Typically, metadata of images are stored in a specific data segment of the image file. However, to securely detect changes, data can also be embedded within images. This follows the goal to invisibly and robustly embed as much information as possible to, ideally, even survive compression. This work searches for embedding principles which allow to distinguish between unintended changes by lossy image compression and malicious manipulation of the embedded message based on the change of its perceptual or robust hash. Different embedding and compression algorithms are compared. The study shows that embedding a message via integer wavelet transform and compression with Karhunen-Loeve-transform yields the best results. However, it was not possible to distinguish between manipulation and compression in all cases.