Diffeomorphic Registration for Retinotopic Mapping Via Quasiconformal Mapping

Human visual cortex is organized into several functional regions/areas. Identifying these visual areas of the human brain (i.e., V1, V2, V4, etc) is an important topic in neurophysiology and vision science. Retinotopic mapping via functional magnetic resonance imaging (fMRI) provides a non-invasive way of defining the boundaries of the visual areas. It is well known from neurophysiology studies that retinotopic mapping is diffeomorphic within each local area (i.e. locally smooth, differentiable, and invertible). However, due to the low signal-noise ratio of fMRI, the retinotopic maps from fMRI are often not diffeomorphic, making it difficult to delineate the boundaries of visual areas. The purpose of this work is to generate diffeomorphic retinotopic maps and improve the accuracy of the retinotopic atlas from fMRI measurements through the development of a specifically designed registration procedure. Although existing cortical surface registration methods are very advanced, most of them have not fully utilized the features of retinotopic mapping. By considering those features, we form a mathematical model for registration and solve it with numerical methods. We compared our registration with several popular methods on synthetic data. The results demonstrate that the proposed registration is superior to conventional methods for the registration of retinotopic maps. The application of our method to a real retinotopic mapping dataset also resulted in much smaller registration errors.