An improved differential box-counting method to estimate fractal dimensions of gray-level images

•Three modifications are implemented in our improved DBC method.•Our improved method can solve the two kinds of problems simultaneously.•The method can improve the accuracy by 24.1% from the original DBC method. The differential box-counting (DBC) method is one of the frequently used techniques to estimate the fractal dimension (FD) of a 2D gray-level image. This paper presents an improved DBC method based on the original one for improvement of the accuracy. By adopting the modifying box-counting mechanism, shifting box blocks in (x,y) plane and selecting appropriate grid box sizes, it can solve the two kinds of problems which the DBC has: over-counting boxes along z direction and under-counting boxes just at the border of two neighboring box blocks where there is a sharp gray-level abruption exits. The experiments using two sets of synthetic images and one set of real natural texture images demonstrate that the improved DBC method can solve the two kinds of problems perfectly, simultaneously, and can outperform other DBC methods in the accuracy.