Optimal Smoothness of Orientation Preference Maps

We propose a mathematical description for the spatial organization of orientation preference in the visual cortex. The theory is derived from the principle of optimal smoothness and predicts the spatial pattern of orientation preference from position and chirality of its singularities (i.e. “pinwheels”). The model exhibits long range order in the sense that, given the configuration of singularities, the specification of orientation preference at a single location fixes the entire map. A comparison with optically recorded images of cortical maps suggests that orientation preference can indeed be predicted over a much larger spatial range than previously estimated on the basis of correlation measurements.