The influence of noise on the generalized dimensions

Digital images of real objects are often interpreted as fractals and computer algorithms enable the determination of fractal dimensions, such as the generalized correlation dimensions. But digital images are restricted representations of the real object and an exact determination or calculation is not possible. Digital images have a limited spatial resolution and they are always contaminated with noise that may disturb the representation of the real object. The influence of noise on the calculated values of the generalized correlation dimensions has been investigated in this study. A practical fractal, a digital image of a cancer spheroid, as well as three mathematically defined fractals, the Sierpinski triangle, a fern and a modified Menger gasket were used and the results were compared. Noise with well defined levels was added to noise free images. Three distinct noise distributions were applied and the results were compared. It turned out, that noise partially has a high and distinct influence on the generalized dimensions but the influence is very similar for each one of the fractals. Because of this similarity, the results are reliable and the representation of real objects by digital images is reliable, too.