A modified approach to estimate fractal dimension of gray scale images

Fractal dimension (FD) is an important feature of fractal geometry to identify surface roughness of digital images. In this regard many methods were presented, among which differential box counting (DBC) method is a commonly used technique to estimate fractal dimension (surface roughness) of digital images. This paper presents modified version of differential box counting technique that addresses three issues found in original DBC; such as minimum roughness variation, computational error and similar fractal dimension (FD) evaluated either by incrementing or decrementing constant value to each intensity points. Based upon these three issues, our proposed method is better than the existing methods like DBC, relative DBC (RDBC) and improved DBC (IDBC). The improved version is achieved by subtracting the minimum intensity value from average intensity value on each grid. The subtraction of the minimum gray level of the block rather than zero gray level is used as a correction factor for accurate estimation of fractal dimension. The proposed methodology was demonstrated on real brodatz texture data base images, smooth images and synthetic texture like images. It shows that our improved method covers all objects with wider range of fractal dimension as compared to the existing methods.