A wireless phone is equipped with a 2D optical sensor, enabling a variety of applications. For example, such a phone may also be provided with a digital watermark decoder, permitting decoding of steganographic data on imaged objects. Movement of a phone may be inferred by sensing movement of an imaged pattern across the optical sensor's field of view, allowing use of the phone as a gestural input device through which a user can signal instructions to a computer-based process. A variety of other arrangements by which electronic devices can interact with the physical world are also detailed, e.g., involving sensing and responding to digital watermarks, bar codes, RFIDs, etc. Other novel arrangements are also detailed.