A New Extended Differential Box-Counting Method by Adopting Unequal Partitioning of Grid for Estimation of Fractal Dimension of Grayscale Images

Abstract

Fractal dimension (FD) is most useful research topic in the field of fractal geometry to evaluate surface roughness of digital images by using the concept of self-similarity, and the FD value should lie between 2 and 3 for surfaces of digital images. In this regard, many researchers have contributed their efforts to estimate FD in the digital domain as reported in many kinds of the literature. The differential box-counting (DBC) method is a well-recognized and commonly used technique in this domain. However, based on the DBC approach, several modified versions of DBC have been presented like relative DBC (RDBC), improved box counting (IBC), improved DBC (IDBC). However, the accuracy of an algorithm for FD estimation is still a great challenge. This article presents an improved version of DBC algorithm by partitioning the box of grid into two asymmetric patterns for more precision box count and provides accurate estimation of FD with less fit error as well as less computational time as compared to existing method like DBC, relative DBC (RDBC), improved box counting (IBC), and improved DBC (IDBC).