# Pixel Interaction Model for Contrast Enhancement: Bridging Social Science and Image Processing
## 4 Experimental Results  
### Experimental Configuration  
To confirm the effectiveness of the proposed image contrast enhancement approach, the experiment was designed as follows:  
* The TID2013 dataset [27] was used, which contains 22 different low-contrast reference images in grayscale.
* Five histogram equalization-based algorithms, AVHEQ [19], BBHE [18], ESHE [20], MMBEBE [17], and RSEIHE [16], were used to compare with the proposed method.
* Six metrics were considered to measure the quality of the images generated by the proposed and comparison methods. The parameters used in the proposed approach for conducting the experiments were threshold = 0 and maximum number of iterations = 150. This proposed value is based on experimental evidence.  
Figure 6: Effect of the iterative process with the presented approach, (**a**) input image, (**b**) 50, (**c**) 100, and (**d**) 150 iterations.  
* The experiments were conducted in MATLAB R2022b on a computer (Computer Ghia, Guadalajara, Mexico) with an AMD Ryzen 3-3.50 GHz processor and Windows 10 (64-bit, 8 GB of memory). To evaluate the performance of each method, six metrics were considered for this study: root mean square (RMS), entropy (E), mean-squared error (MSE), absolute measure of enhancement (AME), signal-to-noise ratio (SNR), and weighted signal-to-noise ratio (WSNR). The RSM (root mean square) defined by Equation (6), calculates the average difference between each pixel of two images, the reference image (R) and the enhanced image (I). It is considered better when the difference between the two images is smaller, indicating higher similarity. \[\text{RMS}=\sqrt{\frac{1}{\text{MN}}}\sum_{i=0}^{\text{M}-1}\sum_{j=0}^{\text{ N}-1}\left(\text{I}_{ij}-\text{R}_{ij}\right)^{2}\] (6) The entropy (E) measures the information content of the enhanced image I. A high value of (E) indicates that the enhanced image contains more information. (E) is calculated according to Equation (7): \[\text{E}=-\sum_{i=0}^{\text{L}-1}\text{P}(\text{q})*\log(\text{P}(\text{q}))\] (7) In the enhanced image I, \(\text{P}(\text{q})\) represents the probability density function of the intensity level \(\text{q}\), \((\text{q}\in{0,\ldots,\text{L}-1})\). L represents the entire number of grayscale levels present in image I. The mean-squared error (MSE) is presented in Equation (8): \[\text{MSE}=\frac{1}{\text{mn}}\sum_{i=0}^{\text{m}-1}\sum_{j=0}^{\text{n}-1} \left[\text{R}(\text{i},\text{j})-\text{I}(\text{i},\text{j})\right]^{2}\] (8) where the pixel intensity values at position \((\text{i},\text{j})\) in the reference image and the enhanced image are represented by R and I, respectively. The variables m and n represent the width and height of the images. Lower values of this indicator indicate better image quality, with greater similarity to the original image and less distortion. Another metric used is the absolute measure of enhancement (AME) [28]. This metric has the characteristic that small values correspond to a suitable image quality. The signal-to-noise ratio (SNR) is calculated according to Equation (9): \[\text{SNR}=\frac{\text{P}\_\text{signal}}{\text{P}\_\text{noise}}\] (9) where P is the average power. To measure SNR accurately, both the signal and the noise should be measured at the same points in the system and with the same bandwidth. A higher value indicates that the signal is stronger and clearer than the background noise. The final index in our analysis is the weighted signal-to-noise ratio (WSNR) [29], which evaluates the ratio of average weighted signal power to average weighted noise power. A high value of WSN corresponds to a signal that is strong and distinguishable from the background noise across a wide range of frequencies. For this reason, it means a better response.