Two-Layer Fragile Watermarking Method Secured with Chaotic Map for Authentication of Digital Holy Quran

Table 2

Common image quality metrics.

Number	Image quality measurement	Equation
1	Mean square error (MSE)	1MSE=𝑚𝑛^𝑚−1∑∑𝑖=0^𝑛−1𝑗=0𝐼𝑖,𝑗−𝐾𝑖,𝑗^2
2	Root mean square error (RMSE)	RMSE=1𝑚𝑛^𝑚−1∑∑𝑖=0^𝑛−1𝑗=0𝐼𝑖,𝑗−𝐾𝑖,𝑗^2
3	Peak signal-to-noise ratio (PSNR)	PSNR=10⋅log10MAX^2𝐼MSE
4	Universal image quality index (IQI)	1𝑄=𝑀^𝑀𝑗∑=1𝑄𝑗
5	Measure of enhancement (EME)	1EME=𝑘1𝑘2^𝑘2∑∑^𝑘𝑖=1^1𝑘=1𝐼max(𝑘,𝑙)𝐼min()𝐼𝑘,𝑙log^max(𝑘,𝑙)𝐼min(𝑘,𝑙)
6	Pearson correlation coefficient (PCC)	PCC𝑥,𝑦=𝑛∑𝑥𝑖𝑦𝑖−∑𝑥𝑖∑𝑦𝑖𝑛∑𝑥^2𝑖−∑𝑥𝑖^2𝑛∑𝑦^2𝑖−∑𝑦𝑖^2
7	Signal-to-signal noise ratio (SNR)	SNRdb=10log10𝑃signal𝑃noise
8	Mean absolute error (MAE)	1MAE=𝑛^𝑛𝑖∑=1𝑓𝑖−𝑦𝑖
9	Structural similarity (SSIM)	SSIM𝑥,𝑦=2𝜇𝑥𝜇𝑦+𝐶12𝜎𝑥𝑦+𝐶2𝜇^2𝑥+𝜇^2𝑦+𝐶1𝜎^2𝑥+𝜎^2𝑦+𝐶2
10	Weight peak signal-to-noise ratio (WPSNR)	WPSNR=20log10255NVF×RMSE
11	Normalized Hamming distance (NHD)	NHD𝑎𝑖,𝑎^′𝑖=1𝑏^𝑏𝑘∑=1𝑎𝑘⊕𝑎^′𝑖
12	Bit error rate (BER)	𝐸(𝑡)BER=𝑁(𝑡)