A cell 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.