Map-Seeking Circuit theory is a biologically based computational theory of vision applicable to difficult machine vision problems such as recognition of 3D objects in arbitrary poses amid distractors and clutter, as well as to non-recognition problems such as terrain interpretation. It provides a general computational mechanism for tractable discovery of correspondences in massive transformation spaces by exploiting an ordering property of superpositions. The latter allows a set of transformations of an input image to be formed into a sequence of superpositions which are then "culled" to a composition of single mappings by a competitive process which matches each superposition against a superposition of inverse transformations of memory patterns. The architecture that performs this is based on a number of neuroanatomical features of the visual cortices, including reciprocal dataflows and inverse mappings.