Spatial transformations (STs) constitute an important class of image operations, which include the well-known affine transformation, image rotation, scaling, warping, etc. Less well known are the anisomorphic transformations among cartographic projections such as the Mercator, gnomonic, and equal-area formats. In this preliminary study, we introduce a unifying theory of spatial transformation, expressed in terms of the Image Algebra, a rigorous, inherently parallel notation for image and signal processing. Via such theory, we can predict the implementational cost of various STs. Since spatial operations are frequently I/O-intensive, we first analyze the I/O performance of well-known architectures, in order to determine their suitability for ST implementation. Analyses are verified by simulation, with emphasis upon vision-based navigation applications. An additional applications area concerns the remapping of visual receptive fields, which facilitates visual rehabilitation in the presence of retinal damage.