A numerical solution to the generalized mapmaker's problem: flattening nonconvex polyhedral surfaces

Methods are described to unfold and flatten the curved, convoluted surfaces of the brain in order to study the functional architectures and neural maps embedded in them. In order to do this, it is necessary to solve the general mapmaker's problem for representing curved surfaces by planar models. This algorithm has applications in areas other than computer-aided neuroanatomy, such as robotics motion planning and geophysics. The algorithm maximizes the goodness of fit distances in these surfaces to distances in a planar configuration of points. It is illustrated with a flattening of monkey visual cortex, which is an extremely complex folded surface. Distance errors in the range of several percent are found, with isolated regions of larger error, for the class of cortical surfaces studied so far.>