Quantitative texture measurement of gray-scale images: Fractal dimension using an improved differential box counting method

Texture analysis methods have been used in various image processing applications, such as segmentation, classification, and recognition, shape analysis. The performance of computer vision and image processing algorithms depend on visual texture patterns. However, it is difficult to define. Fractal Dimension (FD) helps to measure the level of roughness present in an image. A significant amount of work is available in literature to measure FD. Differential Box Counting (DBC) is one such successful method exploited in image texture analysis study, because it is simple and easy to understand. DBC is modified several times to yield a better FD value. However, most of the state-of-the-art methods suffer from the over-counting and under-counting of boxes, larger box-height, less number of grid sizes, inappropriate line fitting method. This work introduces a gray-level shift-invariant DBC method, which uses a new formula for counting boxes along z-direction to solve over-counting of boxes, a partitioning-shifting-partitioning mechanism to fix under-counting of boxes along xy-direction, a smaller box-height to enhance the FD value and robust least squares regression to estimate a line accurately. All the experiments are performed on synthesized Fractal Brownian Motion image dataset and four real datasets. The obtained results illustrate that the proposed DBC method outperforms state-of-the-art DBC methods. (C) 2019 Elsevier Ltd. All rights reserved.