  Images of natural systems may represent patterns of network-like structure,
which could reveal important information about the topological properties of
the underlying subject. However, the image itself does not automatically
provide a formal definition of a network in terms of sets of nodes and edges.
Instead, this information should be suitably extracted from the raw image data.
Motivated by this, we present a principled model to extract network topologies
from images that is scalable and efficient. We map this goal into solving a
routing optimization problem where the solution is a network that minimizes an
energy function which can be interpreted in terms of an operational and
infrastructural cost. Our method relies on recent results from optimal
transport theory and is a principled alternative to standard image-processing
techniques that are based on heuristics. We test our model on real images of
the retinal vascular system, slime mold and river networks and compare with
routines combining image-processing techniques. Results are tested in terms of
a similarity measure related to the amount of information preserved in the
extraction. We find that our model finds networks from retina vascular network
images that are more similar to hand-labeled ones, while also giving high
performance in extracting networks from images of rivers and slime mold for
which there is no ground truth available. While there is no unique method that
fits all the images the best, our approach performs consistently across
datasets, its algorithmic implementation is efficient and can be fully
automatized to be run on several datasets with little supervision.
