One of the methods to improve image quality, which consists in increasing the resolution of image details by contrast enhancement, is to hyperbolize the image histogram. Herewith this increase in local contrast is carried out indirectly. It is due to the nature of the change in the histogram of the transformed image. Usually the histogram of the input image is transformed so that it has a uniform distribution, which illustrates the same contribution of pixels gray level to the image structure. However, there is a method that is based on modeling the human visual system, which is characterized by the logarithmic dependence of the human reaction to light stimulation. It consists in the hyperbolic transformation of the histogram of the image. Then, due to its perception by the visual system, at its output, during the psychophysical perception of the image, an approximately uniform distribution of the histogram of the levels of gray pixels is formed. But the drawback is the lack of effectiveness of this approach for excessively light or dark images. The modified method of image histogram hyperbolization has been developed. It is based on the power transformation of the probability distribution function, which in the discrete version of the images is approximated by a normalized cumulative histogram. The power index is a control parameter of the transformation. to improve the darkened images we use the value of the control parameter less than one, and for light images more than one. The effectiveness of the proposed method is shown by examples.

1. Jahne, B. Digital Image Processing, Springer, Berlin, 2006.

2. Pratt, W.K. Digital Image Processing, Wiley, Los Altos, 2007. https://doi.org/10.1002/0470097434

3. Gonzales, R.C.; Woods, R.E. Digital Image Processing, Prentice Hall, 2008.

4. Vorobel R.A. Logarithmic image processing, Naukova dumka, Kyiv, 2012.

5. Pratt, W.K. Digital Image Processing, Wiley, Los Altos, 2007. https://doi.org/10.1002/0470097434

6. Yaroslavsky, L.P. Digital signal processing in optics and holography. Introduction to Digital Optics, Radio i svyaz, Moscow, 1987.

7. Vorobel R.A. Local contrast as a base for construction of methods of the image improvement, Information Extraction and Processing, 2001, 15(91), 154-163. (in Ukrainian)

8. Vorobel, R.; Berehulyak, O. Gray Image Contrast Enhancement by Optimal Fuzzy Transformation, Artificial Intelligence and Soft Computing, L.Rutkowski et al. (Eds.), Lecture Notes in Artificial Intelligence, Springer-Verlag, Berlin Heidelberg, 2006, 4029, 860-869. https://doi.org/10.1007/11785231_90

9. Hall, E.L. Computer Image Processing and Recognition, Academic Press., New York, 1979.

10. Vorobel R.A. A method for images contrast enhancement using nonlinear transformations of histogram component, Information Extraction and Processing, 2000, 14(90), 105-110. (in Ukrainian)

11. Frei, W. Image Enhancement by Histogram Hyperbolization, Computer Graphics and Image Processing, 1977, 6, 3, 286-294. https://doi.org/10.1016/S0146-664X(77)80030-0