On estimation of Fractal Dimension of Grayscale images using Modified Differential Box-counting Method

Fractal Dimension (FD) is most useful Research topic in the field of fractal geometry to identify surface roughness of digital images, which FD lies between 2 to 3 for the image surfaces. In this regard, many researchers have contributed their efforts to estimate FD of gray scale images, among these methods differential box-counting (DBC) method are well-recognized methods but DBC method having many demerits like over-counting and under-counting presented in many kinds of literature. In this regard, most of these approaches focus on the improvement of selecting the suitable height of box-counts to overcome either the under-counting and over-counting problem, but none of these approaches attempt to overcome the both problem simultaneously. Therefore, this paper proposes a more accurate FD estimation by using modified differential box-counting by adopting appropriate grid estimation on spatial coordinates of x and y-direction to solve both undercounting and overcounting problem simultaneously and provides a wider range of fractal dimension with less fit error as compared to existing methods like DBC, relative DBC and improved DBC (IDBC). The proposed methodology was demonstrated on real brodatz texture images, smooth synthetic transformed images and synthetic texture like images. It shows that our modified method covers all objects with a wider range of fractal dimension as compared to the existing methods.