NDFNGO: Enhanced Northern Goshawk Optimization Algorithm for Image Segmentation.

The gradual deterioration of fresco pictorial information presents a formidable obstacle for conservators dedicated to protecting humanity's shared cultural legacy. Currently, scholars in the field of mural conservation predominantly focus on image segmentation techniques as a vital tool for facilitating mural restoration and protection. However, the existing image segmentation methods frequently fall short of delivering optimal segmentation results. To address this issue, this study introduces a novel mural image segmentation approach termed NDFNGO, which integrates a nonlinear differential learning strategy, a decay factor, and a Fractional-order adaptive learning strategy into the Northern Goshawk Optimization (NGO) algorithm to enhance segmentation performance. Firstly, the nonlinear differential learning strategy is incorporated to harness the diversity and adaptability of differential tactics, thereby augmenting the algorithm's global exploration capabilities and effectively improving its ability to pinpoint optimal segmentation threshold regions. Secondly, drawing on the properties of nonlinear functions, a decay factor is proposed to achieve a more harmonious balance between the exploration and exploitation phases. Finally, by integrating historical individual data, the Fractional-order adaptive learning strategy is employed to reinforce the algorithm's exploitation capabilities, thereby further refining the quality of image segmentation. Subsequently, the proposed method was evaluated through tests on twelve mural image segmentation tasks. The results indicate that the NDFNGO algorithm achieves victory rates of 95.85%, 97.9%, 97.9%, and 95.8% in terms of the fitness function metric, PSNR metric, SSIM metric, and FSIM metric, respectively. These findings demonstrate the algorithm's high performance in mural image segmentation, as it retains a significant amount of original image information, thereby underscoring the superiority of the technology proposed in this study for addressing this challenge.