Differential box counting methods for estimating fractal dimension of gray-scale images: A survey

Fractal dimension is extensively in use as features in computer vision applications to characterize roughness and self-similarity of objects in an image for many years. These features have been adopted successfully mainly in texture segmentation and classification. Differential box counting method is one of the widely accepted approaches, those exist in literature to estimate fractal dimension of an image. In this work, we comprehensively reviewed the available differential box counting methods. First, the differential box counting method is discussed in detail along with its computer vision applications and drawbacks. Second, various variants of differential box counting method are thoroughly studied and grouped using different parameters of differential box counting method. Third, the synthetic and real-world databases, considered for demonstrating experimental results by the state-of-the-art methods have been presented. Fourth, some of the state-of-the-art methods have been implemented and corresponding results obtained in this study are reported. Fifth, three evaluation metrics have also been reviewed. However, these metrics work only for synthetic fractal Brownian motion images because the theoretical fractal dimension values for these images are known and have been used as a set of ground truths. Finally, we concluded the status of differential box counting methods and explored the possible future directions.