  Desire line maps are widely deployed for traffic flow analysis by virtue of
their ease of interpretation and computation. They can be considered to be
simplified traffic flow maps, whereas the computational challenges in
aggregating small scale traffic flows prevent the wider dissemination of high
resolution flow maps. Vehicle trajectories are a promising data source to solve
this challenging problem. The solution begins with the alignment (or map
matching) of the trajectories to the road network. However even the
state-of-the-art map matching implementations produce sub-optimal results with
small misalignments. While these misalignments are negligible for large scale
flow aggregation in desire line maps, they pose substantial obstacles for small
scale flow aggregation in high resolution maps. To remove these remaining
misalignments, we introduce innovative local alignment algorithms, where we
infer road segments to serve as local reference segments, and proceed to align
nearby road segments to them. With each local alignment iteration, the
misalignments of the trajectories with each other and with the road network are
reduced, and so converge closer to a minimal flow map. By analysing a set of
empirical trajectories collected in Hannover, Germany, we confirm that our
minimal flow map has high levels of spatial resolution, accuracy and coverage.
