Computational Mathematics and Modeling, Vol. 29, No. 3, July, 2018
FINDING THE PARAMETERS OF A NONLINEAR DIFFUSION DENOISING METHOD
BY RIDGE ANALYSIS
N. V. Mamaev,
D. V. Yurin,
and A. S. Krylov
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 assess-
ment 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 pro-
duces 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.
Keywords: noise suppression, denoising, optimal denoising parameters, nonlinear diffusion, ridge struc-
tures, mutual information, no-reference quality assessment.
Noise suppression (denoising) is one of the classical image processing tasks, as noise is present in all digital
images. Noise suppression is often a preliminary stage before the application of another method, such as seg-
mentation. It is important to ensure that denoising preserves the object edges as well as the small objects present
in the original image.
In most cases, the noise in digital images is additive Gaussian. Many efficient edge-preserving denoising
methods have been developed for this type of noise. One of the simplest is the family of rank filters (averages
over KNV-neighborhood and
-neighborhood) . In these methods, the intensity of the output pixel is the
average of the intensities of several original-image pixels from its neighborhood. The inclusion of each pixel
is determined by its position relative to the averaged pixel in the ranked intensity series. In the
hood mean method, only pixels with intensities deviating by less than
from the averaged pixel are included
in the averaging, and in the KNV-mean method only the
pixels of nearest intensity (rank) are included.
In this approach, the parameter
can be specified based on the expected spatial configuration of the objects
(such as the acuity of the object corners that must not be lost) rather than the assumed image brightness and
The bilateral filter  is a generalization of the
-neighborhood averaging. Here the value of the output
pixel is the weighted sum of the original-image pixels from some neighborhood, and the weights depend both
on the brightness difference of the averaged pixel and the distance from the averaged pixel. The nonlocal mean
(NLM) method  is a modification of the bilateral filter. Here the weights depend on the distance between
Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia.
Translated from Prikladnaya Matematika i Informatika, No. 56, 2017, pp. 90–102.
334 1046–283X/18/2903–0334 © 2018 Springer Science+Business Media, LLC