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新月形区域中对称星形函数的汉克尔不等式估计及其在图像处理中的应用。

Estimation of Hankel inequalities of symmetric starlike functions in crescent-shaped domains and their application in image processing.

作者信息

Kanwal Bushra, Iman Arooj, Kanwal Shamsa, Alkhalifa Amal K

机构信息

Department of Mathematical Sciences, Fatima Jinnah Women University, The Mall, Rawalpindi, Pakistan.

Department of Computer Sciences, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia.

出版信息

Sci Rep. 2025 Jul 28;15(1):27402. doi: 10.1038/s41598-025-12935-2.

DOI:10.1038/s41598-025-12935-2
PMID:40721847
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC12304290/
Abstract

This study explores some geometric properties of the class of symmetric starlike functions associated with a Crescent-shaped domain denoted by [Formula: see text]. Initially, we establish key coefficient inequalities and investigate upper bounds for the 2nd and 3rd order Hankel determinants. All the obtained results are sharp. These bounds provide deeper insights into the structural behavior of this class and contribute to a broader understanding of Geometric Function Theory. In addition to the theoretical findings, the practical implications of the results obtained are demonstrated in the domain of image processing. We used our estimated sharp Hankel determinants to develop a novel algorithm for image enhancement. The performance of the algorithm is evaluated on different image datasets of varying dimensions, with key quality metrics such as PSNR, SSIM, PCC, and MAE. Our experimental results indicate a significant improvement over conventional image enhancement techniques, particularly in retaining structural integrity and reducing distortions. In addition, a comparative study highlights the effectiveness of the proposed algorithm compared to existing methods reported in the literature, demonstrating its potential to enhance image quality in practical applications.

摘要

本研究探讨了与由[公式：见正文]表示的新月形区域相关的对称星形函数类的一些几何性质。首先，我们建立了关键的系数不等式，并研究了二阶和三阶汉克尔行列式的上界。所有得到的结果都是精确的。这些界为该类的结构行为提供了更深入的见解，并有助于更广泛地理解几何函数理论。除了理论发现之外，所得结果在图像处理领域的实际应用也得到了证明。我们使用估计的精确汉克尔行列式开发了一种用于图像增强的新算法。该算法的性能在不同维度的不同图像数据集上进行评估，使用诸如峰值信噪比（PSNR）、结构相似性指数（SSIM）、皮尔逊相关系数（PCC）和平均绝对误差（MAE）等关键质量指标。我们的实验结果表明，与传统图像增强技术相比有显著改进，特别是在保持结构完整性和减少失真方面。此外，一项比较研究突出了所提出算法与文献中报道的现有方法相比的有效性，证明了其在实际应用中提高图像质量的潜力。

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