Image contrast enhancement based on the Schr\"odinger operator spectrum

TL;DR

This paper introduces a novel image contrast enhancement technique utilizing the spectral properties of the Schrödinger operator, employing eigenfunction projections and multi-objective optimization to improve image quality.

Contribution

The study presents a new contrast enhancement method based on Schrödinger operator eigenfunctions, incorporating fuzzy logic, clustering, and genetic algorithms for parameter optimization.

Findings

Effective contrast enhancement with minimal artifacts.

Preserves spatial adjacency and inherent image characteristics.

Optimized parameters improve enhancement quality.

Abstract

In this study, we propose a novel image contrast enhancement method based on projecting images onto the squared eigenfunctions of the two-dimensional Schr\"odinger operator. This projection relies on a design parameter, $\gamma$, which controls pixel intensity during image reconstruction. The method's performance is evaluated using color images. The selection of $\gamma$ values is guided by priors based on fuzzy logic and clustering, preserving the spatial adjacency information of the image. Additionally, multi-objective optimization using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to determine the optimal values of $\gamma$ and the semi-classical parameter, $h$, from the 2D-SCSA. Results demonstrate that the proposed method effectively enhances image contrast while preserving the inherent characteristics of the original image, producing the desired enhancement with minimal artifacts.