Adaptive Nonlinear Bernstein-Guided Parrot Optimizer for Mural Image Segmentation

During the long-term preservation of murals, the degradation of mural image information poses significant challenges to the restoration and conservation of world cultural heritage. Currently, mural conservation scholars focus on image segmentation techniques for mural restoration and protection. However, existing image segmentation methods suffer from suboptimal segmentation quality. To improve mural image segmentation, this study proposes an efficient mural image segmentation method termed Adaptive Nonlinear Bernstein-guided Parrot Optimizer (ANBPO) by integrating an adaptive learning strategy, a nonlinear factor, and a third-order Bernstein-guided strategy into the Parrot Optimizer (PO). In ANBPO, First, to address PO's limited global exploration capability, the adaptive learning strategy is introduced. By considering individual information disparities and learning behaviors, this strategy effectively enhances the algorithm's global exploration, enabling a thorough search of the solution space. Second, to mitigate the imbalance between PO's global exploration and local exploitation phases, the nonlinear factor is proposed. Leveraging its adaptability and nonlinear curve characteristics, this factor improves the algorithm's ability to escape local optimal segmentation thresholds. Finally, to overcome PO's inadequate local exploitation capability, the third-order Bernstein-guided strategy is introduced. By incorporating the weighted properties of third-order Bernstein polynomials, this strategy comprehensively evaluates individuals with diverse characteristics, thereby enhancing the precision of mural image segmentation. ANBPO was applied to segment twelve mural images. The results demonstrate that, compared to competing algorithms, ANBPO achieves a 91.6% win rate in fitness function values while outperforming them by 67.6%, 69.4%, and 69.7% in PSNR, SSIM, and FSIM metrics, respectively. These results confirm that the ANBPO algorithm can effectively segment mural images while preserving the original feature information. Thus, it can be regarded as an efficient mural image segmentation algorithm.