FRACTAL DIMENSION-BASED GENERALIZED BOX-COUNTING TECHNIQUE WITH APPLICATION TO GRAYSCALE IMAGES

Soumya Ranjan Nayak and Jibitesh Mishra
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Soumya Ranjan Nayak: Department of Information Technology, College of Engineering and Technology, Bhubaneswar, Odisha, India
Jibitesh Mishra: ��Department of CSA, College of Engineering and Technology, Bhubaneswar, Odisha, India

FRACTALS (fractals), 2021, vol. 29, issue 03, 1-17

Abstract: Fractal Dimension (FD) estimation in digital image analysis has received much attention due to its dimensional significance and therefore has become an active area of research over the year. The earlier FD-based techniques often followed traditional box-counting and its different variation of differential box-counting (DBC) paradigms, in which the proper choice of box count has remained a major concern. However, most of the state-of-the-art DBC variants suffer from considerable limitations like over-counting (OC), under-counting (UC), and limited their application only to square-shaped images, and it is still a major research problem! In this backdrop, the current investigation proposes a generalized box-counting (graylevel invariant DBC); and compares it with other state-of-the-art techniques. The proposed model is evaluated on five benchmark texture datasets (which include real and generated synthetic images) and obtained better results than the existing methods and achieved all desired outcomes by eliminating both OC and UC problems. This algorithm works for any arbitrarily sized (both squared and rectangular) images. It gives a higher rate of accuracy in terms of less fitting error in detecting exact surface roughness from given datasets.

Keywords: Fractal Dimension; Box-Counting; DBC; Box-Height; Self-Similarity (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500559

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