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Finding the Parameters of a Nonlinear Diffusion Denoising Method by Ridge Analysis

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Noise-suppression (denoising) methods depend on the parameters that regulate filtering intensity. The noise-free image is inaccessible in practice, and we have to choose optimal parameters that use only the original noisy image and a filtered image. Image quality can be measured in the presence of ridge structures (ridges and valleys) by analyzing difference frames. A method for filtering quality assessment is proposed: it evaluates the mutual information between the values of the difference frame points where ridge structures are present. Ridge structures are detected by analyzing the Hessian, which produces the directions and the characteristic width of the ridges and the valleys. The method has been tested for the Perona–Malik nonlinear diffusion on noisy images from the BSDS500 database.

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References

  1. L. P. Yaroslavsky and V. Kim, “Rank algorithms for picture processing,” Comput. Vis. Graph. Image Process, 35, 234–258 (1986).

    Article  Google Scholar 

  2. C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in: Sixth International Conference on Computer Vision (ICCV 1998) (1998), pp. 839–846.

  3. A. Buades, B. Coll, and J. Morel, “A review of image denoising algorithms, with a new one,” SIAM J. Multiscale Model. Simul.: SIAM Interdisc., 4, No. 2, 490–530 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Manzanera, “Local jet based similarity for NL-means filtering,” in: 20th International Conference on Computer Vision and Pattern Recognition (ICPR) (2010), pp. 2668–2671.

  5. P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” in: Proceedings of IEEE Computer Society Workshop on Computer Vision (1987), pp. 16–22.

  6. A. Mitta, A. K. Moorthy, and A. C. Bovik, “No-reference image quality assessment in the spatial domain,” IEEE Trans. Image Process., 21, 4695–4708 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. K. Moorthy and A. C. Bovik, “Blind image quality assessment: from scene statistics to perceptual quality,” IEEE Trans. Image Process., 20, No. 12, 3350–3364 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  8. M. A. Saad and A. C. Bovik, “Blind image quality assessment: a natural scene statistics approach in the DCT domain,” IEEE Trans. Image Process., 21, No. 8, 3339–3352 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Eberly, Ridges in Image and Data Analysis, Springer, Heidelberg (1996).

    Book  MATH  Google Scholar 

  10. T. Lindeberg, “Edge detection and ridge detection with automatic scale selection,” in: Proceedings of the Conference on Computer Vision and Pattern Recognition, San Francisco, CA (1996), pp. 465–470.

  11. R. M. Haralick, K. Shanmugan, and I. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern., SMC–3, 610–621 (1973).

  12. D. Martin, C. Fowlkes, D. Tal, and J. Malik, “A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics,” in: Proc. 8th Int’l Conf. Computer Vision. 2 (2001), pp. 416–423.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    N. V. Mamaev, D. V. Yurin & A. S. Krylov

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  1. N. V. Mamaev
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  2. D. V. Yurin
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  3. A. S. Krylov
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Correspondence to N. V. Mamaev.

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Translated from Prikladnaya Matematika i Informatika, No. 56, 2017, pp. 90–102.

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Mamaev, N.V., Yurin, D.V. & Krylov, A.S. Finding the Parameters of a Nonlinear Diffusion Denoising Method by Ridge Analysis. Comput Math Model 29, 334–343 (2018). https://doi.org/10.1007/s10598-018-9413-6

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