Stabilization of median smoother via variational approach

Zuzana Krbcová; Abduljalil Sireis; Jaromír Kukal; Jan Švihlík; Karel Fliegel

doi:10.1117/12.2321226

17 September 2018 Stabilization of median smoother via variational approach

Zuzana Krbcová, Abduljalil Sireis, Jaromír Kukal, Jan Švihlík, Karel Fliegel

Proceedings Volume 10752, Applications of Digital Image Processing XLI; 107522O (2018) https://doi.org/10.1117/12.2321226
Event: SPIE Optical Engineering + Applications, 2018, San Diego, California, United States

Abstract

Traditional median smoother for 2D images is insensitive to impulse noise but generates flat areas as unwanted artifacts. The proposed approach to overcome this issue is based on the minimization of the regularized form of total variation functional. At first the continuous functional is defined for n-dimensional signal in an integral form with regularization term. The continuous functional is converted to the discrete form using equidistant spatial sampling in point grid of pixels, voxels or other elements. This approach is suitable for traditional signal and image processing. The total variance is then converted to the sum of absolute intensity differences as a minimization criterion. The functional convexity guarantees the existence of global minimum and absence of local extremes. Resulting non-linear filter iteratively calculates local medians using red-black method of Successive Over/Under Relaxation (SOR) scheme. The optimal value of the relaxation parameter is also subject to our study. The sensitivity to regularization parameter enables to design high-pass and nonlinear band-pass filters as the difference between the image and low-pass smoother or as the difference between two different low-pass smoothers, respectively. Various median based approaches are compared in the paper.

Citation Download Citation

Zuzana Krbcová, Abduljalil Sireis, Jaromír Kukal, Jan Švihlík, and Karel Fliegel "Stabilization of median smoother via variational approach", Proc. SPIE 10752, Applications of Digital Image Processing XLI, 107522O (17 September 2018); https://doi.org/10.1117/12.2321226

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KEYWORDS

Signal to noise ratio

Digital filtering

Image filtering

Smoothing

Nonlinear filtering

Image processing

Infinite impulse response filters

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