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Edge-preserving smoothing by convex minimization

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1351))

Abstract

This work presents a new approach for analyzing the problem of edge-preserving image smoothing using convex minimization and for selecting smoothing parameters. The close-form (global) solution is derived as the response of a convex smoothing model to the ideal step edge. Insights into how the minimal solution responds to edges in the data and how the parameter values affect resultant edges in the solution are drawn from the analytic expression of the close-form solution. Based on this, a scheme is proposed for selecting parameters to achieve desirable response at edges.

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References

  1. A. Blake and A. Zisserman. Visual Reconstruction. MIT Press, Cambridge, MA, 1987.

    Google Scholar 

  2. C. Bouman and K. Sauer. “A generalized Gaussian image model for edge preserving MAP estimation”. IEEE Transactions on Image Processing, 2(3):296–310, July 1993.

    Google Scholar 

  3. P. Green. “Bayesian reconstructions from emission tomography data using a modified EM algorithm”. IEEE Transactions on Medical Imaging, 9(1):84–93, March 1990.

    Google Scholar 

  4. H. Jeong and C. I. Kim. “Adaptive determination of filter scales for edge detection”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14:579–585, 1992.

    Google Scholar 

  5. K. Lange. “Convergence of EM image reconstruction algorithm with Gibbs smoothing”. IEEE Transactions on Medical Imaging, 9(4):439–446, December 1990.

    Google Scholar 

  6. S. Z. Li. “On discontinuity-adaptive smoothness priors in computer vision”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(6):576–586, June 1995.

    Google Scholar 

  7. S. Z. Li, Y. H. Huang, and J. Fu. “Convex MRF potential functions”. In Proceedings of IEEE International Conference on Image Processing, volume 2, pages 296–299, Washington, D.C., 23–26 October 1995.

    Google Scholar 

  8. S. G. Nadabar and A. K. Jain. “Parameter estimation in Markov random field contextual models using geometric models of objects”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18:326–329, 1996.

    Google Scholar 

  9. P. Perona and J. Malik. “Scale-space and edge detection using anisotropic diffusion”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):629–639, July 1990.

    Google Scholar 

  10. M. Petrou and J. Kittler. “Optimal edge detection for ramp edges”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(5):483–490, 1991.

    Google Scholar 

  11. I. Pitas and A. N. Venetsanopoulos. “Edge detectors based on nonlinear filters”. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8:538–550, 1986.

    Google Scholar 

  12. D. Shulman and J. Herve. “Regularization of discontinuous flow fields”. In Proc. Workshop on Visual Motion, pages 81–86, 1989.

    Google Scholar 

  13. R. L. Stevenson, B. E. Schmitz, and E. J. Delp. “Discontinuity preserving regularization of inverse visual problems”. IEEE Transactions on Systems, Man and Cybernetics, 24(3):455–469, March 1994.

    Google Scholar 

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Roland Chin Ting-Chuen Pong

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© 1997 Springer-Verlag Berlin Heidelberg

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Li, S.Z., Huang, Y.H., Fu, J.S., Chan, K.L. (1997). Edge-preserving smoothing by convex minimization. In: Chin, R., Pong, TC. (eds) Computer Vision — ACCV'98. ACCV 1998. Lecture Notes in Computer Science, vol 1351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63930-6_190

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  • DOI: https://doi.org/10.1007/3-540-63930-6_190

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63930-5

  • Online ISBN: 978-3-540-69669-8

  • eBook Packages: Springer Book Archive

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