A watermark system includes an embedder, detector, and reader. The watermark embedder encodes a watermark signal in a host signal to create a combined signal. The detector looks for the watermark signal in a potentially corrupted version of the combined signal, and computes its orientation. Finally, a reader extracts a message in the watermark signal from the combined signal using the orientation to approximate the original state of the combined signal. While adapted for images, video and audio, the watermark system applies to other electronic and physical media. For example, it can be applied to mark graphical models, blank paper, film and other substrates, texturing objects for ID purposes, etc.