The calculus of two-dimensional mappings is reviewed. Currently
available data suggests that a conformal (isotropic) mapping is
sufficient to model the global topography of primate striate
cortex. The addition of a shear component to this mapping is
outlined. A similar analysis is applied to the local map structure of
striate cortex. Models based on a local reiteration of the complex
logarithm and on Radon (and backprojection) mappings are presented. A
variety of computational functions associated with the novel
architectures for image processing suggested by striate cortex
neuroanatomy are discussed. Applications to segmentation, perceptual
invariances, shape analysis, and visual data compression are
included. Finally, recent experimental results on shape analysis by
neurons of infero-temporal cortex are presented.