Figure Field Analysis of Linear Scale-Space Image

This paper deals with the figure field, which is defined as the negative of the gradient vector field of the linear scale-space image. The scale-space hierarchy is obtained from the connectivity of stationary points determined by figure-field fluxes and trajectories of the stationary points in the scale space. A point at infinity plays an important role in this theory. The figure-field fluxes and the configuration of stationary points at each scale define a graph in the scale-space image. This graph describes the topological relations of segments in the original image. We employ the Voronoi tessellation to extract boundaries of the segments from the blurred linear scale-space image.