Is Box-Height Really a Issue in Differential Box Counting Based Fractal Dimension?

Chinmaya Panigrahy, Ayan Seal, Nihar Kumar Mahato

Abstract: Differential box counting method (DBC) is one of the most popular methods to estimate the fractal dimension (FD) of gray-scale images due to its simplicity and efficiency. Different parameters of DBC are modified several times to obtain a better FD value. One such parameter is box-height, which greatly affects the computed FD values. Different state-of-the-art box-heights either suffer from the random selection, approximation, larger value or depend on the image characteristics. This paper resolves the issues related to the selection of box-height by proposing a no-box-height rule to count the boxes, which is derived from the computation mechanism. Experiments on the generated fractal Brownian motion (FBM) images and images of Brodatz database, using four state-of-the-art methods show that the proposed no-box-height mechanism not only enhances the FD value but also generates no higher distance error (DE) values.