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Image contrast enhancement based on the Schrödinger operator spectrum

Juan M. Vargas, Taous-Meriem Laleg-Kirati

TL;DR

This study proposes a novel image contrast enhancement method based on projecting images onto the squared eigenfunctions of the two-dimensional Schrodinger operator, which relies on a design parameter, $\gamma$, which controls pixel intensity during image reconstruction.

Abstract

In this study, we propose a novel image contrast enhancement method based on projecting images onto the squared eigenfunctions of the two-dimensional Schrödinger operator. This projection relies on a design parameter, $γ$, which controls pixel intensity during image reconstruction. The method's performance is evaluated using color images. The selection of $γ$ 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 $γ$ 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.

Image contrast enhancement based on the Schrödinger operator spectrum

TL;DR

This study proposes a novel image contrast enhancement method based on projecting images onto the squared eigenfunctions of the two-dimensional Schrodinger operator, which relies on a design parameter, , which controls pixel intensity during image reconstruction.

Abstract

In this study, we propose a novel image contrast enhancement method based on projecting images onto the squared eigenfunctions of the two-dimensional Schrödinger operator. This projection relies on a design parameter, , which controls pixel intensity during image reconstruction. The method's performance is evaluated using color images. The selection of 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 and the semi-classical parameter, , 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.
Paper Structure (20 sections, 1 theorem, 21 equations, 9 figures, 4 tables, 1 algorithm)

This paper contains 20 sections, 1 theorem, 21 equations, 9 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Two-dimensional semi-classical signal analysis background
  3. Definition
  4. Numerical implementation: Windowed pixel-wise 2D-SCSA
  5. Effect of parameter gamma on 2D-SCSA
  6. Contrast enhancement using gamma-SCSA
  7. Contrast enhancement algorithm
  8. gamma prior
  9. Weighted Multitask Fuzzy C-means (WMT-FCM)
  10. Frequency-Tuned Gaussian Mixture Model (FTGMM)
  11. Prior selection
  12. Multi-objective optimization
  13. Parameter initialization
  14. Cost function
  15. Parameter selection
  16. ...and 5 more sections

Key Result

Proposition 1

Let $I$ be a low contrast image, and $P$ a prior image generated with the main idea of separate the pixel images into $K$ different groups of pixels ($C_k$), with $k=1,\cdots,K$. These groups are composed of pixels with similar properties such as pixel intensity or texture, allowing for better manipulation of the different intensities present in the image, that will create better and more precise

Figures (9)

  • Figure 1: Separation of variables approach for the two-dimensional Semi-Classical Signal Analysis (2D-SCSA) computation.
  • Figure 2: Effect of the $\gamma$ parameter of the 2D-SCSA for image reconstruction using $h=1$. (a) Original. (b) $\gamma=0.5$.(c) $\gamma=2$.(d) $\gamma=8$.(e) $\gamma=18$. It can be seen that the intensity of the pixels starts to increase with the increase of the parameter $\gamma$, while also the contrast of the pixel increases. Finally, it can be seen that higher values of $\gamma$ caused a loss of the image information by creating artifacts in the images.
  • Figure 3: Effect of the upper limit of the $\gamma$ parameter for the 2D-SCSA for image reconstruction using $h=1$. (a) $\gamma=16$.(b) $\gamma=18$.(c) $\gamma=19$.(d) $\gamma=20$. It can be seen that with the increase of the $\gamma$, the pixels with the higher intensity are converted to NaN until all the pixels are converted to this value.
  • Figure 4: Relation between $\gamma$ and $h$ values for image reconstruction using 2D-SCSA. (a) Original image. (b) MSE surface plot. (c) PSNR surface plot. This figure shows the relationship between the two parameters of the 2D-SCSA for some well-known reconstruction metrics used to evaluate the performance in the reconstruction and filtering capacity between the original images and the image generated by 2D-SCSA. The red dot indicates the values of $h_{min}$ and $\gamma$ for the image calculated as is proposed in Vargas.
  • Figure 5: Contrast enhancement using $\gamma$-SCSA. (a)Original image. (b) Enhanced image. (c) Original histogram. (d) Enhance histogram. It can be seen that the $\gamma$-SCSA increases the contrast of the image increasing the difference between the pixels of the different objects in the images improving the quality of the image.
  • ...and 4 more figures

Theorems & Definitions (2)

  • Definition 1
  • Proposition 1