  We propose a minimal path method to simultaneously compute segmentation masks
and extract centerlines of tubular structures with line-topology. Minimal path
methods are commonly used for the segmentation of tubular structures in a wide
variety of applications. Recent methods use features extracted by CNNs, and
often outperform methods using hand-tuned features. However, for CNN-based
methods, the samples used for training may be generated inappropriately, so
that they can be very different from samples encountered during inference. We
approach this discrepancy by introducing a novel iterative training scheme,
which enables generating better training samples specifically tailored for the
minimal path methods without changing existing annotations. In our method,
segmentation masks and centerlines are not determined after one another by
post-processing, but obtained using the same steps. Our method requires only
very few annotated training images. Comparison with seven previous approaches
on three public datasets, including satellite images and medical images, shows
that our method achieves state-of-the-art results both for segmentation masks
and centerlines.
