Direction field diffusion on cortical surface via graph cuts

The direction field on cortical surface conveys important information. Diffusion of direction field, which aims to smooth noise and meanwhile preserve major geometric structures and inherent discontinuity in the direction field, is useful for cortical surface analysis. In this paper, we propose a novel method for tangential direction field diffusion on cortical surface, which is formulated as an energy minimization problem. To minimize the energy function, we first convert it to a discrete labeling problem, in which the space of solution is represented using a set of labels corresponding to a set of predefined diffused directions. Then we solve the labeling problem efficiently by the graph cuts method. At last, we project the labeled diffused directions to the tangential spaces of the cortical surface and normalize them in order to obtain the final diffused direction field. We validate the proposed direction field diffusion method on both synthesized surfaces and real cortical surfaces, and obtain promising results.