Two Commonly Used Digital Watermark Evaluation Functions: SNR and PSNR

This document introduces two fundamental digital watermark evaluation functions: Signal-to-Noise Ratio (SNR) and Peak Signal-to-Noise Ratio (PSNR). These metrics are crucial for assessing the performance and quality of digital watermarks in various applications. SNR measures the ratio between the original signal power and the noise power, while PSNR specifically evaluates the ratio between the maximum possible signal power and the corrupting noise power. From an implementation perspective, SNR calculation typically involves computing the mean squared values of both the original signal and the noise component. The mathematical formula can be implemented using array operations to calculate squared differences between the original and watermarked images. PSNR, being derived from SNR, incorporates the maximum possible pixel value (typically 255 for 8-bit images) and uses logarithmic scaling to provide a more perceptually relevant metric. In practical code implementation, these functions often require: - Input validation for image dimensions and data types - Pixel value normalization when working with different bit depths - Efficient matrix operations for calculating mean squared error (MSE) - Logarithmic transformation using base-10 or natural logarithms depending on standards These evaluation metrics enable researchers and developers to quantitatively assess watermark visibility characteristics and protection capabilities, helping optimize watermark embedding strength while maintaining image quality. The implementation typically involves comparing the original host signal with the watermarked version to compute the distortion introduced by the watermarking process.