Transactions on Pattern Analysis

We describe methods 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. Our algorithm maximizes the goodness of fit of distances in these surfaces to distances in a planar configuration of points. We illustrate this algorithm with a flattening of monkey visual cortex, which is an extremely complex folded surface. We find distance errors in the range of several percent, with isolated regions of larger error, for the class of cortical surfaces which we have so far studied. Zndex Terms-Cortex, flattened surface, geodesic distance, map.