Constructing minimal geodesics, flat maps, and topographic models of primate visual cortex

The mapping of the visual field to many areas of the primate visual cortex is largely continuous. The measurement and characterization of the topography of these maps is useful for validating and calibrating several functional brain imaging methods. However, this task is significantly complicated by the curvature of the cerebral cortex. Furthermore, the mathematical modeling of topography has been limited to a single area of visual cortex: area V1. Three methods that address these problems are described in this thesis.; First, an algorithm for computing minimal geodesics and shortest paths on a triangular mesh representing the surface of visual cortex is presented. This algorithm is simple to implement and computes exact distances rapidly on meshes with thousands of triangles, and can therefore be used to evaluate faster schemes that compute approximations to these distances.; Second, two algorithms for flattening triangular meshes are presented. The first algorithm optimally preserves the lengths of shortest paths, as computed by the previous algorithm. However, it is not computationally practical for meshes with more than a few thousand triangles. To flatten large-scale meshes, a second algorithm is proposed. This algorithm operates at multiple scales, using the first algorithm at the coarsest scale and iteratively refining the flat map at finer scales. Together, these algorithms significantly improve the speed and accuracy of quasi-isometric flattening methods.; Third, given a quasi-isometric flattening of visual cortex, a model of the topography of areas V1, V2, and V3 is proposed. This model captures what is currently known about the differential structure of the topography in these areas, in terms of their local magnification factor and shear, using five independent parameters. Furthermore, the ability to model V1, V2, and V3 with a single map function raises the possibility that they develop in a coordinated way and suggests that they be grouped together into a single structure: the V1-V2-V3 complex.