This study proposes a novel image contrast enhancement method based on image projection onto the squared eigenfunctions of the two dimensional Schr\"odinger operator. This projection depends on a design parameter \texorpdfstring{\(\gamma\)}{gamma} which is proposed to control the pixel intensity during image reconstruction. The performance of the proposed method is investigated through its application to color images. The selection of \texorpdfstring{\(\gamma\)}{gamma} values is performed using k-means, which helps preserve the image spatial adjacency information. Furthermore, multi-objective optimization using the Non dominated Sorting Genetic Algorithm II (NSAG2) algorithm is proposed to select the optimal values of \texorpdfstring{\(\gamma\)}{gamma} and the semi-classical parameter h from the 2DSCSA. The results demonstrate the effectiveness of the proposed method for enhancing image contrast while preserving the inherent characteristics of the original image, producing the desired enhancement with almost no artifacts.

翻译：本研究提出了一种新颖的图像对比度增强方法，该方法基于图像在二维薛定谔算子平方本征函数上的投影。该投影依赖于一个设计参数 \(\gamma\)，该参数被提议用于控制图像重建过程中的像素强度。通过将该方法应用于彩色图像来研究其性能。\(\gamma\) 值的选择使用 k-means 算法执行，这有助于保留图像的空间邻接信息。此外，提出了使用非支配排序遗传算法 II (NSAG2) 进行多目标优化，以从 2DSCSA 中选择 \(\gamma\) 和半经典参数 h 的最优值。结果表明，所提出的方法在增强图像对比度的同时能有效保留原始图像的固有特征，产生所需的增强效果且几乎无伪影。