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Chromaticity Denoising using Solution to the Skorokhod Problem

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Image Processing Based on Partial Differential Equations

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References

  1. G. Aubert and P. Kornprobst. Mathematical problems in image processing, volume 147 of Applied Mathematical Sciences. Springer-Verlag, New York, 2002. Partial differential equations and the calculus of variations, With a foreword by Olivier Faugeras.

    Google Scholar 

  2. V. Bally. Approximation scheme for solutions of BSDE. In Backward stochastic differential equations (Paris, 1995-1996), volume 364 of Pitman Res. Notes Math. Ser., pages 177–191. Longman, Harlow, 1997.

    Google Scholar 

  3. V. Caselles, G. Sapiro, and B. Tang. Diffusion on general data on non-flat manifolds via harmonic maps theory: the direction diffusion case. Int. J. Comput. Vis., 36(2):149–161, 2000.

    Article  Google Scholar 

  4. V. Caselles, G. Sapiro, and . Tang. Color image enhancement via chromaticity diffusion. IEEE Trans. Image Process., 10(5):701–707, 2001.

    Article  Google Scholar 

  5. T. Cecil, S. Osher, and L. Vese. Numerical methods for minimization problems constrained to S 1 and S 2 . J. Comput. Phys., 198(2):567–579, 2004.

    Article  MathSciNet  Google Scholar 

  6. T. Chan, S. H. Kang, and J. Shen. Total variation denoising and enhancement of color image based on the CB and HSV color models. J. Vis. Comm. Image Represent., 12(4):422–435, 2001.

    Article  Google Scholar 

  7. T. Chan and J. Shen. Variational restoration of nonflat image features: models and algorithms. SIAM J. Appl. Math., 61(4):1338–1361 (electronic), 2000/01.

    Article  MathSciNet  Google Scholar 

  8. D. Chevance. Numerical methods for backward stochastic differential equations. In Numerical methods in finance, Publ. Newton Inst., pages 232–244. Cambridge Univ. Press, Cambridge, 1997.

    Google Scholar 

  9. R. Deriche and D. Tschumperlé. Diffusion PDE’s on vector-valued images: local approach and geometric viewpoint. IEEE Signal Process. Mag., 19(5):16–25, 2002.

    Article  Google Scholar 

  10. S. Di Zenzo. A note on the gradient of a multi-image. Comput. Vis. Graph. Image Process., 33(1):116–125, 1986.

    Article  Google Scholar 

  11. A. Gégout-Petit and E. Pardoux.Équations différentielles stochastiques rétrogrades réfléchies dans un convexe. Stochast. Stochast. Rep., 57(1-2):111-128,1996.

    Google Scholar 

  12. J. Ma, P. Protter, J. San Martin, and S. Torres. Numerical method for backward stochastic differential equations. Ann. Appl. Probab., 12(1):302–316, 2002.

    Article  MathSciNet  Google Scholar 

  13. J. Malik and P. Perona. Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell., 12(7):629–639, 1990.

    Article  Google Scholar 

  14. S. J. Osher and L. A. Vese. Numerical methods for p-harmonic flows and applications to image processing. SIAM J. Numer. Anal., 40(6):2085–2104 (electronic) (2003),2002.

    Article  MathSciNet  Google Scholar 

  15. E. Pardoux. Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order. In Stochastic analysis and related topics, VI (Geilo, 1996), volume 42 of Progr. Probab., pages 79–127. Birkhäuser Boston, Boston, MA, 1998.

    Google Scholar 

  16. Y. Saisho. Stochastic differential equations for multidimensional domain with reflecting boundary. Probab. Theor. Relat. Field., 74(3):455–477, 1987.

    Article  MathSciNet  Google Scholar 

  17. H. Tanaka. Stochastic differential equations with reflecting boundary condition in convex regions. Hiroshima Math. J., 9(1):163–177, 1979.

    MathSciNet  Google Scholar 

  18. J. Zhang. A numerical scheme for BSDEs. Ann. Appl. Probab., 14(1):459–488, 2004.

    Article  MathSciNet  Google Scholar 

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Borkowski, D. (2007). Chromaticity Denoising using Solution to the Skorokhod Problem. In: Tai, XC., Lie, KA., Chan, T.F., Osher, S. (eds) Image Processing Based on Partial Differential Equations. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33267-1_9

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  • DOI: https://doi.org/10.1007/978-3-540-33267-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33266-4

  • Online ISBN: 978-3-540-33267-1

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