An anti-noise determination on fractal dimension for digital images

Abstract

Since most images coming from nature show the fractal characteristic, the fractal dimension can be used to quantitative characterization and analysis on these images. However, noise may have an effect on the fractal dimension. In this work, the effects of salt & pepper noise, Gaussian white noise and multiplicative noise on the fractal dimension are studied by using different material images. The study shows that the three kinds of noises all have a significant effect on the fractal dimension. Digital images with added noise become coarser, and their corresponding fractal dimensions increase. An anti-noise determination on fractal dimension based on differential box counting (DBC) algorithm and noise character is proposed. Pixel values in a box are all used and the deviation between the maximum and minimum within the box is replaced with double standard deviation. Compared with the general pretreatment method, the proposed method is valid and convenient. © 2011 Springer-Verlag Berlin Heidelberg.