Many of the detailed technologies are useful in enabling a smart phone to respond to a user's environment, e.g., so it can serve as an intuitive hearing and seeing device. A few of the detailed arrangements involve using radio base station SDR equipment (e.g., at a cell tower) to perform image recognition operations for phones; forecasting service needs from remote processors, and reserving such capacity in advance of use; delegating a remote execution task to a service provider chosen in a competitive process, such as by a reverse auction; using nearby processors, e.g., in an automobile, another phone, or set-top box, for remote execution tasks; phones with separable camera and/or illumination components; phone camera illumination using different colors of light; using search tree methods with image frames captured at different focuses; using a phone's microprojector to aid in object identification; correcting lens aberrations by texture mapping captured imagery onto a corrective polygon surface using a phone GPU; etc. A great variety of other features and arrangements are also detailed.