This disclosure describes a method for encoding a digital watermark into an image signal that is robust to geometric distortion. The digital watermark is adapted to the host image signal in which it is embedded so as to be imperceptible or substantially imperceptible in the watermarked image when displayed or printed. This digital watermark may be used to determine the geometric distortion applied to a watermarked image, may be used to carry auxiliary information, and may be used to detect and decode a digital watermark embedded in a geometrically distorted version of a watermarked image. Because of its robustness to geometric distortion, the digital watermark is useful for a number of applications for embedding auxiliary data in image signals, including still pictures and video, where the image signal is expected to survive geometric distortion. This method may adapted to other types of media signals such as audio.