Multifractal Detrended Fluctuation Analysis Combined with Allen–Cahn Equation for Image Segmentation

This study proposes a novel image segmentation method, MF-DFA combined with the Allen–Cahn equation (MF-AC-DFA). By utilizing the Allen–Cahn equation instead of the least squares method employed in traditional MF-DFA for fitting, the accuracy and robustness of image segmentation are significantly improved. The article first conducts segmentation experiments under various conditions, including different target shapes, image backgrounds, and resolutions, to verify the feasibility of MF-AC-DFA. It then compares the proposed method with gradient segmentation methods and demonstrates the superiority of MF-AC-DFA. Finally, real-life wire diagrams and transmission tower diagrams are used for segmentation, which shows the application potential of MF-AC-DFA in complex scenes. This method is expected to be applied to the real-time state monitoring and analysis of power facilities, and it is anticipated to improve the safety and reliability of the power grid.