Topology-preserving smoothing of vector fields

In this paper, we propose a technique for topology-preserving smoothing of sampled vector fields. The vector field data is first converted into a scalar representation in which time surfaces implicitly exist as level-sets. We then locally analyze the dynamic behavior of level-sets by placing geometric primitives in the scalar field and by subsequently distorting these primitives with respect to local variations in this field. From the distorted primitives, we calculate the curvature normal and we use the normal magnitude and its direction to separate distinct flow features. Geometrical and topological considerations are then combined to successively smooth dense flow fields, at the same time retaining their topological structure.