TCBR and TCBD: Evaluation metrics for tamper coincidence problem in fragile image watermarking

This paper proposed two evaluation metrics of the tamper coincidence in a block map design for image watermarking. These evaluation metrics are called Tamper Coincidence Block Ratio (TCBR) and Tamper Coincidence Block Density (TCBD). A tamper coincidence occurred in image authentication and self-recovery when the recovery data and the original block location were tampered with simultaneously. A high tamper coincidence limits image inpainting's capability to recover the region, leading to an imprecise recovered image. The ratio and density of the tamper coincidence may significantly affect the final recovered image quality. Previously, researchers mentioned the tamper coincidence in their experiment but did not evaluate it with any metrics. They evaluated the robustness of their technique based on the final recovered image quality using the Peak Signal-toNoise Ratio (PSNR) and Structural Similarity Index Measure (SSIM). Tamper coincidences are primarily affected by the block map design implemented by the researcher. Thus, TCBR and TCBD provide valuable insight into the block map design's effectiveness in preventing tamper coincidence. The experimental result shows that the TCBR and TCBD values are inversely proportional to the recovered image quality. A high TCBR and TCBD value leads to low recovered image quality. Therefore, this paper will help the researchers design an effective block map by minimizing the TCBR and TCBD values to obtain the highest recovered image quality.