The known physiological substrate of the front-end visual system can be interpreted in terms of abstract geometrical objects and relations. It is pointed out which structures can be interpreted as the implementation of tangent quantities, etc., and how the global visual areas can be interpreted as (co-)vector bundles (of which the fibers are "cortical columns") and similar structures. The possible implementations of an affine connection and a gauge field for the metric are investigated. This theory not only permits one to describe the existing structure in a particularly attractive, modular way, but also enables one to predict the type of connections necessary for the embodiment of specific visual capabilities, and to find the neural assemblies involved in specific visual tasks.