The optical or mechanical registration processes introduce same systematical and accidental disfigurement in the fracture image. Differentiation between chaotic and determined components of the investigated images is a main problem of the presented work. Fractals and Multifractals based-theory and estimating of the Hurst exponent have been used for this differentiation. The aim of the paper was the selection of the most suitable method for the fracture surface analysis using modern tools to the mathematical verification of dataset containing irregular data values and the considerable variability of the amplitude. In the paper, the efficiency of several most popular methods used of this exponent has been checked on several chosen examples. There are three methods of the estimations of the Hurst exponent: R/S method, Roughness - Length (R - L) method and Variogram. The basic dependences have following forms [1÷4]:
1.) R_(w)/S_(w)^*=cw^H, 2.) S_(w)=cw^H, 3.) V_(w)={[y(x)-y(x+w)]²},^*
4.) V_(w)=cw^2H
where: R_(w) - the difference of the height of the profile in the window, c - the constant , S_(w) - the standard deviation, H - the Hurst exponent,w the width of the window (section), x and y are data coordinates . Exponent H is a slope of interpolated straight line in the log - log system.
(The mark * denotes of the mean value for the data on each of the windows)
The surface research of the fracture could be executed on the light microscope with two situated lenses in relation to the examined surface at an angle of 45⁰. The noise in the range of high frequencies is generated on the edge dark and lucid areas of the microscopy images. Proposed procedure of the Hurst exponent calculating is verified for profiles obtained from the surface of the fracture of steel 18G2A in the rough and after Wavelet approximations. Described methods give considerably differed results. The R - L method is offering the best approximation for the investigated case

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