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.

本研究提出了一种基于 Schrodinger 算子二维平方特征函数的图像对比增强方法，该方法通过在图像重建过程中控制像素强度的设计参数 γ 进行投影。使用 k-means 选择 γ 值，以保留图像的空间邻近性信息，同时提出了基于非支配排序遗传算法 II（NSAG2）的多目标优化来选择 γ 和 2DSCSA 中半经典参数 h 的最佳值。实验证明该方法在增强图像对比度的同时保持原始图像的内在特征，几乎不产生伪影。