Research on a precise differential box-counting method of eliminating image background

Abstract

Differential box-counting (DBC) method has been widely used to calculate fractal dimension. analyzing the result of fractal dimension with background image by estimating this traditional method,we find that this algorithm has the limitation to estimate fractal dimension of images with background accurately. In order to solve this issue ,in this paper, an improved differential box-counting(IDBC) method has been proposed to eliminate influence of background on fractal dimension .The mainly improved steps of IDBC as follow: firstly ,the background pixels values Gb of image need to be found out using probability .Secondly, the nq ( nq is the numbers of boxes in a grid) is set to zero when the maximum and minimum in a grid are equal to image background values. To validate IDBC method’s performance ,we designed an experiment that the fractal dimension of both original texture images and these ones put in different size frame with black-background are estimated and compared through four different algorithms, including DBC, relevant differential box-counting (RDBC) method, shifting differential box-counting (SDBC) method and IDBC method. The experimental results demonstrate that the IDBC method developed in this work has the ability to improve the measurement accuracy by avoiding the influence caused by background.