An improved method for estimating fractal dimension of images

Because of the prominent performance to characterize roughness and self-similarity for an image, fractal dimension (FD) has been widely used in shape analysis, texture classification, texture segmentation and other fields. An effective and efficient method for estimating FD is the key to optimize the performance in such applications. There are several approaches proposed to pursue this goal, and the most prevailing one is differential box-counting (DBC) approach. Although this approach has had excellent achievement, there is still some room left for improving. Considering that different fractal dimensions calculated on different scales might have influence in different degrees to the final result, this paper proposes an improved weighted linear least squares fit method to improve the original DBC one. The result shows that the improved method successfully mitigates the underestimation of fractal dimension by the original DBC approach.