Issue 3 (189), article 3


Kibern. vyčisl. teh., 2017, Issue 3 (189), pp.

Balovsyak S.V., PhD (Phys-Math), Docent
Associate Professor (Docent) of the Department of Computer Systems and Networks
Odaiska Kh.S., Postgraduate Student of the Department of Computer Systems and Networks
Yuriy Fedkovych Chernivtsi National University,
Kotsyubynsky St., 2, 58032, Chernivtsi, Ukraine


Introduction. The noise level is an important parameter for common application tasks of digital image processing: noise removal, segmentation, recognition and other. At the experimental image processing the noise level in most cases is unknown, so development of a method for automatic and accurate determination of noise level in images is an actual and important for practice task [1–7]. Additive White Gaussian Noise (AWGN) belongs to the widespread noise model, since many noises in the real images are described rather accurately by the AWGN model [1]. For this reason this article will consider the methods of noise level determination in the images within the AWGN model, and this noise will further be called Gaussian noise for the sake of simplicity. Level of Gaussian noise is expressed by standard deviation of noise.
The purpose of the article is to develop an automatic method of Gaussian noise level determination in digital images, which uses the selection of image region based on its low-frequency filtering and performs calculation of noise level by analyzing of histograms of the selected region. The article is aimed at software implementation of the elaborated method in the MATLAB system and estimation of its accuracy by processing the collection of test images.
Methods. The method of the selected regions for calculation of Gaussian noise level, which involves the selection of image region and analysis of its histogram is used. Convolution operation to filter digital images is applied. For estimation of accuracy of noise level determination the root mean square error (RMSE) between the experimental and theoretical noise levels for the test images is used.
Results. The method of automatic determination of level of Gaussian noise in digital images is developed. A method consists in the selection of the image ROI (Region Of Interest) [1, 3], where the noise is mainly present, in the calculation of histogram of the selected region and standard deviation of histogram and in the calculation of experimental level of noise based on value . If the variation does not exceed the established limit, the process of the ROI clarification is completed. The proposed method is software implemented in MATLAB system [3].
Conclusion. The mathematical model of image filtering with Gaussian noise is created. The created model allows selecting the ROI regions with the prevailed Gaussian noise [8, 9]. The modification of the algorithm for determining the level of Gaussian noise in images is implemented [10–12], which specifies the minimum permissive value of the ROI area, leading to reducing the root mean square error of calculation of noise level on 0.1%.
The accuracy of the proposed method is studied by processing the set of 100 test images [11, 12], and the root mean square error of calculation equals to 0.257%. The resulting error of calculation is less, than the one obtained for the most accurate modern methods of determination of noise level [4, 5]. With the use of more precise method of the ROI noise level determination, different from histogram analysis, the accuracy of the proposed method can be improve.
Keywords: digital image processing, noise level determination, standard deviation of Gaussian noise, histogram of image.

Download full text (ua)!


1 Gonzalez R., Woods R. Digital image processing. M.: Technosphere, 2005. 1072 p. (in Russian).

2 Bovik A.L. The Essential Guide to Image Processing. Elsevier Inc., 2009. 853 p.

3 Gonzalez R., Woods R., Eddins S. Digital image processing using MATLAB. M.: Technosphere, 2006. 616 p. (in Russian).

4 Liu X., Tanaka M., Okutomi M. Single-Image Noise Level Estimation for Blind Denoising. IEEE Transactions on Image Processing. 2013. Vol. 22, No. 12. P. 5226–5237.

5 Pyatykh S., Hesser J., Zheng L. Image noise level estimation by principal component analysis. IEEE Transaction on Image Processing. 2013. Vol. 22, No. 2. P.687–699.

6 Goltsev A.D., Gritsenko V.I. Algorithm of sequential finding the textural features characterizing homogeneous texture segments for the image segmentation task. Cybernetics and Computer Engineering. 2013. Vol. 173.P. 25–35. (in Russian).

7 Zoran D., Weiss Y. Scale invariance and noise in natural images. Proc. IEEE 12th Int. Conf. Comput. Vis., Sep./ Oct. 2009. P. 2209–2216.

8 GmurmanV.E. Theory of Probability and Mathematical Statistics : Textbook for high schools. M. : Vyssh. shk., 2003. 479 p. (in Russian).

9 Korn G., Korn T. Mathematical handbook. For scientists and engineers. M.: Nauka, 1974. 832 p. (in Russian).

10 Image Processing Place. Image Databases. URL: root_files_V3/image_databases.htm.

11 Fowlkes C., Martin D., Malik J. Local Figure/Ground Cues are Valid for Natural Images. Journal of Vision. 2007. Vol. 7 (8), No. 2. P. 1–9.

12 The Berkeley Segmentation Dataset and Benchmark. BSDS300. URL:

Received 17.02.2017