An improvement of the box-covering method for solving noisy image processing tasks

• Дата: 2025
• Автори: Терлецький, С. В., Гофман, Є. О.
• Формат: Стаття
• Мова: Українська
• Опубліковано: Інститут проблем реєстрації інформації НАН України 2025
• Теми: box-covering; fractal dimension; digital images; logarithmic sequence; Fibonacci sequence
• Онлайн доступ: http://drsp.ipri.kiev.ua/article/view/345594
• Назва журналу: Data Recording, Storage & Processing

Fractal analysis is widely used for analysing complex structured digital images. The standard box-covering algorithm for calculating fractal dimensions uses uniform covering, which poorly adapts to non-uniform structures and exhibits sensitivity to noise and scale discretization. To ensure a more accurate estimation of the fractal dimension, the use of non-uniform coverings based on logarithms and based on the Fibonacci sequence was proposed. The logarithmic approach employs a scaling factor α = 0,8 for progressive box size reduction, while the Fibonacci method utilizes the mathematical sequence properties for non-uniform scale distribution. Based on the MAE and E metrics, it was shown that for complex structured images, logarithmic covering and Fibonacci sequence-based covering allow for improving the accuracy of the fractal dimension determination algorithm. An experimental study was conducted using cartographic images of the US Atlantic coastline with artificial salt-and-pepper noise applied at levels ranging from 0 % to 90 %. The results demonstrated that for clean images, the proposed methods achieved MAE values of 0,057–0,062 compared to 0,076 for the standard algorithm. For a high level of noise, the errors of the improved algorithms approach the error of the standard algorithm; however, the Fibonacci sequence-based algorithm provides greater stability in the calculation of the fractal dimension for images with varying levels of noise. The study shows that the improved methods maintain better accuracy at low to moderate noise levels, with their advantage diminishing only at noise levels above 70 %. Tabl.: 1. Fig.: 5. Refs: 9 titles.