Flow-based Geometric Interpolation of Fiber Orientation Distribution Functions.

The fiber orientation distribution function (FOD) is an advanced model for high angular resolution diffusion MRI representing complex fiber geometry. However, the complicated mathematical structures of the FOD function pose challenges for FOD image processing tasks such as interpolation, which plays a critical role in the propagation of fiber tracts in tractography. In FOD-based tractography, linear interpolation is commonly used for numerical efficiency, but it is prone to generate false artificial information, leading to anatomically incorrect fiber tracts. To overcome this difficulty, we propose a flowbased and geometrically consistent interpolation framework that considers peak-wise rotations of FODs within the neighborhood of each location. Our method decomposes a FOD function into multiple components and uses a smooth vector field to model the flows of each peak in its neighborhood. To generate the interpolated result along the flow of each vector field, we develop a closed-form and efficient method to rotate FOD peaks in neighboring voxels and realize geometrically consistent interpolation of FOD components. By combining the interpolation results from each peak, we obtain the final interpolation of FODs. Experimental results on Human Connectome Project (HCP) data demonstrate that our method produces anatomically more meaningful FOD interpolations and significantly enhances tractography performance.