Planar maps have been proposed as a powerful and easy-to-use representation for various kinds of image analysis results, but so far they are restricted to pixel accuracy. This leads to limitations in the representation of complex structures (such as junctions, triangulations, and skeletons) and discards the sub-pixel information available in grayvalue and color images. We extend the planar map formalism to sub-pixel accuracy and introduce various algorithms to create such a map, thereby demonstrating significant gains over the existing approaches.