M. A. Naimark, Linear Differential Operators (2nd ed., Nauka, Moscow, 1969; Ungar, New York, 1967).Google Scholar

Copyright information

© Allerton Press, Inc. 2008

Authors and Affiliations

  1. 1.Department of Mathematical Physics, Faculty of Computational Mathematics and CyberneticsMoscow State UniversityLeninskie Gory, MoscowRussia

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