Imaging Brain Activation Streams from Optical Flow Computation on 2-Riemannian Manifolds

We report on mathematical methods for the exploration of spatiotemporal dynamics of Magneto- and Electro-Encephalography (MEG / EEG) surface data and/or of the corresponding brain activity at the cortical level, with high temporal resolution. In this regard, we describe how the framework and numerical computation of the optical flow--a classical tool for motion analysis in computer vision--can be extended to non-flat 2-dimensional surfaces such as the scalp and the cortical mantle. We prove the concept and mathematical well-posedness of such an extension through regularizing constraints on the estimated velocity field, and discuss the quantitative evaluation of the optical flow. The method is illustrated by simulations and analysis of brain image sequences from a ball-catching paradigm.